├── .gitignore
├── 05_ProbabilityDistributionsInReliabilityAnalysis
├── 05_04_SomeTimeToFailureDistributions
│ ├── 05_04_02_TheGammaDistribution.ipynb
│ ├── 05_04_03_TheWeibullDistribution.ipynb
│ ├── 05_04_04_TheNormalDistribution.ipynb
│ └── 05_04_05_TheLognormalDistribution.ipynb
└── 05_07_AdditionalContinuousDistributions
│ └── 05_07_02_TheBetaDistribution.ipynb
├── 06_SystemReliabilityAnalysis
└── 06_03_NonRepairableSystems
│ └── 06_03_02_NonrepairableParallelStructures.ipynb
├── 10_CountingProcesses
└── 10_07_Problems
│ ├── 10_07_Dataset_Problem_10_13.txt
│ └── TestDataLoading.ipynb
├── 11_MarkovAnalysis
├── 11_09_TimeDependentSolution.ipynb
├── 11_11_MultiphaseMarkovProcesses
│ ├── 11_11_01_ChangingTheTransitionRates.ipynb
│ └── 11_11_02_ChangingTheInitialState.ipynb
├── 11_12_PiecewiseDeterministicMarkovProcesses
│ └── 11_12_03_ASpecificCase.ipynb
└── 11_13_SimulationOfAMarkovProcess.ipynb
├── 12_PreventiveMaintenance
├── 12_04_DegradationModels
│ ├── 12_04_02_TrendModelsRegressionBasedModels.ipynb
│ └── 12_04_03_ModelsWithIncrements.ipynb
└── 12_05_ConditionBasedMaintenance
│ ├── 12_05_02_ContinuousMonitoringAndFiniteDiscreteStateSpace1.ipynb
│ ├── 12_05_02_ContinuousMonitoringAndFiniteDiscreteStateSpace2.ipynb
│ ├── 12_05_02_ContinuousMonitoringAndFiniteDiscreteStateSpace3.ipynb
│ ├── 12_05_04_InspectionBasedMonitoringAndFiniteDiscreteStateSpace.ipynb
│ └── 12_05_05_InspectionBasedMonitoringAndContinuousStateSpace.ipynb
├── 14_ReliabilityDataAnalysis
├── 14_02_SomeBasicConcepts
│ └── 14_02_02_SurvivalTimes.ipynb
├── 14_03_ExploratoryDataAnalysis
│ ├── 14_03_01_ACompleteDataset.ipynb
│ ├── 14_03_02_SampleMetrics.ipynb
│ ├── 14_03_03_Histogram.ipynb
│ ├── 14_03_04_DensityPlot.ipynb
│ ├── 14_03_05_EmpiricalSurvivorFunction.ipynb
│ ├── 14_03_06_QQPlot.ipynb
│ └── 14_03_dataset.txt
├── 14_04_ParameterEstimation
│ ├── 14_04_03_MethodOfMomentsEstimation.ipynb
│ ├── 14_04_04_MaximumLikelihoodEstimation.ipynb
│ ├── 14_04_06_WeibullDistributedLifetimes.ipynb
│ └── 14_04_dataset.txt
├── 14_05_TheKaplanMeierEstimate
│ └── 14_05_02_TheKaplanMeierEstimatorForACensoredDataset.ipynb
├── 14_06_CumulativeFailureRatePlots
│ └── 14_06_01_TheNelsonAalenEstimateOfTheCumulativeFailureRate.ipynb
├── 14_07_TotalTimeOnTestPlotting
│ └── 14_07_01_TotalTimeOnTestPlotForCompleteDatasets.ipynb
└── 14_09_Problems
│ ├── 14_09_Dataset_Problem_14_01.txt
│ ├── 14_09_Dataset_Problem_14_02.txt
│ ├── 14_09_Dataset_Problem_14_03.txt
│ ├── 14_09_Dataset_Problem_14_11.txt
│ ├── 14_09_Dataset_Problem_14_12.txt
│ ├── 14_09_Dataset_Problem_14_13.txt
│ ├── 14_09_Dataset_Problem_14_16.txt
│ ├── 14_09_Dataset_Problem_14_17.txt
│ ├── 14_09_Dataset_Problem_14_18.txt
│ └── TestDataLoading.ipynb
├── 15_BayesianReliabilityAnalysis
└── 15_03_SelectionOfPriorDistribution
│ └── 15_03_01_BinomialModel.ipynb
├── Errata
└── errata.pdf
├── LICENSE.txt
├── README.md
├── ReliabilityBookEnv.yml
└── images
├── Schema_11_09.png
├── Schema_11_11_02.png
├── Schema_12_05_02.png
└── srt.png
/.gitignore:
--------------------------------------------------------------------------------
1 | .venv/
2 | .ipynb_checkpoints
3 |
--------------------------------------------------------------------------------
/05_ProbabilityDistributionsInReliabilityAnalysis/05_04_SomeTimeToFailureDistributions/05_04_03_TheWeibullDistribution.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## The Weibull distribution"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [
15 | {
16 | "data": {
17 | "image/png": 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18 | "text/plain": [
19 | "plot without title"
20 | ]
21 | },
22 | "metadata": {},
23 | "output_type": "display_data"
24 | }
25 | ],
26 | "source": [
27 | "t<-seq(0, 1000, length=300) # Set time axis\n",
28 | "# Set the parameters\n",
29 | "a<-2.5 # shape parameter (alpha)\n",
30 | "th<-200 # scale parameter (theta)\n",
31 | "# Calculate the Weibull density (y) for each t\n",
32 | "y<-dweibull(t, a, th, log=FALSE)\n",
33 | "plot(t, y, type=\"l\")"
34 | ]
35 | },
36 | {
37 | "cell_type": "code",
38 | "execution_count": null,
39 | "metadata": {},
40 | "outputs": [],
41 | "source": []
42 | }
43 | ],
44 | "metadata": {
45 | "kernelspec": {
46 | "display_name": "R",
47 | "language": "R",
48 | "name": "ir"
49 | },
50 | "language_info": {
51 | "codemirror_mode": "r",
52 | "file_extension": ".r",
53 | "mimetype": "text/x-r-source",
54 | "name": "R",
55 | "pygments_lexer": "r",
56 | "version": "3.6.1"
57 | }
58 | },
59 | "nbformat": 4,
60 | "nbformat_minor": 2
61 | }
62 |
--------------------------------------------------------------------------------
/05_ProbabilityDistributionsInReliabilityAnalysis/05_04_SomeTimeToFailureDistributions/05_04_05_TheLognormalDistribution.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## The Lognormal Distribution"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [
15 | {
16 | "data": {
17 | "image/png": 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B67QxrR3vAggB67Q7rofMODAHrsDqnbVYYHAfTYHVLrWw0PAuixO6TDHjQ8CKAn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\nkVv4pwAAAABJRU5ErkJggg==",
18 | "text/plain": [
19 | "plot without title"
20 | ]
21 | },
22 | "metadata": {},
23 | "output_type": "display_data"
24 | }
25 | ],
26 | "source": [
27 | "t<-seq(0, 10, length=300) # Set the time axis\n",
28 | "# Set the parameters\n",
29 | "nu<-5\n",
30 | "tau<-2\n",
31 | "# Calculate the lognormal density y for each t\n",
32 | "y<-dlnorm(t, nu, tau, log=FALSE)\n",
33 | "plot(t, y, type=\"l\")"
34 | ]
35 | },
36 | {
37 | "cell_type": "code",
38 | "execution_count": null,
39 | "metadata": {},
40 | "outputs": [],
41 | "source": []
42 | }
43 | ],
44 | "metadata": {
45 | "kernelspec": {
46 | "display_name": "R",
47 | "language": "R",
48 | "name": "ir"
49 | },
50 | "language_info": {
51 | "codemirror_mode": "r",
52 | "file_extension": ".r",
53 | "mimetype": "text/x-r-source",
54 | "name": "R",
55 | "pygments_lexer": "r",
56 | "version": "3.6.1"
57 | }
58 | },
59 | "nbformat": 4,
60 | "nbformat_minor": 2
61 | }
62 |
--------------------------------------------------------------------------------
/05_ProbabilityDistributionsInReliabilityAnalysis/05_07_AdditionalContinuousDistributions/05_07_02_TheBetaDistribution.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## The Beta Distribution"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [
15 | {
16 | "data": {
17 | "image/png": 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EH0NK8U1TX/4K9QilS92hOzxKBZpxGmCrZIJ70rCFNoK7X649wRrBNKkV4OF3kR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\nAARQJAACKBIAgf8H/55thcdh18AAAAAASUVORK5CYII=",
18 | "text/plain": [
19 | "plot without title"
20 | ]
21 | },
22 | "metadata": {},
23 | "output_type": "display_data"
24 | }
25 | ],
26 | "source": [
27 | "x<-seq(0, 1, length=300) # Set the values for the x-axis\n",
28 | "# Set the parameters a (=alpha) and b (=beta)\n",
29 | "a<-2\n",
30 | "b<-5\n",
31 | "# Calculate the beta density y for each x\n",
32 | "y<-dbeta(x, a, b, log=FALSE)\n",
33 | "plot(x, y, type=\"l\", xlab=\"x\", ylab=\"f(x)\")"
34 | ]
35 | },
36 | {
37 | "cell_type": "code",
38 | "execution_count": null,
39 | "metadata": {},
40 | "outputs": [],
41 | "source": []
42 | }
43 | ],
44 | "metadata": {
45 | "kernelspec": {
46 | "display_name": "R",
47 | "language": "R",
48 | "name": "ir"
49 | },
50 | "language_info": {
51 | "codemirror_mode": "r",
52 | "file_extension": ".r",
53 | "mimetype": "text/x-r-source",
54 | "name": "R",
55 | "pygments_lexer": "r",
56 | "version": "3.6.1"
57 | }
58 | },
59 | "nbformat": 4,
60 | "nbformat_minor": 2
61 | }
62 |
--------------------------------------------------------------------------------
/06_SystemReliabilityAnalysis/06_03_NonRepairableSystems/06_03_02_NonrepairableParallelStructures.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## Nonrepairable parallel structures\n",
8 | "\n",
9 | "Failure rate function for a parallel structure of two independent and identical components that are Weibull distributed with $\\alpha=1.8$ and $\\theta=1$"
10 | ]
11 | },
12 | {
13 | "cell_type": "code",
14 | "execution_count": 1,
15 | "metadata": {},
16 | "outputs": [
17 | {
18 | "data": {
19 | "image/png": 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LDj4Rtcz+CM1ZBODc+qOflR/ug4V+RX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",
20 | "text/plain": [
21 | "plot without title"
22 | ]
23 | },
24 | "metadata": {},
25 | "output_type": "display_data"
26 | }
27 | ],
28 | "source": [
29 | "t<-seq(0, 3, length=300) # time axis\n",
30 | "a<-1.8\n",
31 | "# the Weibull shape parameter\n",
32 | "th<-1 # the Weibull scale parameter\n",
33 | "th1<-2^(-1/a)*th # the transformed scale parameter\n",
34 | "m<-(2*th-th1)*gamma(1+1/a) # the MTTF\n",
35 | "x<-2*dweibull(t, a, th, log=FALSE) -\n",
36 | "dweibull(t, a, th1, log=FALSE)\n",
