Application of Bayesian Techniques to Reliability Demonstration, Estimation and Updating of the Prior Distribution.

摘要

A method is presented for the estimation of the shape and scale parameters of an inverted gamma prior distribution of the mean-time-to-failure for equipment having exponential time-to-failure distribution. This method, akin to the Maximum Likelihood Method, allows the use of all sorts of existing failure data on the equipment in question, provided a certain sufficient condition is satisfied. Further, this method (we call it the Generalized Maximum Likelihood Method) is usable to update the prior distribution, when new failure data become available. In the long run, this updating process will give rise to a solid prior, which can confidently be used in Reliability Demonstration. Various facets of the sufficient condition for the applicability of this estimation method are exposed, the variance--covariance matrix of the estimators is given under various randomness assumptions and some numerical considerations are discussed. There is a brief discussion of alternate estimators in the case of a truncated test data. (Author)