Compound estimation procedures in reliability

Abstract

At NASA, components and subsystems of components in the Space Shuttle and Space Station generally go through a number of redesign stages. While data on failures for various design stages are sometimes available, the classical procedures for evaluating reliability only utilize the failure data on the present design stage of the component or subsystem. Often, few or no failures have been recorded on the present design stage. Previously, Bayesian estimators for the reliability of a single component, conditioned on the failure data for the present design, were developed. These new estimators permit NASA to evaluate the reliability, even when few or no failures have been recorded. Point estimates for the latter evaluation were not possible with the classical procedures. Since different design stages of a component (or subsystem) generally have a good deal in common, the development of new statistical procedures for evaluating the reliability, which consider the entire failure record for all design stages, has great intuitive appeal. A typical subsystem consists of a number of different components and each component has evolved through a number of redesign stages. The present investigations considered compound estimation procedures and related models. Such models permit the statistical consideration of all design stages of each component and thus incorporate all the available failure data to obtain estimates for the reliability of the present version of the component (or subsystem). A number of models were considered to estimate the reliability of a component conditioned on its total failure history from two design stages. It was determined that reliability estimators for the present design stage, conditioned on the complete failure history for two design stages have lower risk than the corresponding estimators conditioned only on the most recent design failure data. Several models were explored and preliminary models involving bivariate Poisson distribution and the Consael Process (a bivariate Poisson process) were developed. Possible short comings of the models are noted. An example is given to illustrate the procedures. These investigations are ongoing with the aim of developing estimators that extend to components (and subsystems) with three or more design stages