37 | "y<-1+pweibull(t, a, th1, log=FALSE) -\n",
38 | "2*pweibull(t, a, th, log=FALSE)\n",
39 | "z<-x/y\n",
40 | "plot(t, z, type=\"l\")\n",
41 | "segments(m, 0, m, 2.1)\n",
42 | "text(m, 2.6, expression(MTTF[S]))"
43 | ]
44 | },
45 | {
46 | "cell_type": "code",
47 | "execution_count": null,
48 | "metadata": {},
49 | "outputs": [],
50 | "source": []
51 | }
52 | ],
53 | "metadata": {
54 | "kernelspec": {
55 | "display_name": "R",
56 | "language": "R",
57 | "name": "ir"
58 | },
59 | "language_info": {
60 | "codemirror_mode": "r",
61 | "file_extension": ".r",
62 | "mimetype": "text/x-r-source",
63 | "name": "R",
64 | "pygments_lexer": "r",
65 | "version": "3.6.1"
66 | }
67 | },
68 | "nbformat": 4,
69 | "nbformat_minor": 2
70 | }
71 |
--------------------------------------------------------------------------------
/10_CountingProcesses/10_07_Problems/10_07_Dataset_Problem_10_13.txt:
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1 | Failure,Item1,Item2,Item3,Item4,Item5
2 | 1,2099,2504,4081,1015,382
3 | 2,5352,3060,5210,3686,1621
4 | 3,8116,3626,6722,4535,1629
5 | 4,9085,5559,15584,5279,6726
6 | 5,10581,6691,17759,5860,8356
7 | 6,12672,11848,21397,7454,12832
8 | 7,13042,17688,21858,12412,12910
9 | 8,14114,18955,24192,15361,23659
10 | 9,15310,19454,25468,15542,24169
11 | 10,15483,19590,29063,19305,24572
12 |
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/10_CountingProcesses/10_07_Problems/TestDataLoading.ipynb:
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1 | {
2 | "cells": [
3 | {
4 | "cell_type": "code",
5 | "execution_count": 2,
6 | "metadata": {},
7 | "outputs": [
8 | {
9 | "data": {
10 | "text/html": [
11 | "\n",
12 | "| Failure | Item1 | Item2 | Item3 | Item4 | Item5 |
|---|
\n",
13 | "\n",
14 | "\t| 1 | 2099 | 2504 | 4081 | 1015 | 382 |
\n",
15 | "\t| 2 | 5352 | 3060 | 5210 | 3686 | 1621 |
\n",
16 | "\t| 3 | 8116 | 3626 | 6722 | 4535 | 1629 |
\n",
17 | "\t| 4 | 9085 | 5559 | 15584 | 5279 | 6726 |
\n",
18 | "\t| 5 | 10581 | 6691 | 17759 | 5860 | 8356 |
\n",
19 | "\t| 6 | 12672 | 11848 | 21397 | 7454 | 12832 |
\n",
20 | "\t| 7 | 13042 | 17688 | 21858 | 12412 | 12910 |
\n",
21 | "\t| 8 | 14114 | 18955 | 24192 | 15361 | 23659 |
\n",
22 | "\t| 9 | 15310 | 19454 | 25468 | 15542 | 24169 |
\n",
23 | "\t| 10 | 15483 | 19590 | 29063 | 19305 | 24572 |
\n",
24 | "\n",
25 | "
\n"
26 | ],
27 | "text/latex": [
28 | "\\begin{tabular}{r|llllll}\n",
29 | " Failure & Item1 & Item2 & Item3 & Item4 & Item5\\\\\n",
30 | "\\hline\n",
31 | "\t 1 & 2099 & 2504 & 4081 & 1015 & 382\\\\\n",
32 | "\t 2 & 5352 & 3060 & 5210 & 3686 & 1621\\\\\n",
33 | "\t 3 & 8116 & 3626 & 6722 & 4535 & 1629\\\\\n",
34 | "\t 4 & 9085 & 5559 & 15584 & 5279 & 6726\\\\\n",
35 | "\t 5 & 10581 & 6691 & 17759 & 5860 & 8356\\\\\n",
36 | "\t 6 & 12672 & 11848 & 21397 & 7454 & 12832\\\\\n",
37 | "\t 7 & 13042 & 17688 & 21858 & 12412 & 12910\\\\\n",
38 | "\t 8 & 14114 & 18955 & 24192 & 15361 & 23659\\\\\n",
39 | "\t 9 & 15310 & 19454 & 25468 & 15542 & 24169\\\\\n",
40 | "\t 10 & 15483 & 19590 & 29063 & 19305 & 24572\\\\\n",
41 | "\\end{tabular}\n"
42 | ],
43 | "text/markdown": [
44 | "\n",
45 | "| Failure | Item1 | Item2 | Item3 | Item4 | Item5 |\n",
46 | "|---|---|---|---|---|---|\n",
47 | "| 1 | 2099 | 2504 | 4081 | 1015 | 382 |\n",
48 | "| 2 | 5352 | 3060 | 5210 | 3686 | 1621 |\n",
49 | "| 3 | 8116 | 3626 | 6722 | 4535 | 1629 |\n",
50 | "| 4 | 9085 | 5559 | 15584 | 5279 | 6726 |\n",
51 | "| 5 | 10581 | 6691 | 17759 | 5860 | 8356 |\n",
52 | "| 6 | 12672 | 11848 | 21397 | 7454 | 12832 |\n",
53 | "| 7 | 13042 | 17688 | 21858 | 12412 | 12910 |\n",
54 | "| 8 | 14114 | 18955 | 24192 | 15361 | 23659 |\n",
55 | "| 9 | 15310 | 19454 | 25468 | 15542 | 24169 |\n",
56 | "| 10 | 15483 | 19590 | 29063 | 19305 | 24572 |\n",
57 | "\n"
58 | ],
59 | "text/plain": [
60 | " Failure Item1 Item2 Item3 Item4 Item5\n",
61 | "1 1 2099 2504 4081 1015 382\n",
62 | "2 2 5352 3060 5210 3686 1621\n",
63 | "3 3 8116 3626 6722 4535 1629\n",
64 | "4 4 9085 5559 15584 5279 6726\n",
65 | "5 5 10581 6691 17759 5860 8356\n",
66 | "6 6 12672 11848 21397 7454 12832\n",
67 | "7 7 13042 17688 21858 12412 12910\n",
68 | "8 8 14114 18955 24192 15361 23659\n",
69 | "9 9 15310 19454 25468 15542 24169\n",
70 | "10 10 15483 19590 29063 19305 24572"
71 | ]
72 | },
73 | "metadata": {},
74 | "output_type": "display_data"
75 | },
76 | {
77 | "data": {
78 | "text/html": [
79 | "\n",
80 | "\t- 10
\n",
81 | "\t- 6
\n",
82 | "
\n"
83 | ],
84 | "text/latex": [
85 | "\\begin{enumerate*}\n",
86 | "\\item 10\n",
87 | "\\item 6\n",
88 | "\\end{enumerate*}\n"
89 | ],
90 | "text/markdown": [
91 | "1. 10\n",
92 | "2. 6\n",
93 | "\n",
94 | "\n"
95 | ],
96 | "text/plain": [
97 | "[1] 10 6"
98 | ]
99 | },
100 | "metadata": {},
101 | "output_type": "display_data"
102 | }
103 | ],
104 | "source": [
105 | "x<-read.table(\"10_07_Dataset_Problem_10_13.txt\", header=TRUE, dec=\".\", sep=\",\")\n",
106 | "x\n",
107 | "dim(x)"
108 | ]
109 | },
110 | {
111 | "cell_type": "code",
112 | "execution_count": null,
113 | "metadata": {},
114 | "outputs": [],
115 | "source": []
116 | }
117 | ],
118 | "metadata": {
119 | "kernelspec": {
120 | "display_name": "R",
121 | "language": "R",
122 | "name": "ir"
123 | },
124 | "language_info": {
125 | "codemirror_mode": "r",
126 | "file_extension": ".r",
127 | "mimetype": "text/x-r-source",
128 | "name": "R",
129 | "pygments_lexer": "r",
130 | "version": "3.6.1"
131 | }
132 | },
133 | "nbformat": 4,
134 | "nbformat_minor": 4
135 | }
136 |
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/11_MarkovAnalysis/11_13_SimulationOfAMarkovProcess.ipynb:
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1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "# 11.13 Simulation of a Markov Process\n",
8 | "\n",
9 | "In this notebook is the Python implementation of the pseudocode provided in section 11.13 (cf. figures 11.21 and 11.22). System description is provided in example 11.12 and depicted figure 11.20.\n",
10 | "\n",
11 | "### IMPORT"
12 | ]
13 | },
14 | {
15 | "cell_type": "code",
16 | "execution_count": 21,
17 | "metadata": {},
18 | "outputs": [],
19 | "source": [
20 | "import numpy as np\n",
21 | "from scipy.linalg import expm"
22 | ]
23 | },
24 | {
25 | "cell_type": "markdown",
26 | "metadata": {},
27 | "source": [
28 | "### Subfunction *Single history*"
29 | ]
30 | },
31 | {
32 | "cell_type": "code",
33 | "execution_count": 22,
34 | "metadata": {},
35 | "outputs": [],
36 | "source": [
37 | "def GetOneHistory(lambdaA, lambdaB):\n",
38 | " # Time to failure initialization\n",
39 | " ttf = 0\n",
40 | " # Initial state\n",
41 | " state = 3\n",
42 | " # Change of notations\n",
43 | " lambda30 = lambdaA\n",
44 | " lambda32 = lambdaB\n",
45 | " lambda20 = lambdaA\n",
46 | " lambda21 = lambdaB\n",
47 | " # Loop while any of the final states is reached\n",
48 | " while (state!=1) and (state!=0):\n",
49 | " # If current state is 3\n",
50 | " if state==3:\n",
51 | " # Draw duration until component A failure\n",
52 | " t30 = np.random.exponential(scale=1/lambda30)\n",
53 | " # Draw duration until component B_1 failure\n",
54 | " t32 = np.random.exponential(scale=1/lambda32)\n",
55 | " # If next event is component A failure\n",
56 | " if t30<=t32:\n",
57 | " state = 0 # Update the system state\n",
58 | " ttf = ttf+t30 # Update the time to failure\n",
59 | " else:\n",
60 | " state = 2 # Update the system state\n",
61 | " ttf = ttf+t32 # Update the time to failure\n",
62 | " # If current state is 2\n",
63 | " else:\n",
64 | " # Draw duration until component A failure # (Exponential law's property)\n",
65 | " t20 = np.random.exponential(scale=1/lambda20)\n",
66 | " # Draw duration until component B2 failure\n",
67 | " t21 = np.random.exponential(scale=1/lambda21)\n",
68 | " # If next event is component A failure\n",
69 | " if t20<=t21:\n",
70 | " state = 0 # Update the system state\n",
71 | " ttf = ttf+t20 # Update the time to failure\n",
72 | " # If next event is component B_2 failure\n",
73 | " else:\n",
74 | " state = 1 # Update the system state\n",
75 | " ttf = ttf+t21 # Update the time to failure\n",
76 | " # return time to failure and final state\n",
77 | " return (ttf, state)"
78 | ]
79 | },
80 | {
81 | "cell_type": "markdown",
82 | "metadata": {},
83 | "source": [
84 | "### Subfunction providing *Estimate of MTTF and failure states probabilities*"
85 | ]
86 | },
87 | {
88 | "cell_type": "code",
89 | "execution_count": 23,
90 | "metadata": {},
91 | "outputs": [],
92 | "source": [
93 | "def SystemMonteCarlo(N, lambdaA, lambdaB):\n",
94 | " # Initialize variables\n",
95 | " mttf = 0\n",
96 | " state0 = 0\n",
97 | " # Loop on N histories\n",
98 | " for i in range(0,N):\n",
99 | " # Get outputs of a single history\n",
100 | " ttf, state = GetOneHistory(lambdaA, lambdaB)\n",
101 | " # Sum time to failure\n",
