Abstract
ABSTRACT The objectives of this dissertation are: To introduce a modified EM-algorithm for finding estimates of the parameters of the failure time distribution based on time-censored Wiener degradation data (Part I); To design an optimal degradation test to minimize the asymptotic variance of the percentile estimates of the failure time distribution, subject to certain budget constraint (Part II). Being the solution to the stochastic linear growth model, the Wiener process has recently been used to model the degradation (or cumulative decay) of certain characteristics of test units in lifetime data analyses. When the failure threshold is constant or linear in time, the failure time, which is defined as the first-passage time of the Wiener process over the failure threshold, will follow an inverse Gaussian (IG) distribution. In this thesis we consider a time-censored degradation test, where, in addition to the failure times of the failed units, we assume that the degradation values at the censor times of the censored units are also available. Then for Part I, based on these degradation values, we use a modified EM-algorithm to predict the failure times of the censored units. The resulting estimator of the mean failure time is shown to be a consistent estimator, and is also an estimator that maximizes the (modified) likelihood function of the available failure times and degradation values. For the scale parameter of the IG distribution, the algorithm produces an inconsistent estimator, for which we introduce two modified estimators to reduce the bias. Analytical as well as numerical comparisons show that our proposed estimators perform well, as compared to the traditional MLEs and the modified MLEs, for both IG parameters. For Part II, we have derived Fisher’s information, and asymptotic variance of sample percentile, for the time-censored case as objection function, and expected total cost as the constraint for finding optimal accelerated path. And we give some necessary conditions for optimality of the stress function in an optimal design. For the complete case, we find that the optimal accelerated path is in fact a one-step test. As the accelerating cost is lower than measurement cost, the optimal accelerated path is to use the highest stress level from the beginning of the experiment. On the other hand, if the accelerating cost is higher than the measurement cost, the optimal test is not to be accelerated at all. For the time-censored case, we find that the optimal accelerated path is also step stress accelerated path and the optimal step stress number is two. Therefore the second stress level usually use the highest level,, so the problem is to determine the optimal change time.