Do Sun Bai

The authors present the optimum simple time-step and failure-step stress accelerated life tests for the case where a prespecified censoring time is involved. An exponential life distribution with a mean that is a log-linear function of stress, and a cumulative exposure model are assumed. The authors obtain the optimum test plans to minimize the asymptotic variance of the maximum-likelihood estimator of the mean life at a design stress. Nomographs for the optimum time-step stress test are also gi

Optimal designs for two partially accelerated life tests (PALTs) in which items are run at both accelerated and use conditions until a predetermined time are considered. The step PALT allows the test to be changed from use to accelerated condition at a specified time; the constant PALT runs each item at either use or accelerated condition only. For items having constant hazard (failure) rate, maximum-likelihood estimators (MLEs) of the hazard rate at use condition and the acceleration factor, th

This paper proposes a heuristic method based on a weighted variance concept of setting up control limits of X̄ and R charts for skewed populations. It provides asymmetric control limits in accordance with the direction and degree of skewness estimated from the sample data, by using different variances in computing upper and lower control limits. For symmetric populations, however, these control limits are equivalent to those of Shewhart control charts. The new heuristic control charts are compar

Abstract This paper proposes a heuristic method of constructing $\bar{X}$ , cumulative sum and exponentially weighted moving average control charts for skewed populations with weighted standard deviations obtained by decomposing the standard deviation into upper and lower deviations adjusted in accordance with the direction and degree of skewness. These control charts, however, reduce to standard control charts when the underlying distribution is symmetric. Simple formulae are derived to estimat

Abstract This paper proposes a new method of constructing process capability indices (PCIs) for skewed populations. It is based on a weighted standard deviation method which decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts the value of the PCI using decomposed deviations in accordance with the skewness estimated from sample data. For symmetric populations, the proposed PCIs reduce to standard PCIs. The performance of the proposed PCIs is c

This article presents an optimum simple step-stress accelerated life test for the Weibull distribution under Type I censoring. It is assumed that a log-linear relationship exists between the Weibull scale parameter and the (possibly transformed) stress and that a certain cumulative exposure model for the effect of changing stress holds. The optimum plan—low stress and stress change time—is obtained, which minimizes the asymptotic variance of the maximum likelihood estimator of a stated percentil

Optimum simple step-stress accelerated life tests (ALTs) for products with competing causes of failure are presented. The life distribution of each failure cause, which is independent of the others, is assumed to be exponential with a mean that is a log-linear function of the stress, and a cumulative exposure model is assumed. Optimum plans for time-step and failure-step ALTs are obtained which minimize the sum over all failure causes of asymptotic variances of the maximum likelihood estimators

The problem of determining the optimal number of redundant units in k-out-of-n systems with common-cause failures (CCFs) is discussed. The mean cost rate is obtained, its behavior is examined considering both CCFs and random failures of the units, and the number of redundant units minimizing the mean cost rate is shown to be finite and unique. For the problem of determining the optimal number of redundant units and inspection period, the mean cost rate is obtained and a solution procedure is pre

A generalized replacement policy based both on the system age and the minimal repair cost limit is proposed. The system is replaced when it fails for the first time after age T. If it fails before age T, the repair cost is estimated and minimal repair is then undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. The mean cost rate is obtained, its behavior is examined, and ways of obtaining optimal T and L are explored.

An optimum simple ramp test-accelerated life test with two different linearly increasing stresses-is presented for the Weibull distribution under type I censoring. It is assumed that the inverse power law holds between the Weibull scale parameter and the constant stress and that the cumulative exposure model for the effect of changing stress applies. The optimum plan-low stress rate and proportion of test units allocated to low stress mode-is found. It minimizes the asymptotic variance of the ma