Reliability Engineering: Probabilistic Models and Maintenance Methods

395 Pages·2016·40.2 MB·English

by  Joel A.Nachlas

RELIABILITY
ENGINEERING
Probabilistic Models and
Maintenance Methods
Second Edition

RELIABILITY
ENGINEERING
Probabilistic Models and
Maintenance Methods
Second Edition
JOEL A. NACHLAS
Boca Raton London New York
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Dedicated to the memory of Betty Nachlas

Contents
Preface ...................................................................................................................xiii
Author .....................................................................................................................xv
1 Introduction .....................................................................................................1
2 System Structures ...........................................................................................5
2.1 Status Functions ....................................................................................5
2.2 System Structures and Status Functions ...........................................7
2.2.1 Series Systems ..........................................................................7
2.2.2 Parallel System .........................................................................8
2.2.3 k-out-of-n Systems ..................................................................10
2.2.4 Equivalent Structures ............................................................12
2.3 Modules of Systems ............................................................................17
2.4 Multistate Components and Systems ...............................................18
Exercises ..........................................................................................................19
3 Reliability of System Structures ...............................................................23
3.1 Probability Elements ...........................................................................23
3.2 Reliability of System Structures ........................................................24
3.2.1 Series Systems ........................................................................24
3.2.2 Parallel Systems ......................................................................25
3.2.3 k-out-of-n Systems ..................................................................25
3.2.4 Equivalent Structures ............................................................26
3.3 Modules ................................................................................................31
3.4 Reliability Importance ........................................................................32
3.5 Reliability Allocation ..........................................................................35
3.6 Conclusion ............................................................................................36
Exercises ..........................................................................................................37
4 Reliability over Time ...................................................................................39
4.1 Reliability Measures ...........................................................................39
4.2 Life Distributions ................................................................................44
4.2.1 Exponential Distribution ......................................................45
4.2.2 Weibull Distribution ..............................................................46
4.2.3 Normal Distribution ..............................................................49
4.2.4 Lognormal Distribution ........................................................51
4.2.5 Gamma Distribution .............................................................52
4.2.6 Other Distributions ...............................................................52
4.3 System-Level Models ..........................................................................54
Exercises ..........................................................................................................58
vii
viii Contents
5 Failure Processes ...........................................................................................61
5.1 Mechanical Failure Models ...............................................................62
5.1.1 Stress–Strength Interference ................................................62
5.1.2 Shock and Cumulative Damage ..........................................64
5.2 Electronic Failure Models ..................................................................71
5.2.1 Arrhenius Model ....................................................................71
5.2.2 Eyring Model ..........................................................................72
5.2.3 Power Law Model ..................................................................72
5.2.4 Defect Model...........................................................................72
5.3 Other Failure Models..........................................................................73
5.3.1 Diffusion Process Model .......................................................73
5.3.2 Proportional Hazards ...........................................................78
5.3.3 Competing Risks ....................................................................80
Exercises ..........................................................................................................83
6 Age Acceleration ...........................................................................................85
6.1 Age Acceleration for Electronic Devices ..........................................87
6.2 Age Acceleration for Mechanical Devices .......................................89
6.3 Step Stress Strategies ..........................................................................92
6.4 Concluding Comment ........................................................................93
Exercises ..........................................................................................................93
7 Nonparametric Statistical Methods ..........................................................95
7.1 Data Set Notation and Censoring .....................................................96
7.2 Estimates Based on Order Statistics .................................................98
7.3 Estimates and Confidence Intervals .................................................99
7.4 Kaplan–Meier Estimates ..................................................................102
7.4.1 Continuous Monitoring of Test Unit Status .....................102
7.4.2 Periodic Monitoring of Test Unit Status ...........................105
7.5 Tolerance Bounds ..............................................................................107
7.6 TTT Transforms .................................................................................109
7.6.1 Theoretical Construction ....................................................109
7.6.2 Application to Complete Data Sets ....................................113
7.6.3 Application to Censored Data Sets ....................................118
7.7 Nelson Cumulative Hazard Estimation Method .........................122
Exercises ........................................................................................................124
8 Parametric Statistical Methods ................................................................129
8.1 Graphical Methods ...........................................................................129
8.2 Method of Moments .........................................................................135
8.2.1 Estimation Expressions .......................................................136
8.2.2 Confidence Intervals for the Estimates .............................139
8.3 Method of Maximum Likelihood ...................................................143
8.4 Maximum Likelihood Method with Data Censoring .................159
Contents ix
8.5 Special Topics .....................................................................................161
8.5.1 Method of Moments with Censored Data ........................161
8.5.2 Data Analysis under Step Stress Testing ..........................164
Exercises ........................................................................................................167
9 Repairable Systems I: Renewal and Instantaneous Repair ...............173
9.1 Renewal Processes ............................................................................174
9.2 Classification of Distributions and Bounds on Renewal
Measures ............................................................................................181
9.3 Residual Life Distribution ...............................................................186
9.4 Conclusion ..........................................................................................189
Exercises ........................................................................................................190
10 Repairable Systems II: Nonrenewal and Instantaneous Repair .......193
10.1 Minimal Repair Models ...................................................................194
10.2 Imperfect Repair Models .................................................................200
10.3 Equivalent Age Models ....................................................................203
10.3.1 Kijima Models ......................................................................203
10.3.2 Quasi-Renewal Process .......................................................210
10.4 Conclusion ..........................................................................................214
Exercises ........................................................................................................214
11 Availability Analysis .................................................................................217
11.1 Availability Measures .......................................................................220
11.2 Example Computations ....................................................................223
11.2.1 Exponential Case .................................................................223
11.2.2 Numerical Case ....................................................................225
11.3 System-Level Availability ................................................................227
11.4 Nonrenewal Cases ............................................................................232
11.4.1 Availability under Imperfect Repair .................................233
11.4.2 Availability Analysis for the Quasi-Renewal Model ......235
11.5 Markov Models .................................................................................239
Exercises ........................................................................................................245
12 Preventive Maintenance ............................................................................247
12.1 Replacement Policies.........................................................................248
12.1.1 Elementary Models ..............................................................248
12.1.2 Availability Model for Age Replacement .........................253
12.1.3 Availability Model for Block Replacement .......................255
12.1.4 Availability Model for Opportunistic Age
Replacement ...................................................................257
12.1.4.1 Failure Model ........................................................262
12.1.4.2 Opportunistic Failure Replacement Policy ......265