Assessing high reliability via Bayesian approach and accelerated tests

Sometimes the assessment of very high reliability levels is difficult for the following main reasons:

the high reliability level of each item makes it impossible to obtain, in a reasonably short time, a sufficient number of failures;

the high cost of the high reliability items to submit to life tests makes it unfeasible to collect enough data for ‘classical’ statistical analyses.

In the above context, this paper presents a Bayesian solution to the problem of estimation of the parameters of the Weibull–inverse power law model, on the basis of a limited number (say six) of life tests, carried out at different stress levels, all higher than the normal one.The over-stressed (i.e. accelerated) tests allow the use of experimental data obtained in a reasonably short time. The Bayesian approach enables one to reduce the required number of failures adding to the failure information the available a priori engineers' knowledge. This engineers' involvement conforms to the most advanced management policy that aims at involving everyone's commitment in order to obtain total quality.A Monte Carlo study of the non-asymptotic properties of the proposed estimators and a comparison with the properties of maximum likelihood estimators closes the work.     

Index to Volume 32

ABSTRACT

Most of the recently developed methods on optimum planning for accelerated life tests (ALT) involve “guessing” values of parameters to be estimated, and substituting such guesses in the proposed solution to obtain the final testing plan. In reality, such guesses may be very different from true values of the parameters, leading to inefficient test plans. To address this problem, we propose a sequential Bayesian strategy for planning of ALTs and a Bayesian estimation procedure for updating the parameter estimates sequentially. The proposed approach is motivated by ALT for polymer composite materials, but are generally applicable to a wide range of testing scenarios. Through the proposed sequential Bayesian design, one can efficiently collect data and then make predictions for the field performance. We use extensive simulations to evaluate the properties of the proposed sequential test planning strategy. We compare the proposed method to various traditional non-sequential optimum designs. Our results show that the proposed strategy is more robust and efficient, as compared to existing non-sequential optimum designs. Supplementary materials for this article are available online.     

高分子电容湿敏传感器加速寿命试验统计模型的验证

针对目前普遍存在的加速寿命试验可靠性统计模型的准确性问题,结合加速寿命试验的几个基本假设条件,利用某高分子电容湿敏传感器恒定双应力加速寿命试验数据对加速模型准确性进行了验证。结果表明该产品加速寿命试验满足基本假设条件,所做的加速寿命试验合理,为后续加速寿命试验的分析和评估奠定了基础。     

A Bayesian generalized Eyring-Weibull accelerated life testing model

In this paper, a novel approach to a Bayesian accelerated life testing model is presented. The Weibull distribution is used as the life distribution and the generalized Eyring model as the time transformation function. This is a model that allows for the use of more than one stressor, whereas other commonly used acceleration models, such as the Arrhenius and power law models, incorporate one stressor. The use of the generalized Eyring-Weibull model developed in this paper is demonstrated in a case study, where Markov chain Monte Carlo methods are utilized to generate samples for posterior inference.