102 | " mttf = mttf+ttf\n",
103 | " if state==0:\n",
104 | " # Sum histories ending on state 0\n",
105 | " state0 = state0+1\n",
106 | " # Estimate the system MTTF\n",
107 | " mttf = mttf/N\n",
108 | " # Estimate probability that system ends on state 0\n",
109 | " state0 = state0/N\n",
110 | " # Estimate probability that system ends on state 1\n",
111 | " state1 = 1-state0\n",
112 | " # return time to failure and probabilities estimation\n",
113 | " return (mttf, state0, state1)"
114 | ]
115 | },
116 | {
117 | "cell_type": "markdown",
118 | "metadata": {},
119 | "source": [
120 | "### Computation"
121 | ]
122 | },
123 | {
124 | "cell_type": "code",
125 | "execution_count": 24,
126 | "metadata": {},
127 | "outputs": [
128 | {
129 | "name": "stdout",
130 | "output_type": "stream",
131 | "text": [
132 | "MTTF: 736103.721683\n",
133 | "Ending in state 0 probability: 0.742000\n",
134 | "Ending in state 1 probability: 0.258000\n"
135 | ]
136 | }
137 | ],
138 | "source": [
139 | "mttf, state0, state1 = SystemMonteCarlo(N=1000, lambdaA=1e-6, lambdaB=1e-6)\n",
140 | "print('MTTF: {:f}'.format(mttf))\n",
141 | "print('Ending in state 0 probability: {:f}'.format(state0))\n",
142 | "print('Ending in state 1 probability: {:f}'.format(state1))"
143 | ]
144 | },
145 | {
146 | "cell_type": "code",
147 | "execution_count": null,
148 | "metadata": {},
149 | "outputs": [],
150 | "source": []
151 | }
152 | ],
153 | "metadata": {
154 | "kernelspec": {
155 | "display_name": "Python 3",
156 | "language": "python",
157 | "name": "python3"
158 | },
159 | "language_info": {
160 | "codemirror_mode": {
161 | "name": "ipython",
162 | "version": 3
163 | },
164 | "file_extension": ".py",
165 | "mimetype": "text/x-python",
166 | "name": "python",
167 | "nbconvert_exporter": "python",
168 | "pygments_lexer": "ipython3",
169 | "version": "3.7.7"
170 | }
171 | },
172 | "nbformat": 4,
173 | "nbformat_minor": 4
174 | }
175 |
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/12_PreventiveMaintenance/12_05_ConditionBasedMaintenance/12_05_02_ContinuousMonitoringAndFiniteDiscreteStateSpace2.ipynb:
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1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "# 12.5.2 Continuous monitoring and finite discrete state space\n",
8 | "\n",
9 | "This notebook is dedicated to the Case 4 when $\\mu_{13}$ is not constant \n",
10 | "\n",
11 | "The notebook is structured as follows:\n",
12 | "+ Functions\n",
13 | "+ Case 4 a: rate $\\mu_{13}$ is constant (for comparison)\n",
14 | "+ Case 4 b: rate $\\mu_{13}$ is not constant: it depends on the time spend in state 2 according to a linear relation given in function `OneHistory`\n",
15 | "+ Compare cases\n",
16 | "\n"
17 | ]
18 | },
19 | {
20 | "cell_type": "code",
21 | "execution_count": 1,
22 | "metadata": {},
23 | "outputs": [],
24 | "source": [
25 | "import numpy as np\n",
26 | "import pandas as pd\n",
27 | "from scipy.interpolate import interp1d\n",
28 | "\n",
29 | "%matplotlib notebook\n",
30 | "import matplotlib.pyplot as plt"
31 | ]
32 | },
33 | {
34 | "cell_type": "markdown",
35 | "metadata": {},
36 | "source": [
37 | "### Functions"
38 | ]
39 | },
40 | {
41 | "cell_type": "code",
42 | "execution_count": 2,
43 | "metadata": {},
44 | "outputs": [],
45 | "source": [
46 | "def RandExp(rate):\n",
47 | " '''Draw random samples from an exponential distribution.\n",
48 | " If rate is null, output is set to infinity.'''\n",
49 | " if rate==0:\n",
50 | " return np.inf\n",
51 | " else:\n",
52 | " return np.random.exponential(scale=1/rate)"
53 | ]
54 | },
55 | {
56 | "cell_type": "code",
57 | "execution_count": 3,
58 | "metadata": {},
59 | "outputs": [],
60 | "source": [
61 | "def UpdateVar(horizonTime, currentTime, currentState, dT, nextState, \n",
62 | " timeState, transMatrix):\n",
63 | " '''Update system state and time spent in the different states and achieved transitions.'''\n",
64 | " currentTime = currentTime+dT\n",
65 | " flagSim = True\n",
66 | " if currentTime>=horizonTime:\n",
67 | " flagSim = False\n",
68 | " dT = dT-(currentTime-horizonTime)\n",
69 | " currentTime = currentTime+dT\n",
70 | " timeState[currentState] = timeState[currentState]+dT\n",
71 | " transMatrix[currentState,nextState] = transMatrix[currentState,nextState]+1\n",
72 | " currentState = nextState\n",
73 | " return (flagSim, currentTime, currentState, timeState, transMatrix)"
74 | ]
75 | },
76 | {
77 | "cell_type": "code",
78 | "execution_count": 4,
79 | "metadata": {},
80 | "outputs": [],
81 | "source": [
82 | "def OneHistory(para):\n",
83 | " '''Simulate one history of the system until simulation time horizon is reached.\n",
84 | " '''\n",
85 | " # Definition of the interpolation function to determine mu3 depending on the time spent in state 2\n",
86 | " fmu3 = interp1d(np.array([para['mu13']['tinf'], para['mu13']['tsup']]),\n",
87 | " np.array([para['mu13']['vinf'], para['mu13']['vsup']]),\n",
88 | " bounds_error=False, fill_value=(para['mu13']['vinf'], para['mu13']['vsup']))\n",
89 | " # Intial conditions\n",
90 | " currentState = 3\n",
91 | " currentTime = 0\n",
92 | " flagSim = True\n",
93 | " # Counters initialization\n",
94 | " nState = 4\n",
95 | " timeState = np.zeros(nState)\n",
96 | " transMatrix = np.zeros((nState, nState))\n",
97 | " while flagSim:\n",
98 | " if (currentState==3):\n",
99 | " # Evaluate concurrent transitions and determine the actual one\n",
100 | " dT = RandExp(rate=para['lambda32'])\n",
101 | " nextState = 2\n",
102 | " elif (currentState==2):\n",
103 | " # Evaluate concurrent transitions and determine the actual one\n",
104 | " dT23 = RandExp(rate=para['mu23'])\n",
105 | " dT21 = RandExp(rate=para['lambda21'])\n",
106 | " dT = np.min([dT23, dT21])\n",
107 | " if (dT==dT23):\n",
108 | " nextState = 3\n",
109 | " elif (dT==dT21):\n",
110 | " nextState = 1\n",
111 | " else:\n",
112 | " raise ValueError('Approximation error')\n",
113 | " elif (currentState==1):\n",
114 | " # POSSIBLY NOT CONSTANT TRANSITION RATE\n",
115 | " mu13 = fmu3(dT)\n",
116 | " # Evaluate concurrent transitions and determine the actual one\n",
117 | " dT12 = RandExp(rate=para['mu12'])\n",
118 | " dT13 = RandExp(rate=mu13)\n",
119 | " dT10 = RandExp(rate=para['lambda10'])\n",
120 | " dT = np.min([dT12, dT13, dT10])\n",
121 | " if (dT==dT12):\n",
122 | " nextState = 2\n",
123 | " elif (dT==dT13):\n",
124 | " nextState = 3\n",
125 | " elif (dT==dT10):\n",
126 | " nextState = 0\n",
127 | " else:\n",
128 | " raise ValueError('Approximation error')\n",
129 | " elif (currentState==0):\n",
130 | " # Evaluate concurrent transitions and determine the actual one\n",
131 | " dT = RandExp(rate=para['mu03'])\n",
132 | " nextState = 3\n",
133 | " else:\n",
134 | " raise ValueError('Unknown state')\n",
135 | " # Update variables\n",
136 | " (flagSim, currentTime, currentState, timeState, transMatrix) = UpdateVar(\n",
137 | " para['horizon'], currentTime, currentState, dT, nextState, \n",
138 | " timeState, transMatrix)\n",
139 | " return (timeState, transMatrix)"
140 | ]
141 | },
142 | {
143 | "cell_type": "code",
144 | "execution_count": 5,
145 | "metadata": {},
146 | "outputs": [],
147 | "source": [
148 | "def NHistories(nbN, para):\n",
149 | " '''Simulate several histories and aggregate time spent in the different states and achieved\n",
150 | " transitions (Monté-carlo approach).\n",
151 | " '''\n",
152 | " # Simulate a first history to assess output shapes\n",
153 | " (timeStateOne, transMatrixOne) = OneHistory(para)\n",
154 | " timeState = np.empty((nbN, timeStateOne.shape[0]))\n",
155 | " transMatrix = np.empty((nbN, transMatrixOne.shape[0], transMatrixOne.shape[1]))\n",
156 | " # Main loop\n",
157 | " for id in range(nbN):\n",
158 | " (timeState[id,:], transMatrix[id,:,:]) = OneHistory(para)\n",
159 | " return (timeState, transMatrix)"
160 | ]
161 | },
162 | {
163 | "cell_type": "code",
164 | "execution_count": 6,
165 | "metadata": {},
166 | "outputs": [],
167 | "source": [
168 | "def GetResults(timeState, transMatrix, case):\n",
169 | " '''Get and display simulations results'''\n",
170 | " # Probability of each states\n",
171 | " res = {'Case': case}\n",
172 | " for id in range(4):\n",
173 | " res['State{:d}'.format(id)] = np.mean(timeState[:, id]/np.sum(timeState[:, :], axis=1))\n",
174 | " print('State {:d} -> Probability: {:.5f}'.format(id, res['State{:d}'.format(id)], axis=1))\n",
175 | " # Average simulated time\n",
176 | " res['AveSimTime'] = np.mean(np.sum(timeState[:, :], axis=1))\n",
177 | " print('Average simulated time (h): {:.2f}'.format(res['AveSimTime']))\n",
178 | " # Average operating time\n",
179 | " res['AveOpeTime'] = np.mean(np.sum(timeState[:, 1:], axis=1))\n",
180 | " print('Average operating time (h): {:.2f}'.format(res['AveOpeTime']))\n",
181 | " # Average repairing time\n",
182 | " res['aveRepTime'] = np.mean(timeState[:, 0])\n",
