An inference method for temperature step‐stress accelerated life testing

Self Cite

Step-stress accelerated life testing is a design strategy where the stress is modified several times during the test. In this work we address the problem of designing such a test. We focus on temperature accelerated life testing and we address the problems of setting the step duration and the stress levels. Assuming an Arrhenius model, maximum likelihood estimates of the parameters are computed. Relying on the properties of these estimators we compare different criteria for assessing the optimality of the plans produced. Some tables are presented to illustrate the method. For a fixed number of steps and a set of temperatures, a table of optimal length steps can be computed. For fixed step lengths, sets of temperatures leading to optimal plans are also available. Thus, this work provides useful tools to help engineers make decisions in testing strategy.

Section: Introductionmentioning

confidence: 99%

Optimum step‐stress for temperature accelerated life testing

Gouno¹

2007

Self Cite

“…Among these methods, the maximum likelihood (ML) methods are most successfully applied since they are automatic and applicable to almost all types of data and stress loadings. In addition, as an ML estimator is asymptotically normal, confidence limits for the ML estimator can also be easily approximated [3][4][5][6][7][8][9] . However, nothing is perfect in God's perfect plan.…”

Section: Introductionmentioning

confidence: 99%

A sequential constant‐stress accelerated life testing scheme and its Bayesian inference

Liu

Tang

2008

In the analysis of accelerated life testing (ALT) data, some stress-life model is typically used to relate results obtained at stressed conditions to those at use condition. For example, the Arrhenius model has been widely used for accelerated testing involving high temperature. Motivated by the fact that some prior knowledge of particular model parameters is usually available, this paper proposes a sequential constant-stress ALT scheme and its Bayesian inference. Under this scheme, test at the highest stress is firstly conducted to quickly generate failures. Then, using the proposed Bayesian inference method, information obtained at the highest stress is used to construct prior distributions for data analysis at lower stress levels. In this paper, two frameworks of the Bayesian inference method are presented, namely, the all-at-one prior distribution construction and the full sequential prior distribution construction. Assuming Weibull failure times, we (1) derive the closed-form expression for estimating the smallest extreme value location parameter at each stress level, (2) compare the performance of the proposed Bayesian inference with that of MLE by simulations, and (3) assess the risk of including empirical engineering knowledge into ALT data analysis under the proposed framework.Step-by-step illustrations of both frameworks are presented using a real-life ALT data set.

“…Some typical examples are automobile air bags, fuel injectors, disposable napkins, missiles Olwell 34 and fire extinguishers and munition Newby. 33 Mainly motivated by the work of Fan et al, 18 Balakrishnan and Ling [9][10][11] developed efficient EM algorithms for the estimation of model parameters under the assumption of exponential, Weibull and gamma lifetime distributions, respectively. One may refer to the recent book by Balakrishnan et al 8 for a detailed review of all these works.…”

mentioning

confidence: 99%

Robust inference for nondestructive one‐shot device testing under step‐stress model with exponential lifetimes

Castilla

Jaenada

Pardo

2023

One‐shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one‐shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step‐stress tests allow the experimenter to increase the stress levels at prefixed times gradually during the life‐testing experiment. The cumulative exposure model is commonly assumed for step‐stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z‐type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for nondestructive one‐shot devices under the step‐stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and confidence intervals for different lifetime characteristic such as reliability, distribution quantiles, and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real‐life data sets are analyzed finally for illustrative purpose.