Contributions to reliability data analysis

Abstract

Evaluation of product reliability can be based either on laboratory test data or field warranty data, and should be carefully performed to obtain statistically valid results. For the analysis of laboratory test data, the problem of choosing an appropriate lifetime distribution for a given data set is considered in this thesis. The Weibull and lognormal distributions are assumed most often in analyzing lifetime data, and in many cases, they are competing with each other. However, little attention has been paid to the selection problems for the case of censored samples despite its importance in practice. In the first part of this thesis, relative performances of the existing three selection procedures are compared for selecting between the Weibull and lognormal distribution. The three procedures are respectively based on the maximized likelihood function, scale invariant statistic, and Pearson correlation coefficient. Monte Carlo simulation experiments are conducted for various combinations of the censoring rate and sample size, and the performance of each procedure is evaluated in terms of the probability of correct selection and average error rate. For the cases where a procedure has a preference for one distribution over the other, the threshold values used to discriminate between the Weibull and lognormal distributions are adjusted to yield balanced performances for both distributions. The warranty data encountered in the automotive industry has received much attention since they contain useful information on the product reliability under actual use conditions. The life of an automobile is characterized by time in service and usage, the latter being measured by mileage. In other words, the automotive warranty data are two-dimensional unlike other types of warranty data, and this necessitates a special treatment. In the second part of this thesis, a method for analyzing two-dimensional warranty data is developed considering competing failure modes. The maxim...