183 | " print('Average repairing time (h): {:.2f}'.format(res['aveRepTime']))\n",
184 | " # Average number of corrective maintenance\n",
185 | " res['aveCorMaint'] = np.mean(transMatrix[:, 0, 3])\n",
186 | " print('Average number of corrective maintenance: {:.2f}'.format(res['aveCorMaint']))\n",
187 | " # Average number of preventive maintenance\n",
188 | " res['avePreMaint'] = np.mean(transMatrix[:, 1, 2])+np.mean(transMatrix[:, 1, 3]+np.mean(transMatrix[:, 2, 3])) \n",
189 | " print('Average number of preventive maintenance: {:.2f}'.format(res['avePreMaint'])) \n",
190 | " return res"
191 | ]
192 | },
193 | {
194 | "cell_type": "markdown",
195 | "metadata": {},
196 | "source": [
197 | "### CASE 4 : TWO LEVELS PREVENTIVE MAINTENANCE (a. $\\mu_{13}$ constant)"
198 | ]
199 | },
200 | {
201 | "cell_type": "code",
202 | "execution_count": 7,
203 | "metadata": {},
204 | "outputs": [
205 | {
206 | "name": "stdout",
207 | "output_type": "stream",
208 | "text": [
209 | "Case 4: Two levels preventive maintenance\n",
210 | "\n",
211 | "State 0 -> Probability: 0.00003\n",
212 | "State 1 -> Probability: 0.00082\n",
213 | "State 2 -> Probability: 0.02803\n",
214 | "State 3 -> Probability: 0.97112\n",
215 | "Average simulated time (h): 87600.00\n",
216 | "Average operating time (h): 87597.60\n",
217 | "Average repairing time (h): 2.40\n",
218 | "Average number of corrective maintenance: 0.00\n",
219 | "Average number of preventive maintenance: 2.55\n"
220 | ]
221 | }
222 | ],
223 | "source": [
224 | "# Parameters\n",
225 | "nbHist = int(1e5)\n",
226 | "# By setting same values at `vinf` and `vsup`, a constant rate is forced\n",
227 | "para = {\n",
228 | " 'horizon' : 10*365*24,\n",
229 | " 'lambda32': 3e-5,\n",
230 | " 'lambda21': 3e-5,\n",
231 | " 'lambda10': 3e-5,\n",
232 | " 'mu03': 1e-3,\n",
233 | " 'mu12': 0,\n",
234 | " 'mu13': {'tinf': 100, 'vinf': 1e-3, 'tsup': 2500, 'vsup': 1e-3},\n",
235 | " 'mu23': 1e-3}\n",
236 | "# Simulation\n",
237 | "(timeState, transMatrix) = NHistories(nbHist, para)\n",
238 | "# Get simulations results\n",
239 | "print('Case 4: Two levels preventive maintenance\\n')\n",
240 | "res4a = GetResults(timeState, transMatrix, 4)"
241 | ]
242 | },
243 | {
244 | "cell_type": "code",
245 | "execution_count": 8,
246 | "metadata": {},
247 | "outputs": [],
248 | "source": [
249 | "### CASE 4 : TWO LEVELS PREVENTIVE MAINTENANCE (b. $\\mu_{13}$ not constant)"
250 | ]
251 | },
252 | {
253 | "cell_type": "code",
254 | "execution_count": 9,
255 | "metadata": {},
256 | "outputs": [
257 | {
258 | "name": "stdout",
259 | "output_type": "stream",
260 | "text": [
261 | "Case 4: Two levels preventive maintenance\n",
262 | "\n",
263 | "State 0 -> Probability: 0.00005\n",
264 | "State 1 -> Probability: 0.00151\n",
265 | "State 2 -> Probability: 0.02796\n",
266 | "State 3 -> Probability: 0.97048\n",
267 | "Average simulated time (h): 87600.00\n",
268 | "Average operating time (h): 87595.80\n",
269 | "Average repairing time (h): 4.20\n",
270 | "Average number of corrective maintenance: 0.00\n",
271 | "Average number of preventive maintenance: 2.54\n"
272 | ]
273 | }
274 | ],
275 | "source": [
276 | "# Parameters\n",
277 | "nbHist = int(1e5)\n",
278 | "para = {\n",
279 | " 'horizon' : 10*365*24,\n",
280 | " 'lambda32': 3e-5,\n",
281 | " 'lambda21': 3e-5,\n",
282 | " 'lambda10': 3e-5,\n",
283 | " 'mu03': 1e-3,\n",
284 | " 'mu12': 0,\n",
285 | " 'mu13': {'tinf': 100, 'vinf': 1e-5, 'tsup': 2500, 'vsup': 1e-1},\n",
286 | " 'mu23': 1e-3}\n",
287 | "# Simulation\n",
288 | "(timeState, transMatrix) = NHistories(nbHist, para)\n",
289 | "# Get simulations results\n",
290 | "print('Case 4: Two levels preventive maintenance\\n')\n",
291 | "res4b = GetResults(timeState, transMatrix, 4)"
292 | ]
293 | },
294 | {
295 | "cell_type": "code",
296 | "execution_count": 10,
297 | "metadata": {},
298 | "outputs": [],
299 | "source": [
300 | "### Compare cases"
301 | ]
302 | },
303 | {
304 | "cell_type": "code",
305 | "execution_count": 11,
306 | "metadata": {},
307 | "outputs": [
308 | {
309 | "data": {
310 | "text/html": [
311 | "\n",
312 | "\n",
325 | "
\n",
326 | " \n",
327 | " \n",
328 | " | \n",
329 | " State0 | \n",
330 | " State1 | \n",
331 | " State2 | \n",
332 | " State3 | \n",
333 | " AveSimTime | \n",
334 | " AveOpeTime | \n",
335 | " aveRepTime | \n",
336 | " aveCorMaint | \n",
337 | " avePreMaint | \n",
338 | "
\n",
339 | " \n",
340 | " | Case | \n",
341 | " | \n",
342 | " | \n",
343 | " | \n",
344 | " | \n",
345 | " | \n",
346 | " | \n",
347 | " | \n",
348 | " | \n",
349 | " | \n",
350 | "
\n",
351 | " \n",
352 | " \n",
353 | " \n",
354 | " | 4 | \n",
355 | " 0.000027 | \n",
356 | " 0.000819 | \n",
357 | " 0.028032 | \n",
358 | " 0.971122 | \n",
359 | " 87600.0 | \n",
360 | " 87597.600955 | \n",
361 | " 2.399045 | \n",
362 | " 0.00236 | \n",
363 | " 2.54559 | \n",
364 | "
\n",
365 | " \n",
366 | " | 4 | \n",
367 | " 0.000048 | \n",
368 | " 0.001515 | \n",
369 | " 0.027962 | \n",
370 | " 0.970475 | \n",
371 | " 87600.0 | \n",
372 | " 87595.802581 | \n",
373 | " 4.197419 | \n",
374 | " 0.00429 | \n",
375 | " 2.54249 | \n",
376 | "
\n",
377 | " \n",
378 | "
\n",
379 | "
\n",
21 | "\t- 17.88
\n",
22 | "\t- 28.92
\n",
23 | "\t- 33
\n",
24 | "\t- 41.52
\n",
25 | "\t- 42.12
\n",
26 | "\t- 45.6
\n",
27 | "\t- 48.4
\n",
28 | "\t- 68.88
\n",
29 | "\t- 84.12
\n",
30 | "\t- 93.12
\n",
31 | "\t- 98.64
\n",
32 | "\t- 105.12
\n",
33 | "\t- 105.84
\n",
34 | "\t- 51.84
\n",
35 | "\t- 51.96
\n",
36 | "\t- 54.12
\n",
37 | "\t- 55.56
\n",
38 | "\t- 67.8
\n",
39 | "\t- 68.64
\n",
40 | "\t- 68.64
\n",
41 | "\t- 127.92
\n",
42 | "\t- 138.04
\n",
43 | "
\n"
44 | ],
45 | "text/latex": [
46 | "\\begin{enumerate*}\n",
47 | "\\item 17.88\n",
48 | "\\item 28.92\n",
49 | "\\item 33\n",
50 | "\\item 41.52\n",
51 | "\\item 42.12\n",
52 | "\\item 45.6\n",
53 | "\\item 48.4\n",
54 | "\\item 68.88\n",
55 | "\\item 84.12\n",
56 | "\\item 93.12\n",
57 | "\\item 98.64\n",
58 | "\\item 105.12\n",
59 | "\\item 105.84\n",
60 | "\\item 51.84\n",
61 | "\\item 51.96\n",
62 | "\\item 54.12\n",
63 | "\\item 55.56\n",
64 | "\\item 67.8\n",
65 | "\\item 68.64\n",
66 | "\\item 68.64\n",
67 | "\\item 127.92\n",
68 | "\\item 138.04\n",
69 | "\\end{enumerate*}\n"
70 | ],
71 | "text/markdown": [
72 | "1. 17.88\n",
73 | "2. 28.92\n",
74 | "3. 33\n",
75 | "4. 41.52\n",
76 | "5. 42.12\n",
77 | "6. 45.6\n",
78 | "7. 48.4\n",
79 | "8. 68.88\n",
80 | "9. 84.12\n",
81 | "10. 93.12\n",
82 | "11. 98.64\n",
83 | "12. 105.12\n",
84 | "13. 105.84\n",
85 | "14. 51.84\n",
86 | "15. 51.96\n",
87 | "16. 54.12\n",
88 | "17. 55.56\n",
89 | "18. 67.8\n",
90 | "19. 68.64\n",
91 | "20. 68.64\n",
92 | "21. 127.92\n",
93 | "22. 138.04\n",
94 | "\n",
95 | "\n"
96 | ],
97 | "text/plain": [
98 | " [1] 17.88 28.92 33.00 41.52 42.12 45.60 48.40 68.88 84.12 93.12\n",
99 | "[11] 98.64 105.12 105.84 51.84 51.96 54.12 55.56 67.80 68.64 68.64\n",
100 | "[21] 127.92 138.04"
101 | ]
102 | },
103 | "metadata": {},
104 | "output_type": "display_data"
105 | }
106 | ],
107 | "source": [
108 | "survtime <-c(17.88, 28.92, 33, 41.52, 42.12, 45.6, 48.4,\n",
109 | " 68.88, 84.12, 93.12, 98.64, 105.12, 105.84,\n",
110 | " 51.84, 51.96, 54.12, 55.56, 67.8, 68.64, 68.64,\n",
111 | " 127.92, 138.04)\n",
112 | "survtime"
113 | ]
114 | },
115 | {
116 | "cell_type": "code",
117 | "execution_count": 2,
118 | "metadata": {},
119 | "outputs": [
120 | {
121 | "name": "stdout",
122 | "output_type": "stream",
123 | "text": [
124 | "survtime:\n",
125 | " [1] 17.88 28.92 33.00 41.52 42.12 45.60 48.40 68.88 84.12 93.12\n",
126 | "[11] 98.64 105.12 105.84 51.84 51.96 54.12 55.56 67.80 68.64 68.64\n",
127 | "[21] 127.92 138.04\n",
128 | "\n",
129 | "sort(survtime):\n",
130 | " [1] 17.88 28.92 33.00 41.52 42.12 45.60 48.40 51.84 51.96 54.12\n",
131 | "[11] 55.56 67.80 68.64 68.64 68.88 84.12 93.12 98.64 105.12 105.84\n",
132 | "[21] 127.92 138.04\n"
133 | ]
134 | }
135 | ],
136 | "source": [
137 | "cat('survtime:\\n')\n",
138 | "print(survtime)\n",
139 | "cat('\\nsort(survtime):\\n')\n",
140 | "print(sort(survtime))"
141 | ]
142 | },
143 | {
144 | "cell_type": "markdown",
145 | "metadata": {},
146 | "source": [
147 | "Statistics on the samples stored in the vector `survtime` are obtained, for example, through the following commands: "
148 | ]
149 | },
150 | {
151 | "cell_type": "markdown",
152 | "metadata": {},
153 | "source": [
154 | "## Remark 14.1 An advise\n",
155 | "\n",
156 | "Data may be loaded from a txtfile through the command `read.table`. The output of this command is a dataset structured on columns. Columns labels are by default `Vi` where `i` is the column indice starting at 1. To apply a function on the first column `V1`, for example, the following command can be used:\n",
157 | "`survtime[, 1]`, `survtime[, 'V1']` or `survtime$V1`."
