ABSTRACT
All the methods and types of analyses described in this text up to now fall in the realm of “classical statistical analysis.” There is another set of tools and techniques that can be used to extract answers from sample data known as “Bayesian methodology.” Bayesian methodology can often yield more information from smaller sample sizes than classical analysis. There is a price, of course. You need to make more assumptions, and the results can be controversial to the point of being not acceptable to some analysts. Many applications of Bayesian methodology encounter a highly polarized reception
consisting of strong supporters and equally strong detractors. To the believer, a Bayesian approach offers an intuitively pleasing way to harness past experience and “expert judgment” toward a goal of reducing costs and test time, while still coming up with accurate estimates and sound decisions. This approach is especially attractive when estimating the failure rate of highly reliable components, where we have seen that sample sizes and test times can be very large if we want precise results. On the other hand, those against this approach feel that the price you pay for what almost seems like “something for nothing” is the loss of credibility of the —nal results. This chapter will —rst look at the differences between classical and Bayesian analysis,
with an emphasis on explaining the different assumptions, bene—ts, and risks behind each approach. Then, we will show how Bayesian methods can be applied to solve some common reliability problems. The applications described in detail will be carried out using spreadsheet software. There are other powerful Bayesian techniques that are either much more advanced than the material covered here or require special software. These will be brieµy described in Section 14.7 at the end of the chapter (with references for readers who want to explore these Bayesian applications further).
