Some of the advances made during the past 25 years in the statistical treatment of reliability problems are reviewed. The impact of statistical methods on reliability is discussed, and some areas where work is needed are suggested.

Statistical Methods in Reliability

Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observation.

This paper concerns general right censoring and some of the difficulties it creates in the analysis of survival data. A general formulation of censored-survival processes leads to the partition of all models into those based on noninformative and informative censoring. Nearly all statistical methods for censored data assume that censoring is noninformative. Topics considered within this class include: the relationships between three models for noninformative censoring, the use of likelihood methods for inferences about the distribution of survival time, the effects of censoring on the K-sample problem, and the effects of censoring on model testing. Also considered are several topics which relate to informative censoring models. These include: problems of nonidentifiability that can be encountered when attempting to assess a set of data for the type of censoring in effect, the consequences of falsely assuming that censoring is noninformative, and classes of informative censoring models.

General right censoring and its impact on the analysis of survival data.

This paper deals with the problem of making inferences about the mean of an exponential distribution when the sample is “time-censored”. The exact sampling distribution of the maximum likelihood estimate is obtained and used to show that the asymptotic sampling theory is inadequate unless the sample size is very large. An approximation to the distribution is proposed for use in small samples and compared with a method suggested by Bartlett (1953a). An alternative estimate is suggested which is both simple and highly efficient in certain circumstances. The methods are illustrated by examples.

The Sampling Distribution of an Estimate Arising in Life Testing

The National Institute on Drug Abuse Collaborative Cocaine Treatment Study is a large, multisite psychotherapy clinical trial for outpatients who meet the DSM-IV criteria for cocaine dependence. For 480 randomized patients, the outcomes of 4 treatments are compared for an 18-month period. All treatments include group drug counseling. One treatment also adds cognitive therapy, one adds supportive-expressive psychodynamic therapy, and one adds individual drug counseling; one consists of group drug counseling alone. In addition, 2 specific interaction hypotheses, one involving psychiatric severity and the other involving degree of antisocial personality characteristics, are being tested. This article describes the main aims of the project, the background and rationale for the study design, the rationale for the choice of treatments and patient population, and a brief description of the research plan.

The National Institute on Drug Abuse Collaborative Cocaine Treatment Study. Rationale and methods.

Almost all the statistical procedures in current use for evaluating the reliability of components or equipment rest on the assumption that the failure times follow the exponential distribution. However, in practical situations one rarely has enough data to determine whether failure times are actually exponential. This paper studies the behavior of several statistical life testing procedures based on the exponential failure law if the true failure law is the Weibull distribution. It is found that these statistical techniques, which are widely used, are very sensitive to departures from initial assumptions. Applying these techniques to lie test data when the exponential failure law is not satisfied may result in substantially increasing the probability of accepting components or equipments having poor mean-timsto-failure. This paper also develops convenient analytic techniques for approximating (i) the distribution of sums of independent random variables, and (ii) the characteristics of sequential procedure...

M. Zelen

Papers

The Robustness of Life Testing Procedures Derived from the Exponential Distribution