Statistical Reliability Analysis Posterior Bayes Estimates

Abstract

This chapter is a continuation of Chapter 9, generalizing the results in the case of a posterior estimation when experimental data about the parameters of the tested system are known. When we project and build technical devices, it is customary that two types of testing are carried out: functional and exploratory ones. The purpose of the researches of the first type is to establish factual levels of the functional capability of the system with the help of tests in laboratories or on test benches. With the help of the second type of tests, one verifies a model’s working capacity under the exploitation conditions or under the conditions which are similar to them. In the problem considered below, we unite both such results in order to define more exactly the errors of the working capacity model and the time to failure probability. The solution of this problem follows the general scheme of the Bayes statistical estimation including the definition of a likelihood function, construction of a posterior distribution, and the obtaining of a corresponding estimate starting with a chosen loss function. At the end of this chapter we shall give some examples of using the proposed procedures of a Bayes posterior estimation for the solution of some applied problems.