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E-grāmata: Reliability Modelling: A Statistical Approach

(City University, London, England)
  • Formāts: 272 pages
  • Izdošanas datums: 03-Oct-2018
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781351419093
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  • Formāts: 272 pages
  • Izdošanas datums: 03-Oct-2018
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781351419093
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Reliability is an essential concept in mathematics, computing, research, and all disciplines of engineering, and reliability as a characteristic is, in fact, a probability. Therefore, in this book, the author uses the statistical approach to reliability modelling along with the MINITAB software package to provide a comprehensive treatment of modelling, from the basics through advanced modelling techniques.

The book begins by presenting a thorough grounding in the elements of modelling the lifetime of a single, non-repairable unit. Assuming no prior knowledge of the subject, the author includes a guide to all the fundamentals of probability theory, defines the various measures associated with reliability, then describes and discusses the more common lifetime models: the exponential, Weibull, normal, lognormal and gamma distributions. She concludes the groundwork by looking at ways of choosing and fitting the most appropriate model to a given data set, paying particular attention to two critical points: the effect of censored data and estimating lifetimes in the tail of the distribution.

The focus then shifts to topics somewhat more difficult:

the difference in the analysis of lifetimes for repairable versus non-repairable systems and whether repair truly "renews" the system

methods for dealing with system with reliability characteristic specified for more than one component or subsystem

the effect of different types of maintenance strategies

the analysis of life test data

The final chapter provides snapshot introductions to a range of advanced models and presents two case studies that illustrate various ideas from throughout the book.

Recenzijas

"This is a lucid introduction to many important ideas in reliability. In describing the various models and techniques the author includes plenty of practical advice about their usuage. Frequent and well-developed examples illustrate and extend the techniques and there are two brief case studies at the end of the book. By studying these examples carefully, the student will learn much about the difficult art of formulating useful models." --Biometrics, June 2000

List of figures
xi
Preface xv
Basic Concepts
1(20)
Introduction
1(1)
Events and probability
1(2)
Rules of probability
3(2)
Dependent events
5(3)
Random variables and probability distributions
8(3)
The reliability function
11(5)
The hazard function
16(3)
Expectation
19(2)
Common Lifetime Models
21(16)
Introduction
21(1)
The Poisson process
22(2)
The Weibull distribution
24(3)
The Gumbel distribution
27(2)
The normal and lognormal distributions
29(2)
The gamma distribution
31(2)
The logistic and log logistic distributions
33(1)
The Pareto distribution
33(2)
Order statistics and extreme value distributions
35(2)
Model Selection
37(18)
Introduction
37(1)
Non-parametric estimation of R(t) and h(t)
37(2)
Censoring
39(2)
Kaplan-Meier estimator
41(3)
Graphical methods
44(1)
Straight line fitting
45(1)
Weibull plotting
45(2)
Normal plotting
47(2)
Other model family plots
49(3)
Comparison of distributions
52(3)
Model Fitting
55(26)
Parameter estimation
55(1)
The variance of estimators
55(1)
Confidence interval estimates
56(2)
Maximum likelihood
58(5)
Estimating quantiles
63(2)
Estimation methods using sample moments
65(2)
General probability plots
67(3)
Goodness of fit
70(2)
Pearson's X2 test
72(3)
Kolmogorov-Smirnov test
75(2)
Tests for normality
77(1)
A2 and W2 tests
78(2)
Stabilized probability plots
80(1)
Censored data
80(1)
Repairable Systems
81(20)
Introduction
81(1)
Graphical methods
82(4)
Testing for trend
86(6)
Repair time
92(1)
Maintainability and availability
92(1)
Introduction to renewal theory
93(1)
Laplace transforms
94(1)
The renewal function
95(3)
Alternating renewal processes
98(2)
The distribution of N(t)
100(1)
System Reliability
101(26)
Systems and system logic
101(2)
Tie and cut sets
103(1)
Probability bounds
104(3)
Fault trees
107(3)
Failure over time
110(3)
Quorum or m-out-of-n systems
Redundancy
113(2)
Analysis of systems using state spaces
115(6)
Mean time to failure (MTTF)
121(1)
Considerations due to `switching'
122(3)
Common cause failures
125(2)
Models for Functions of Random Variations
127(22)
Combinations and transformations of random variables
127(1)
Expectations of functions of random variables
127(2)
Approximations for E[ g(X)] and V[ g(X)]
129(2)
Distribution of a function of random variables
131(2)
Probabilistic engineering design
133(1)
Stress and strength distributions
134(1)
Interference theory and reliability computations
135(3)
Normally distributed stress and strength
138(4)
Safety factors and reliability
142(1)
Graphical approach for empirically determined distributions
143(6)
Maintenance Strategies
149(26)
Maintained systems
149(2)
Availability
151(2)
Markovian systems
153(3)
Mean time between failures (MTBF)
156(4)
Age replacement
160(6)
Scheduled maintenance
166(3)
Systems with failure detection/fail safe devices
169(4)
Down-time distributions
173(2)
Life Testing and Inference
175(36)
Life test plans
175(2)
Prediction of time on test
177(3)
Inference for the exponential distribution
180(3)
The effect of data rounding
183(1)
Parametric reliability bounds
184(3)
Likelihood-based methods
187(3)
The likelihood ratio test
190(5)
Binomial experiments
195(5)
Non-parametric estimation and confidence intervals for R(t)
200(2)
Estimating system reliability from subsystem test data
202(6)
Accelerated testing
208(3)
Advanced Models
211(28)
Covariates
211(1)
Proportional hazards models
212(4)
Accelerated life models
216(1)
Mixture models
217(4)
Competing risks
221(4)
Dependent failures
225(1)
Load-sharing systems
226(2)
Bayesian reliability
228(4)
Case studies
232(7)
Appendix 239(10)
A.1 Partial fractions
239(1)
A.2 Series
240(1)
A.3 Taylor expansions
241(1)
A.4 Newton-Raphson iteration
242(1)
A.5 Numerical integration
243(1)
A.6 Matrix algebra
244(2)
A.7 The principle of least squares
246(3)
References 249(4)
Index 253
Wolstenholme, Linda C.