158 | ]
159 | },
160 | {
161 | "cell_type": "code",
162 | "execution_count": 3,
163 | "metadata": {},
164 | "outputs": [],
165 | "source": [
166 | "survtime<-read.table(\"14_03_dataset.txt\", header=FALSE, dec=\".\")\n",
167 | "# survtime # To simply display the dataset"
168 | ]
169 | },
170 | {
171 | "cell_type": "code",
172 | "execution_count": 4,
173 | "metadata": {},
174 | "outputs": [
175 | {
176 | "name": "stdout",
177 | "output_type": "stream",
178 | "text": [
179 | "survtime:\n",
180 | " [1] 17.88 28.92 33.00 41.52 42.12 45.60 48.40 68.88 84.12 93.12\n",
181 | "[11] 98.64 105.12 105.84 51.84 51.96 54.12 55.56 67.80 68.64 68.64\n",
182 | "[21] 127.92 138.04\n",
183 | "\n",
184 | "sort(survtime):\n",
185 | " [1] 17.88 28.92 33.00 41.52 42.12 45.60 48.40 51.84 51.96 54.12\n",
186 | "[11] 55.56 67.80 68.64 68.64 68.88 84.12 93.12 98.64 105.12 105.84\n",
187 | "[21] 127.92 138.04\n"
188 | ]
189 | }
190 | ],
191 | "source": [
192 | "cat('survtime:\\n')\n",
193 | "print(survtime[, 'V1'])\n",
194 | "cat('\\nsort(survtime):\\n')\n",
195 | "print(sort(survtime[, 'V1']))"
196 | ]
197 | }
198 | ],
199 | "metadata": {
200 | "kernelspec": {
201 | "display_name": "R",
202 | "language": "R",
203 | "name": "ir"
204 | },
205 | "language_info": {
206 | "codemirror_mode": "r",
207 | "file_extension": ".r",
208 | "mimetype": "text/x-r-source",
209 | "name": "R",
210 | "pygments_lexer": "r",
211 | "version": "3.6.1"
212 | }
213 | },
214 | "nbformat": 4,
215 | "nbformat_minor": 2
216 | }
217 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_03_ExploratoryDataAnalysis/14_03_02_SampleMetrics.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## Sample metrics"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [],
15 | "source": [
16 | "# Data loading\n",
17 | "survtime<-read.table(\"14_03_dataset.txt\", header=FALSE, dec=\".\")"
18 | ]
19 | },
20 | {
21 | "cell_type": "code",
22 | "execution_count": 2,
23 | "metadata": {},
24 | "outputs": [
25 | {
26 | "data": {
27 | "text/plain": [
28 | " V1 \n",
29 | " Min. : 17.88 \n",
30 | " 1st Qu.: 46.30 \n",
31 | " Median : 61.68 \n",
32 | " Mean : 68.08 \n",
33 | " 3rd Qu.: 90.87 \n",
34 | " Max. :138.04 "
35 | ]
36 | },
37 | "metadata": {},
38 | "output_type": "display_data"
39 | }
40 | ],
41 | "source": [
42 | "# Data summary\n",
43 | "summary(survtime)"
44 | ]
45 | },
46 | {
47 | "cell_type": "markdown",
48 | "metadata": {},
49 | "source": [
50 | "Above the command `summary`is applied to the whole dataset (here composed by a single column). The function can also be applied to a specific column throug commands: `summary(survtime[, 'V1'])`, `summary(survtime[, 1])` or `summary(survtime$V1)`. In the cells below, basic sample metrics are calculated, some of the functions (e.g. `var`) may be applied on an whole dataset while other ones (e.g. `sd`) require an array of samples and, therefore, the specification of column. For simplicity, functions are here always applied on a specified column. "
51 | ]
52 | },
53 | {
54 | "cell_type": "code",
55 | "execution_count": 3,
56 | "metadata": {},
57 | "outputs": [
58 | {
59 | "name": "stdout",
60 | "output_type": "stream",
61 | "text": [
62 | "Min. : 17.88 \n",
63 | "1st Qu. : 46.3 \n",
64 | "Median : 61.68 \n",
65 | "Mean : 68.07636 \n",
66 | "3rd Qu. : 90.87 \n",
67 | "Max. : 138.04 \n",
68 | "\n",
69 | "Var. : 1024.949 \n",
70 | "S.Dev.* : 32.01483 \n",
71 | "S.Dev. : 32.01483 \n",
72 | "Inter Qu.: 44.57 \n"
73 | ]
74 | }
75 | ],
76 | "source": [
77 | "# Sample metrics calculation\n",
78 | "cat('Min. : ', min((survtime[, 'V1'])), '\\n')\n",
79 | "cat('1st Qu. : ', quantile(survtime[, 'V1'], 0.25), '\\n')\n",
80 | "cat('Median : ', median(survtime[, 'V1']), '\\n')\n",
81 | "cat('Mean : ', mean(survtime[, 'V1']), '\\n')\n",
82 | "cat('3rd Qu. : ', quantile(survtime[, 'V1'], 0.75), '\\n')\n",
83 | "cat('Max. : ', max(survtime[, 'V1'], 0.75), '\\n')\n",
84 | "cat('\\n')\n",
85 | "cat('Var. : ', var(survtime[, 'V1']), '\\n')\n",
86 | "cat('S.Dev.* : ', sqrt(var(survtime[, 'V1'])), '\\n') # Standard deviation as the variance root square\n",
87 | "cat('S.Dev. : ', sd(survtime[, 'V1']), '\\n')\n",
88 | "cat('Inter Qu.: ', \n",
89 | " quantile(survtime[, 'V1'], 0.75, names = FALSE)\n",
90 | " -quantile(survtime[, 'V1'], 0.25, names = FALSE), '\\n')"
91 | ]
92 | },
93 | {
94 | "cell_type": "markdown",
95 | "metadata": {},
96 | "source": [
97 | "Samples moments are available in the package **moments**, that is loaded with the command below:"
98 | ]
99 | },
100 | {
101 | "cell_type": "code",
102 | "execution_count": 4,
103 | "metadata": {},
104 | "outputs": [],
105 | "source": [
106 | "library(moments)"
107 | ]
108 | },
109 | {
110 | "cell_type": "markdown",
111 | "metadata": {},
112 | "source": [
113 | "Again commands below may be applied on a whole dataset or to a specified column. To be consistent with commands above, here these functions are explicitly applied on the single column of the loaded dataset. "
114 | ]
115 | },
116 | {
117 | "cell_type": "code",
118 | "execution_count": 5,
119 | "metadata": {},
120 | "outputs": [
121 | {
122 | "name": "stdout",
123 | "output_type": "stream",
124 | "text": [
125 | "3rd Order Mom (noncentral): 534022.7 \n",
126 | "3rd Order Mom (central) : 18720.53 \n",
127 | "skewness : 0.6117442 \n",
128 | "skewness* : 0.6117442 \n",
129 | "kurtosis : 2.555003 \n",
130 | "kurtosis* : 2.555003 \n"
131 | ]
132 | }
133 | ],
134 | "source": [
135 | "# Moments calculation\n",
136 | "k <-3 # Choose the order of the moment\n",
137 | "cat('3rd Order Mom (noncentral): ', moment(survtime[, 'V1'], order=k, central=FALSE), '\\n')\n",
138 | "cat('3rd Order Mom (central) : ', moment(survtime[, 'V1'], order=k, central=TRUE), '\\n')\n",
139 | "cat('skewness : ', skewness(survtime[, 'V1']), '\\n')\n",
140 | "cat('skewness* : ', \n",
141 | " moment(survtime[, 'V1'], order=3, central=TRUE)/(moment(survtime[, 'V1'], order=2, central=TRUE)^(3/2)), '\\n')\n",
142 | "cat('kurtosis : ', kurtosis(survtime[, 'V1']), '\\n') \n",
143 | "cat('kurtosis* : ', \n",
144 | " moment(survtime[, 'V1'], order=4, central=TRUE)/(moment(survtime[, 'V1'], order=2, central=TRUE)^2), '\\n')\n",
145 | "#cat('kurtosis** : ', \n",
146 | "# moment(survtime[, 'V1'], order=4, central=TRUE)/(moment(survtime[, 'V1'], order=3, central=TRUE)^2)-3, '\\n')"
147 | ]
148 | },
149 | {
150 | "cell_type": "markdown",
151 | "metadata": {},
152 | "source": [
153 | "# RESULTS AND FORMULAE ABOVE TO BE CHECKED!"
