|
Showing 1 - 2 of
2 matches in All Departments
1. Introduction to Bayesian Methods in Reliability.- 1. Why
Bayesian Methods?.- 1.1 Sparse data.- 1.2 Decision problems.- 2.
Bayes' Theorem.- 3. Examples from a Safety Study on Gas
transmission Pipelines.- 3.1 Estimating the probability of the
development of a big hole.- 3.2 Estimating the leak rate of a gas
transmission pipeline.- 4. Conclusions.- References.- 2. An
Overview of the Bayesian Approach.- 1. Background.- 2. Probability
Concepts.- 3. Notation.- 4. Reliability Concepts and Models.- 5.
Forms of Data.- 6. Statistical Problems.- 7. Review of Non-Bayesian
Statistical Methods.- 8. Desiderata for Decision-Oriented
Statistical Methodology.- 9. Decision-Making.- 10. Degrees of
Belief as Probabilities.- 11. Bayesian Statistical Philosophy.- 12.
A Simple Illustration of Bayesian Learning.- 13. Bayesian
Approaches to Typical Statistical Questions.- 14. Assessment of
Prior Densities.- 15. Bayesian Inference for some Univariate
Probability Models.- 16. Approximate Analysis under Great Prior
Uncertainty.- 17. Problems Involving many Parameters: Empirical
Bayes.- 18. Numerical Methods for Practical Bayesian Statistics.-
References.- 3. Reliability Modelling and Estimation.- 1.
Non-Repairable Systems.- 1.1 Introduction.- 1.2 Describing
reliability.- 1.3 Failure time distributions.- 2. Estimation.- 2.1
Introduction.- 2.2 Classical methods.- 2.3 Bayesian methods.- 3.
Reliability estimation.- 3.1 Introduction.- 3.2 Binomial sampling.-
3.3 Pascal sampling.- 3.4 Poisson sampling.- 3.5 Hazard rate
estimation.- References.- 4. Repairable Systems and Growth Models.-
1. Introduction.- 2. Good as New: the Renewal Process.- 3.
Estimation.- 4. The Poisson Process.- 5. Bad as old: the
Non-Homogeneous Poisson Process.- 6. Classical Estimation.- 7.
Exploratory Analysis.- 8. The Duane Model.- 9. Bayesian Analysis.-
References.- 5. The Use of Expert Judgement in Risk Assessment.- 1.
Introduction.- 2. Independence Preservation.- 3. The Quality of
Experts' Judgement.- 4. Calibration Sets and Seed Variables.- 5. A
Classical Model.- 6. Bayesian Models.- 7. Some Experimental
Results.- References.- 6. Forecasting Software Reliability.- 1.
Introduction.- 2. The Software Reliability Growth Problem.- 3. Some
Software Reliability Growth Models.- 3.1 Jelinski and Moranda
(JM).- 3.2 Bayesian Jelinski-Moranda (BJM).- 3.3 Littlewood (L).-
3.4 Littlewood and Verrall (LV).- 3.5 Keiller and Littlewood (KL).-
3.6 Weibull order statistics (W).- 3.7 Duane (D).- 3.8 Goel-Okumoto
(GO).- 3.9 Littlewood NHPP (LNHPP).- 4. Examples of Use.- 5.
Analysis of Predictive Quality.- 5.1 The u-plot.- 5.2 The y-plot,
and scatter plot of u's.- 5.3 Measures of 'noise'.- 5.3.1 Braun
statistic.- 5.3.2 Median variability.- 5.3.3 Rate variability.- 5.4
Prequential likelihood.- 6. Examples of Predictive Analysis.- 7.
Adapting and Combining Predictions; Future Directions.- 8 Summary
and Conclusions.- Acknowledgements.- References.- References.-
Author index.
When data is collected on failure or survival a list of times is
obtained. Some of the times are failure times and others are the
times at which the subject left the experiment. These times both
give information about the performance of the system. The two types
will be referred to as failure and censoring times (cf. Smith
section 5). * A censoring time, t, gives less information than a
failure time, for it is * known only that the item survived past t
and not when it failed. The data is tn and of censoring thus
collected as a list of failure times t , . . . , l * * * times t ,
t , . . . , t * 1 z m 2. 2. Classical methods The failure times are
assumed to follow a parametric distribution F(t;B) with and
reliability R(t;B). There are several methods of estimating density
f(t;B) the parameter B based only on the data in the sample without
any prior assumptions about B. The availability of powerful
computers and software packages has made the method of maximum
likelihood the most popular. Descriptions of most methods can be
found in the book by Mann, Schafer and Singpurwalla (1974). In
general the method of maximum likelihood is the most useful of the
classical approaches. The likelihood approach is based on
constructing the joint probability distrilmtion or density for a
sample.
|
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.