Step-stress Test Plans Research Articles

Optimal design of ramp-stress accelerated degradation tests based on the Wiener process

Ramp-stress accelerated degradation test (ADT) plans are developed under the assumption that the degradation characteristic follows a Wiener process. A ramp-stress (RS) test has an advantage over a constant-stress (CS) or step-stress (SS) test in that the difficulty of choosing appropriate stress levels in the latter can be alleviated. In addition, RS test plans could be more efficient than CS or SS test plans in terms of the test time or the number of test units. Optimal and compromise RSADT plans are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution under the normal use condition is minimized. The above planning methods are illustrated using a numerical example, and a sensitivity analysis procedure for assessing the robustness of the proposed test plan to the uncertainty in the pre-estimate of model parameters is provided.

Planning step-stress test plans under Type-I hybrid censoring for the log-location-scale distribution

The optimal design of a k-level step-stress accelerated life-testing (ALT) experiment with unequal duration steps under Type-I hybrid censoring scheme for a general log-location-scale lifetime distribution is discussed here. Censoring is allowed only at the change-stress point in the final stage. Based on the cumulative exposure model, the determination of the optimal choice for Weibull, lognormal and log-logistic lifetime distributions are considered by minimization of the asymptotic variance of the maximum likelihood estimate of the pth percentile of the lifetime at the normal operating condition. Numerical results show that for these lifetime distributions, the optimal k-step-stress ALT design with unequal duration steps under Type-I hybrid censoring scheme reduces just to a 2-step-stress ALT design.

Planning step-stress test plans under Type-I censoring for the log-location-scale case

In this paper, we consider a k-level step-stress accelerated life-testing (ALT) experiment with unequal duration steps τ=(τ1, …, τ k ). Censoring is allowed only at the change-stress point in the final stage. A general log-location-scale lifetime distribution with mean life which is a linear function of stress, along with a cumulative exposure model, is considered as the working model. Under this model, the determination of the optimal choice of τ for both Weibull and lognormal distributions are addressed using the variance–optimality criterion. Numerical results show that for a general log-location-scale distributions, the optimal k-step-stress ALT model with unequal duration steps reduces just to a 2-level step-stress ALT model.

On designing step-stress partially accelerated life tests under failure-censoring scheme

In this article the maximum likelihood estimates of the model parameters under step-stress partially accelerated life tests (SSPALT) are obtained assuming the Weibull distribution with Type-II censored data. Also, the confidence bounds of the parameters are obtained. In addition, optimum step stress test plans are developed. The optimum test plan determines the optimal stress change point that minimizes the generalized asymptotic variance of the maximum likelihood estimators for the model parameters. That is, improving the quality of the statistical inference.

Step-stress life-testing with random stress-change times for exponential data

This paper studies statistical models in step-stress accelerated life-testing when the stress-change times are random. The marginal lifetime distribution of a test unit under a step-stress test plan when the stress change times are random variables is presented. Maximum likelihood estimates for model parameters based on both the marginal and conditional life distributions are considered. An optimum test plan is explored for simple step-stress test when the stress change time is an order statistic from the exponential lifetime under the low-stress level.

Optimum simple step-stress accelerated life tests with censoring

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 given. Simple step stress test plans with censoring were studied. The optimum failure-step stress test plans are obtained in a closed form, whereas, for the time-step stress test, nomographs are given for finding the optimum plans on the basis of parameters. The parameters must be approximated from experience, similar data, or a preliminary test. For some selected values of the parameters, the effect of incorrect preestimates was studied in terms of the percentage of variance increase. The effect was found to be small. >