154 | ]
155 | }
156 | ],
157 | "metadata": {
158 | "kernelspec": {
159 | "display_name": "R",
160 | "language": "R",
161 | "name": "ir"
162 | },
163 | "language_info": {
164 | "codemirror_mode": "r",
165 | "file_extension": ".r",
166 | "mimetype": "text/x-r-source",
167 | "name": "R",
168 | "pygments_lexer": "r",
169 | "version": "3.6.1"
170 | }
171 | },
172 | "nbformat": 4,
173 | "nbformat_minor": 2
174 | }
175 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_03_ExploratoryDataAnalysis/14_03_04_DensityPlot.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## Density plot"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [
15 | {
16 | "data": {
17 | "image/png": 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aOXKj8dQdTmG631HBakRZ593CWUu6IXdwUOJTVIBTlElLGiTd0xI1NSta595bAg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\nAAIgSAACIEgAAiBIAAL8H8N21GNgknJdAAAAAElFTkSuQmCC",
18 | "text/plain": [
19 | "Plot with title “density.default(x = survtime[, \"V1\"])”"
20 | ]
21 | },
22 | "metadata": {},
23 | "output_type": "display_data"
24 | }
25 | ],
26 | "source": [
27 | "survtime <-read.table(\"14_03_dataset.txt\", header=F, dec=\".\")\n",
28 | "d <- density(survtime[, 'V1']) # Returns the density data\n",
29 | "plot(d) # Plots the results"
30 | ]
31 | }
32 | ],
33 | "metadata": {
34 | "kernelspec": {
35 | "display_name": "R",
36 | "language": "R",
37 | "name": "ir"
38 | },
39 | "language_info": {
40 | "codemirror_mode": "r",
41 | "file_extension": ".r",
42 | "mimetype": "text/x-r-source",
43 | "name": "R",
44 | "pygments_lexer": "r",
45 | "version": "3.6.1"
46 | }
47 | },
48 | "nbformat": 4,
49 | "nbformat_minor": 2
50 | }
51 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_03_ExploratoryDataAnalysis/14_03_dataset.txt:
--------------------------------------------------------------------------------
1 | 17.88
2 | 28.92
3 | 33
4 | 41.52
5 | 42.12
6 | 45.6
7 | 48.4
8 | 68.88
9 | 84.12
10 | 93.12
11 | 98.64
12 | 105.12
13 | 105.84
14 | 51.84
15 | 51.96
16 | 54.12
17 | 55.56
18 | 67.8
19 | 68.64
20 | 68.64
21 | 127.92
22 | 138.04
23 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_04_ParameterEstimation/14_04_03_MethodOfMomentsEstimation.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## Method of Moments Estimation"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 2,
13 | "metadata": {},
14 | "outputs": [],
15 | "source": [
16 | "# Data loading\n",
17 | "survtime<-read.table(\"14_04_dataset.txt\", header=FALSE, dec=\".\")"
18 | ]
19 | },
20 | {
21 | "cell_type": "code",
22 | "execution_count": 3,
23 | "metadata": {},
24 | "outputs": [
25 | {
26 | "name": "stdout",
27 | "output_type": "stream",
28 | "text": [
29 | "alpha : 4.736895 \n",
30 | "lambda : 0.06958208 \n"
31 | ]
32 | }
33 | ],
34 | "source": [
35 | "# Estimation of alpha and lambda (Gamma distribution)\n",
36 | "a<-mean(survtime[, 'V1'])\n",
37 | "b<-mean(survtime[, 'V1']^2)\n",
38 | "lambda<-a/(b-a^2)\n",
39 | "alpha<-lambda*a\n",
40 | "# Display\n",
41 | "cat('alpha : ', alpha, '\\n')\n",
42 | "cat('lambda : ', lambda, '\\n')"
43 | ]
44 | },
45 | {
46 | "cell_type": "code",
47 | "execution_count": null,
48 | "metadata": {},
49 | "outputs": [],
50 | "source": []
51 | }
52 | ],
53 | "metadata": {
54 | "kernelspec": {
55 | "display_name": "R",
56 | "language": "R",
57 | "name": "ir"
58 | },
59 | "language_info": {
60 | "codemirror_mode": "r",
61 | "file_extension": ".r",
62 | "mimetype": "text/x-r-source",
63 | "name": "R",
64 | "pygments_lexer": "r",
65 | "version": "3.6.1"
66 | }
67 | },
68 | "nbformat": 4,
69 | "nbformat_minor": 2
70 | }
71 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_04_ParameterEstimation/14_04_04_MaximumLikelihoodEstimation.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## Maximum Likelihood Estimation"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [],
15 | "source": [
16 | "library(stats4)\n",
17 | "library(bbmle) # Activate the package bbmle"
18 | ]
19 | },
20 | {
21 | "cell_type": "code",
22 | "execution_count": 2,
23 | "metadata": {},
24 | "outputs": [
25 | {
26 | "name": "stderr",
27 | "output_type": "stream",
28 | "text": [
29 | "Warning message in dbinom(mydata, size, prob, log = TRUE):\n",
30 | "“NaNs produced”Warning message in dbinom(mydata, size, prob, log = TRUE):\n",
31 | "“NaNs produced”Warning message in dbinom(mydata, size, prob, log = TRUE):\n",
32 | "“NaNs produced”Warning message in dbinom(mydata, size, prob, log = TRUE):\n",
33 | "“NaNs produced”Warning message in dbinom(mydata, size, prob, log = TRUE):\n",
34 | "“NaNs produced”"
35 | ]
36 | },
37 | {
38 | "data": {
39 | "text/plain": [
40 | "\n",
41 | "Call:\n",
42 | "mle2(minuslogl = myfunc, start = list(prob = 0.5), data = list(size = 40))\n",
43 | "\n",
44 | "Coefficients:\n",
45 | " prob \n",
46 | "0.125 \n",
47 | "\n",
48 | "Log-likelihood: -1.67 "
49 | ]
50 | },
51 | "metadata": {},
52 | "output_type": "display_data"
53 | }
54 | ],
55 | "source": [
56 | "options(digits=3) # Set the precision of the output\n",
57 | "size<-40\n",
58 | "mydata<-c(5)\n",
59 | "myfunc<-function(size, prob){-sum(dbinom(mydata, size, prob, log=TRUE))}\n",
60 | "mle2(myfunc, start=list(prob=0.5), data=list(size=40))"
61 | ]
62 | },
63 | {
64 | "cell_type": "code",
65 | "execution_count": null,
66 | "metadata": {},
67 | "outputs": [],
68 | "source": []
69 | }
70 | ],
71 | "metadata": {
72 | "kernelspec": {
73 | "display_name": "R",
74 | "language": "R",
75 | "name": "ir"
76 | },
77 | "language_info": {
78 | "codemirror_mode": "r",
79 | "file_extension": ".r",
80 | "mimetype": "text/x-r-source",
81 | "name": "R",
82 | "pygments_lexer": "r",
83 | "version": "3.6.1"
84 | }
85 | },
86 | "nbformat": 4,
87 | "nbformat_minor": 2
88 | }
89 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_04_ParameterEstimation/14_04_dataset.txt:
--------------------------------------------------------------------------------
1 | 17.88
2 | 28.92
3 | 33
4 | 41.52
5 | 42.12
6 | 45.6
7 | 48.4
8 | 68.88
9 | 84.12
10 | 93.12
11 | 98.64
12 | 105.12
13 | 105.84
14 | 51.84
15 | 51.96
16 | 54.12
17 | 55.56
18 | 67.8
19 | 68.64
20 | 68.64
21 | 127.92
22 | 138.04
23 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_05_TheKaplanMeierEstimate/14_05_02_TheKaplanMeierEstimatorForACensoredDataset.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## The Kaplan-Meier Estimator for a Censored Dataset"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [],
15 | "source": [
16 | "library(survival)"
17 | ]
18 | },
19 | {
20 | "cell_type": "code",
21 | "execution_count": 2,
22 | "metadata": {},
23 | "outputs": [],
24 | "source": [
25 | "survtime<-c(31.7, 39.2, 57.5, 65.0, 65.8, 70, 0, 75.0, 75.2, \n",
26 | " 87.5, 88.3, 94.2, 101.7, 105.8, 109.2, 110.0, 130.0)\n",
27 | "status<-c(1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1)"
28 | ]
29 | },
30 | {
31 | "cell_type": "code",
32 | "execution_count": 3,
33 | "metadata": {},
34 | "outputs": [
35 | {
36 | "data": {
37 | "image/png": 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QmpQoSUGYRkEyFlBiHZREiZQUg2EVJm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\nhAQoICRAASEBCggJUEBIgAJCAhT8f0yW/TZzj+zSAAAAAElFTkSuQmCC",
38 | "text/plain": [
39 | "plot without title"
40 | ]
41 | },
42 | "metadata": {},
43 | "output_type": "display_data"
44 | }
45 | ],
46 | "source": [
47 | "data<-Surv(survtime, status==1)\n",
48 | "km<-survfit(Surv(survtime, status==1)~1, conf.type=\"plain\")\n",
49 | "plot(km, xlab=\"Time t\", ylab=\"Survival probability\")"
50 | ]
51 | },
52 | {
53 | "cell_type": "code",
54 | "execution_count": 4,
55 | "metadata": {},
56 | "outputs": [
57 | {
58 | "name": "stdout",
59 | "output_type": "stream",
60 | "text": [
61 | "Call: survfit(formula = Surv(survtime, status == 1) ~ 1, conf.type = \"plain\")\n",
62 | "\n",
63 | " time n.risk n.event survival std.err lower 95% CI upper 95% CI\n",
64 | " 31.7 16 1 0.938 0.0605 0.81889 1.000\n",
65 | " 39.2 15 1 0.875 0.0827 0.71295 1.000\n",
66 | " 57.5 14 1 0.812 0.0976 0.62125 1.000\n",
67 | " 65.8 12 1 0.745 0.1105 0.52828 0.961\n",
68 | " 70.0 11 1 0.677 0.1194 0.44309 0.911\n",
69 | " 101.7 5 1 0.542 0.1542 0.23935 0.844\n",
70 | " 109.2 3 1 0.361 0.1797 0.00882 0.713\n",
71 | " 130.0 1 1 0.000 NaN NaN NaN\n"
72 | ]
73 | }
74 | ],
75 | "source": [
76 | "print(summary(km))"
77 | ]
78 | },
79 | {
80 | "cell_type": "code",
81 | "execution_count": null,
82 | "metadata": {},
83 | "outputs": [],
84 | "source": []
85 | }
86 | ],
87 | "metadata": {
88 | "kernelspec": {
89 | "display_name": "R",
90 | "language": "R",
91 | "name": "ir"
92 | },
93 | "language_info": {
94 | "codemirror_mode": "r",
95 | "file_extension": ".r",
96 | "mimetype": "text/x-r-source",
97 | "name": "R",
98 | "pygments_lexer": "r",
99 | "version": "3.6.1"
100 | }
101 | },
102 | "nbformat": 4,
103 | "nbformat_minor": 4
104 | }
105 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_06_CumulativeFailureRatePlots/14_06_01_TheNelsonAalenEstimateOfTheCumulativeFailureRate.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## The Nelson-Aalen Estimate of the Cumulative Failure Rate"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [],
15 | "source": [
16 | "library(survival)"
17 | ]
18 | },
19 | {
20 | "cell_type": "code",
21 | "execution_count": 2,
22 | "metadata": {},
23 | "outputs": [],
24 | "source": [
25 | "# Data to be analyzed\n",
26 | "survtime<-c(31.7, 39.2, 57.5, 65.0, 65.8, 70.0, 75.0, 75.2, \n",
27 | " 87.5, 88.3, 94.2, 101.7, 105.8, 109.2, 110.0, 130.0)\n",
28 | "status<-c(1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1)"
29 | ]
30 | },
