RELIABILITY GROWTH MODELS FOR ATTRIBUTES (BAYES, SMITH).

Abstract

In this dissertation the estimation of reliability for a developmental process generating attribute type data is examined. It is assumed that the process consists of m stages, and the probability of failure is constant or decreasing from stage to stage. Several models for estimating the reliability at each stage of the developmental process are examined. In the classical area, Barlow and Scheuer's model, Lloyd and Lipow's model and a cumulative maximum likelihood estimation model are investigated. In the Bayesian area A.F.M. Smith's model, an empirical Bayes model and a cumulative beta Bayes model are investigated. These models are analyzed both theoretically and by computer simulation. The strengths and weaknesses of each are pointed out, and modifications are made in an attempt to improve their accuracy. The constrained maximum likelihood estimation model of Barlow and Scheuer is shown to be inaccurate when no failures occur at the final stage. Smith's model is shown to be incorrect and a corrected algorithm is presented. The simulation results of these models with the same data indicate that with the exception of the Barlow and Scheuer's model they are all conservative estimators. When reliability estimation with growth is considered, it is reasonable to emphasize data obtained at recent stages and de-emphasize data from the earlier stages. A methodology is developed using geometric weights to improve the estimates. This modification is applied to the cumulative MLE model, Lloyd and Lipow's model, Barlow and Scheuer's model and cumulative beta Bayes model. The simulation results of these modified models show considerable improvement is obtained in the cumulative MLE model and the cumulative beta Bayes model. For Bayesian models, in the absence of prior knowledge, the uniform prior is usually used. A prior with maximum variance is examined theoretically and through simulation experiments for use with the cumulative beta Bayes model. These results show that the maximum variance prior results in faster convergence of the posterior distribution than the uniform prior. The revised Smith's model is shown to provide good estimates of the unknown parameter during the developmental process, particularly for the later stages. The beta Bayes model with maximum variance prior and geometric weights also provides good estimates.