31 | {
32 | "cell_type": "code",
33 | "execution_count": 3,
34 | "metadata": {},
35 | "outputs": [],
36 | "source": [
37 | "# Prepare hazard data\n",
38 | "revrank<-order(survtime, decreasing=TRUE)\n",
39 | "haz<-status/revrank\n",
40 | "cumhaz<-cumsum(haz)"
41 | ]
42 | },
43 | {
44 | "cell_type": "code",
45 | "execution_count": 4,
46 | "metadata": {},
47 | "outputs": [],
48 | "source": [
49 | "# Select only failures for plotting.\n",
50 | "df<-data.frame(survtime, status, cumhaz)\n",
51 | "z<-subset(df, status==1)"
52 | ]
53 | },
54 | {
55 | "cell_type": "code",
56 | "execution_count": 5,
57 | "metadata": {},
58 | "outputs": [
59 | {
60 | "data": {
61 | "image/png": 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GwmQnKbmlNnmR5Bl9bnSNer9g/v8n7d+3QXNUFyKkJylxdzd5geQZdWSDV3ZinV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\nAABJRU5ErkJggg==",
62 | "text/plain": [
63 | "plot without title"
64 | ]
65 | },
66 | "metadata": {},
67 | "output_type": "display_data"
68 | }
69 | ],
70 | "source": [
71 | "# Generate cumulative failure rate plot for exp. distr.\n",
72 | "plot(z$survtime, z$cumhaz, type=\"o\", pch=19, xlab=\"Time\", ylab=\"Cumulative failure rate\")"
73 | ]
74 | },
75 | {
76 | "cell_type": "code",
77 | "execution_count": 6,
78 | "metadata": {},
79 | "outputs": [
80 | {
81 | "name": "stdout",
82 | "output_type": "stream",
83 | "text": [
84 | " survtime status cumhaz\n",
85 | "1 31.7 1 0.0625000\n",
86 | "2 39.2 1 0.1291667\n",
87 | "3 57.5 1 0.2005952\n",
88 | "4 65.0 0 0.2005952\n",
89 | "5 65.8 1 0.2839286\n",
90 | "6 70.0 1 0.3748377\n",
91 | "7 75.0 0 0.3748377\n",
92 | "8 75.2 0 0.3748377\n",
93 | "9 87.5 0 0.3748377\n",
94 | "10 88.3 0 0.3748377\n",
95 | "11 94.2 0 0.3748377\n",
96 | "12 101.7 1 0.5748377\n",
97 | "13 105.8 0 0.5748377\n",
98 | "14 109.2 1 0.9081710\n",
99 | "15 110.0 0 0.9081710\n",
100 | "16 130.0 1 1.9081710\n"
101 | ]
102 | }
103 | ],
104 | "source": [
105 | "print(df)"
106 | ]
107 | },
108 | {
109 | "cell_type": "code",
110 | "execution_count": 7,
111 | "metadata": {},
112 | "outputs": [
113 | {
114 | "name": "stdout",
115 | "output_type": "stream",
116 | "text": [
117 | " survtime status cumhaz\n",
118 | "1 31.7 1 0.0625000\n",
119 | "2 39.2 1 0.1291667\n",
120 | "3 57.5 1 0.2005952\n",
121 | "5 65.8 1 0.2839286\n",
122 | "6 70.0 1 0.3748377\n",
123 | "12 101.7 1 0.5748377\n",
124 | "14 109.2 1 0.9081710\n",
125 | "16 130.0 1 1.9081710\n"
126 | ]
127 | }
128 | ],
129 | "source": [
130 | "print(z)"
131 | ]
132 | },
133 | {
134 | "cell_type": "code",
135 | "execution_count": null,
136 | "metadata": {},
137 | "outputs": [],
138 | "source": []
139 | }
140 | ],
141 | "metadata": {
142 | "kernelspec": {
143 | "display_name": "R",
144 | "language": "R",
145 | "name": "ir"
146 | },
147 | "language_info": {
148 | "codemirror_mode": "r",
149 | "file_extension": ".r",
150 | "mimetype": "text/x-r-source",
151 | "name": "R",
152 | "pygments_lexer": "r",
153 | "version": "3.6.1"
154 | }
155 | },
156 | "nbformat": 4,
157 | "nbformat_minor": 4
158 | }
159 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_01.txt:
--------------------------------------------------------------------------------
1 | 10.2
2 | 89.6
3 | 54.0
4 | 96.0
5 | 23.3
6 | 30.4
7 | 41.2
8 | 0.8
9 | 73.2
10 | 3.6
11 | 28.0
12 | 31.6
13 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_02.txt:
--------------------------------------------------------------------------------
1 | 1.25
2 | 135
3 | 0.08
4 | 5.33
5 | 154
6 | 0.5
7 | 1.25
8 | 2.5
9 | 15
10 | 6
11 | 4.5
12 | 32.5
13 | 9.5
14 | 0.25
15 | 81
16 | 12
17 | 0.25
18 | 1.66
19 | 5
20 | 7
21 | 39
22 | 106
23 | 6
24 | 5
25 | 17
26 | 5
27 | 2
28 | 2
29 | 0.33
30 | 0.17
31 | 0.5
32 | 18
33 | 2.5
34 | 0.33
35 | 0.5
36 | 2
37 | 0.33
38 | 4
39 | 20
40 | 6
41 | 6.3
42 | 15
43 | 23
44 | 4
45 | 5
46 | 28
47 | 16
48 | 11.5
49 | 0.42
50 | 38.33
51 | 10.5
52 | 9.5
53 | 8.5
54 | 17
55 | 34
56 | 0.17
57 | 0.83
58 | 0.75
59 | 1
60 | 0.25
61 | 0.25
62 | 2.25
63 | 13.5
64 | 0.5
65 | 0.25
66 | 0.17
67 | 1.75
68 | 0.5
69 | 1
70 | 2
71 | 2
72 | 38
73 | 0.33
74 | 2
75 | 40.5
76 | 4.28
77 | 1.62
78 | 1.33
79 | 3
80 | 5
81 | 120
82 | 0.5
83 | 3
84 | 3
85 | 11.58
86 | 8.5
87 | 13.5
88 | 29.5
89 | 29.5
90 | 112
91 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_03.txt:
--------------------------------------------------------------------------------
1 | Strength,Censored
2 | 26.8,TRUE
3 | 43.9,FALSE
4 | 52.6,FALSE
5 | 54.8,FALSE
6 | 57.1,FALSE
7 | 59.6,FALSE
8 | 29.6,TRUE
9 | 49.9,FALSE
10 | 52.7,FALSE
11 | 54.8,FALSE
12 | 57.1,FALSE
13 | 60.4,FALSE
14 | 33.4,TRUE
15 | 50.1,FALSE
16 | 53.1,FALSE
17 | 55.1,FALSE
18 | 57.3,FALSE
19 | 60.7,FALSE
20 | 35,TRUE
21 | 50.8,FALSE
22 | 53.6,FALSE
23 | 55.4,FALSE
24 | 57.7,FALSE
25 | 36.3,FALSE
26 | 51.9,FALSE
27 | 53.6,FALSE
28 | 55.9,FALSE
29 | 57.8,FALSE
30 | 40,TRUE
31 | 52.1,FALSE
32 | 53.9,FALSE
33 | 56,FALSE
34 | 58.1,FALSE
35 | 41.7,FALSE
36 | 52.3,FALSE
37 | 53.9,FALSE
38 | 56.1,FALSE
39 | 58.9,FALSE
40 | 41.9,TRUE
41 | 52.3,FALSE
42 | 54.1,FALSE
43 | 56.5,FALSE
44 | 59,FALSE
45 | 42.5,TRUE
46 | 52.4,FALSE
47 | 54.6,FALSE
48 | 56.9,FALSE
49 | 59.1,FALSE
50 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_11.txt:
--------------------------------------------------------------------------------
1 | 12373
2 | 98474
3 | 26947
4 | 107318
5 | 5784
6 | 27838
7 | 9739
8 | 9662
9 | 90682
10 | 13000
11 | 61731
12 | 8086
13 | 12207
14 | 15269
15 | 7905
16 | 63589
17 | 4730
18 | 48162
19 | 31893
20 | 11269
21 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_12.txt:
--------------------------------------------------------------------------------
1 | V1,V2
2 | 31.7,FALSE
3 | 39.2,TRUE
4 | 57.5,FALSE
5 | 65.5,FALSE
6 | 65.8,TRUE
7 | 70,FALSE
8 | 75,TRUE
9 | 75.2,TRUE
10 | 87.5,TRUE
11 | 88.3,TRUE
12 | 94.2,FALSE
13 | 101.7,TRUE
14 | 105.8,TRUE
15 | 109.2,FALSE
16 | 110,FALSE
17 | 130,TRUE
18 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_13.txt:
--------------------------------------------------------------------------------
1 | 413
2 | 14
3 | 58
4 | 37
5 | 100
6 | 65
7 | 9
8 | 169
9 | 447
10 | 184
11 | 36
12 | 201
13 | 118
14 | 34
15 | 31
16 | 18
17 | 18
18 | 67
19 | 57
20 | 62
21 | 7
22 | 22
23 | 34
24 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_16.txt:
--------------------------------------------------------------------------------
1 | 9
2 | 12
3 | 11
4 | 4
5 | 7
6 | 2
7 | 5
8 | 8
9 | 5
10 | 7
11 | 1
12 | 6
13 | 1
14 | 9
15 | 4
16 | 1
17 | 3
18 | 3
19 | 6
20 | 1
21 | 11
22 | 33
23 | 7
24 | 91
25 | 2
26 | 1
27 | 87
28 | 47
29 | 12
30 | 9
31 | 135
32 | 258
33 | 16
34 | 35
35 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_17.txt:
--------------------------------------------------------------------------------
1 | 31.7
2 | 39.2
3 | 57.5
4 | 65
5 | 65.8
6 | 70
7 | 75
8 | 75.2
9 | 87.7
10 | 88.3
11 | 94.2
12 | 101.7
13 | 105.8
14 | 109.2
15 | 110
16 | 130
17 |
--------------------------------------------------------------------------------
/14_ReliabilityDataAnalysis/14_09_Problems/14_09_Dataset_Problem_14_18.txt:
--------------------------------------------------------------------------------
1 | 12000
2 | 93000
3 | 5000
4 | 2000
5 | 11000
6 | 26000
7 | 94000
8 | 12000
9 | 49000
10 | 96000
11 | 9000
12 | 86000
13 | 65000
14 | 5000
15 | 10000
16 | 1000
17 | 8000
18 | 36000
19 | 32000
20 |
--------------------------------------------------------------------------------
/15_BayesianReliabilityAnalysis/15_03_SelectionOfPriorDistribution/15_03_01_BinomialModel.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "## Binomial Model"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [
15 | {
16 | "data": {
17 | "image/png": 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5xkGf+8FWcqmALuZnaReinZeaV/VxVT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\nTMgYhhTpw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18 | "text/plain": [
19 | "plot without title"
20 | ]
21 | },
22 | "metadata": {},
23 | "output_type": "display_data"
24 | }
25 | ],
26 | "source": [
27 | "# Set the range (i.e., [0,1]) and the number of values to calculate\n",
28 | "x<-seq(0, 1, length=100)\n",
29 | "# Specify the parameters r and s\n",
30 | "r<-2.36\n",
31 | "s<-9.44\n",
32 | "# Calculate the beta density for each x\n",
33 | "y<-dbeta(x, r, s, log=FALSE)\n",
34 | "plot(x, y, type=\"l\", xlab=expression(theta), ylab=expression(pi(theta)))"
35 | ]
36 | },
37 | {
38 | "cell_type": "code",
39 | "execution_count": null,
40 | "metadata": {},
41 | "outputs": [],
42 | "source": []
43 | }
44 | ],
45 | "metadata": {
46 | "kernelspec": {
47 | "display_name": "R",
48 | "language": "R",
49 | "name": "ir"
50 | },
51 | "language_info": {
52 | "codemirror_mode": "r",
53 | "file_extension": ".r",
54 | "mimetype": "text/x-r-source",
55 | "name": "R",
56 | "pygments_lexer": "r",
57 | "version": "3.6.1"
58 | }
59 | },
60 | "nbformat": 4,
61 | "nbformat_minor": 4
62 | }
63 |
--------------------------------------------------------------------------------
/Errata/errata.pdf:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/RausandBarros/ReliabilityBookScripts/f6558b57c3198b39cd239e85e7650990e8c1f501/Errata/errata.pdf
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/LICENSE.txt:
--------------------------------------------------------------------------------
1 | MIT License
2 |
3 | Copyright (c) 2020 Marvin RAUSAND, Anne BARROS
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 |
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # **System Reliability Theory - Models, Statistical Methods, and Applications** 3rd edition.
2 |
3 |
4 | ---
5 | In this repository you will find scripts, datasets, examples developped in the book ["System Reliability Theory; Models, Statistical Methods and Applications"](https://www.wiley.com/en-fr/System+Reliability+Theory%3A+Models%2C+Statistical+Methods%2C+and+Applications%2C+3rd+Edition-p-9781119374015 "WILEY book's Wepage") by M. Rausand, A. Barros, A. Høyland.
6 |
7 | 
8 |
9 | ---
10 | ## Table of Contents
11 | 1. Repository description
12 | 2. Get the repository
13 | 3. Get the environment
14 | 4. Bug reports
15 | 5. License
16 |
17 | ---
18 | ## 1. Repository description
19 |
20 | To facilitate the understanding of notebooks, we tried to minimize the call to external subfunctions. The advantage is that notebooks are independent and subfunctions are directly defined at the notebook level and are rather simple. The inconvenient is that several notebooks have the *same* subfunctions and that they might slightly differe from one to another... The reader should be aware of that.
21 |
22 | Below is a tree view of the repository relying on the book's sections numbering:
23 | ```
24 | .
25 | ├── 05_ProbabilityDistributionsInReliabilityAnalysis
26 | │ ├── 05_04_SomeTimeToFailureDistributions --> R Code
27 | │ │ ├── 05_04_02_TheGammaDistribution.ipynb --> R Code
28 | │ │ ├── 05_04_03_TheWeibullDistribution.ipynb --> R Code
29 | │ │ ├── 05_04_04_TheNormalDistribution.ipynb --> R Code
30 | │ │ └── 05_04_05_TheLognormalDistribution.ipynb --> R Code
31 | │ └── 05_07_AdditionalContinuousDistributions
32 | │ └── 05_07_02_TheBetaDistribution.ipynb --> R Code
33 | ├── 06_SystemReliabilityAnalysis
34 | │ └── 06_03_NonRepairableSystems
35 | │ └── 06_03_02_NonrepairableParallelStructures.ipynb --> R Code
36 | ├── 10_CountingProcesses
37 | │ └── 10_07_Problems
38 | │ ├── 10_07_Dataset_Problem_10_13.txt --> Dataset
39 | │ └── TestDataLoading.ipynb --> R Code
40 | ├── 11_MarkovAnalysis
41 | │ ├── 11_09_TimeDependentSolution.ipynb --> Python
42 | │ ├── 11_11_MultiphaseMarkovProcesses
43 | │ │ ├── 11_11_01_ChangingTheTransitionRates.ipynb --> Python
44 | │ │ └── 11_11_02_ChangingTheInitialState.ipynb --> Python
45 | │ ├── 11_12_PiecewiseDeterministicMarkovProcesses
46 | │ │ └── 11_12_03_ASpecificCase.ipynb --> Python
47 | │ └── 11_13_SimulationOfAMarkovProcess.ipynb --> Python
48 | ├── 12_PreventiveMaintenance
49 | │ ├── 12_04_DegradationModels
50 | │ │ ├── 12_04_02_TrendModelsRegressionBasedModels.ipynb --> Python
51 | │ │ └── 12_04_03_ModelsWithIncrements.ipynb --> Python
52 | │ └── 12_05_ConditionBasedMaintenance
53 | │ ├── 12_05_02_ContinuousMonitoringAndFiniteDiscreteStateSpace1.ipynb --> Python
54 | │ ├── 12_05_02_ContinuousMonitoringAndFiniteDiscreteStateSpace2.ipynb --> Python
55 | │ ├── 12_05_02_ContinuousMonitoringAndFiniteDiscreteStateSpace3.ipynb --> Python
56 | │ ├── 12_05_04_InspectionBasedMonitoringAndFiniteDiscreteStateSpace.ipynb --> Python
57 | │ └── 12_05_05_InspectionBasedMonitoringAndContinuousStateSpace.ipynb --> Python
58 | ├── 14_ReliabilityDataAnalysis
59 | │ ├── 14_02_SomeBasicConcepts
60 | │ │ └── 14_02_02_SurvivalTimes.ipynb --> R Code
61 | │ ├── 14_03_ExploratoryDataAnalysis
62 | │ │ ├── 14_03_01_ACompleteDataset.ipynb --> R Code
63 | │ │ ├── 14_03_02_SampleMetrics.ipynb --> R Code
64 | │ │ ├── 14_03_03_Histogram.ipynb --> R Code
65 | │ │ ├── 14_03_04_DensityPlot.ipynb --> R Code
66 | │ │ ├── 14_03_05_EmpiricalSurvivorFunction.ipynb --> R Code
67 | │ │ ├── 14_03_06_QQPlot.ipynb --> R Code
68 | │ │ └── 14_03_dataset.txt --> Dataset
69 | │ ├── 14_04_ParameterEstimation
70 | │ │ ├── 14_04_03_MethodOfMomentsEstimation.ipynb --> R Code
71 | │ │ ├── 14_04_04_MaximumLikelihoodEstimation.ipynb --> R Code
72 | │ │ ├── 14_04_06_WeibullDistributedLifetimes.ipynb --> R Code
73 | │ │ └── 14_04_dataset.txt --> Dataset
74 | │ ├── 14_05_TheKaplanMeierEstimate
75 | │ │ └── 14_05_02_TheKaplanMeierEstimatorForACensoredDataset.ipynb --> R Code
76 | │ ├── 14_06_CumulativeFailureRatePlots
77 | │ │ └── 14_06_01_TheNelsonAalenEstimateOfTheCumulativeFailureRate.ipynb --> R Code
78 | │ ├── 14_07_TotalTimeOnTestPlotting
79 | │ │ └── 14_07_01_TotalTimeOnTestPlotForCompleteDatasets.ipynb --> R Code
80 | │ └── 14_09_Problems
81 | │ ├── 14_09_Dataset_Problem_14_01.txt --> Dataset
82 | │ ├── 14_09_Dataset_Problem_14_02.txt --> Dataset
83 | │ ├── 14_09_Dataset_Problem_14_03.txt --> Dataset
84 | │ ├── 14_09_Dataset_Problem_14_11.txt --> Dataset
85 | │ ├── 14_09_Dataset_Problem_14_12.txt --> Dataset
86 | │ ├── 14_09_Dataset_Problem_14_13.txt --> Dataset
87 | │ ├── 14_09_Dataset_Problem_14_16.txt --> Dataset
88 | │ ├── 14_09_Dataset_Problem_14_17.txt --> Dataset
89 | │ ├── 14_09_Dataset_Problem_14_18.txt --> Dataset
90 | │ └── TestDataLoading.ipynb --> R Code
91 | ├── 15_BayesianReliabilityAnalysis
92 | │ └── 15_03_SelectionOfPriorDistribution
93 | │ └── 15_03_01_BinomialModel.ipynb --> R Code
94 | ├── ReliabilityBookEnv.yml --> Environment definition
95 | ├── LICENSE.txt --> License
96 | └── README.md
97 | ```
98 |
99 | ---
100 |
101 | ## 2. Get the repository
102 |
103 | To get the repository, run:
104 | ```bash
105 | git clone https://github.com/RausandBarros/ReliabilityBookScripts.git
106 | ```
107 | or simply download it as ZIP file from the GitHub page.
108 |
109 | The link with the repository may be removed by deleting the `\.git` folder.
110 |
111 | ---
112 |
113 | ## 3. Python installation
114 |
115 | Anaconda is a package and environment manager. It is a common practice to dedicate a specific environment to each project to ensure its consistency and limit potential interdependence with other projects. This is especially needed when several people share/work on the same project. In the following, we assume that Anaconda’s latest version (Python 3.7) is installed on your computer (Windows, macOS or Linux) and is up to date.
116 |
117 | ### 3.1. Environment installation
118 |
119 | Use command line interface:
120 | - Windows: click Start, search or select `Anaconda Prompt` from the menu
121 | - macOS or Linux: open a terminal window
122 |
123 | Run command with the path to the file `ReliabilityBookEnv.yml` correctly set:
124 | ```bash
125 | conda env create -f ./MY/PATH/TO/ReliabilityBookEnv.yml
126 | ```
127 | You should be able to check the installation by running the following command that list installed environments (i.e. `ReliabilityBookEnv`):
128 | ```bash
129 | conda env list
130 | ```
131 |
132 | ### 3.2. Run Jupyter and notebooks
133 |
134 | Still from the command line interface, start the `ReliabilityBookEnv` environment by running the command:
135 | ```bash
136 | conda activate ReliabilityBookEnv
137 | ```
138 |
139 | Then, launch Jupyter with the command:
140 | ```bash
141 | jupyter notebook
142 | ```
143 |
144 | Then use Jupyter's interface to move to the folder where the repository has been cloned or copied.
145 |
146 | Here are the instructions:
147 | - to install the python's environment according to this repository Requirements;
148 | - to run *Jupyter* and therefore the notebooks provided within this repository.
149 |
150 | At the end of the session, deactivate the environment with command:
151 | ```bash
152 | conda deactivate
153 | ```
154 |
155 | The environment might be deleted with command:
156 | ```bash
157 | conda remove --name ReliabilityBookEnv --all
158 | ```
159 |
160 | ---
161 |
162 | ## 4. Bug reports
163 |
164 | Bug reports would be appreciated and may be filed through the
165 | [issue tracker](https://github.com/RausandBarros/ReliabilityBookScripts/issues). Pull requests won't be accepted except by invitation. Please file an issue first through the former link.
166 |
167 | ---
168 | ## 5. License
169 |
170 | This project is licensed under the terms of the MIT license (see file `License.txt`).
171 |
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/ReliabilityBookEnv.yml:
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1 | name: ReliabilityBookEnv
2 | channels:
3 | - defaults
4 | dependencies:
5 | - python=3.7.7
6 | - numpy=1.18.1
7 | - scipy=1.4.1
8 | - pandas=1.3.1
9 | - matplotlib=3.1.3
10 | - ipykernel=5.1.4
11 | - ipython=7.13.0
12 | - jupyter=1.0.0
13 | - r-irkernel=0.8.15
14 | - r-essentials=3.6.0
15 | - r-base==3.6.1
16 | - r-maxlik=1.3_4
17 | - r-moments=0.14
18 | - r-bbmle=1.0.20
19 | - r-weibullr=1.0.10
20 | - r-adequacymodel=2.0.0
21 |
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