Inference on an Adaptive Accelerated Life Test with Application to Smart-Grid Data-Acquisition-Devices

In the case of operating conditions in a much shorter time, the accelerated life test models are commonly used method since these models let the experimenters control the higher stress levels to be used for components or items in the life tests. Among different accelerated life test methods, constant stress accelerated life test models have a relationship between “failure time” and “stress” and these models are quite popular since they help the experimenters save time and cost. In this study, we evaluate the performances of the parameter estimations of the two-parameter bathtub-shaped lifetime distribution introduced by Chen (Stat Probab Lett 49(2):155–161, 2000) under the constant stress accelerated life test model using the well-known eight different inference methods. Then, we investigate the optimal stress levels using some popular criteria. Then, the performances of the estimations are compared with simulation schemes. Simulation results showed that the maximum likelihood method provides better estimation performances than others. The estimation performances of the other methods can be changed according to the stress level of the accelerated life test model. Further, it is observed that increasing stress levels provide optimal accelerated life test schemes under fixed first stress levels. Finally, we use a real data example to illustrate the theoretical outcomes.

In product research and development, one might wish to select the most reliable of several highly-reliable competing products. Both type-I and type-II accelerated life tests (ALT) are well-known to estimate and compare the life of highly reliable (nonrepairable) products within a reasonable testing time. A common decision problem is to choose the better plan for achieving the above goal. This paper proposes an intuitive selection rule for each ALT plan, and then derives the respective optimal ALT sampling plan when the acceleration factor (AF) is known and unknown. Finally, some criteria of Mackay are used to compare the two plans. From a practical point of view, the type-II ALT sampling plan is more convenient, and needs smaller sample size than the type-I ALT sampling plan. Nevertheless, the latter has shorter mean duration time and life testing time than the former.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Degradation tests are widely used to assess the reliability of highly reliable products which are not likely to fail under traditional life tests or accelerated life tests. However, for some highly reliable products, the degradation may be very slow and hence it is impossible to have a precise assessment within a reasonable amount of testing time. In such cases, an alternative is to use higher stresses to extrapolate the product's reliability at the design stress. This is called an accelerated degradation test (ADT). In conducting an ADT, several decision variables, such s the inspection frequency, sample size and termination time, at each stress level are influential on the experimental efficiency. An inappropriate choice of these decision variables not only wastes experimental resources but also reduces the precision of the estimation of the product's reliability at the use condition. The main purpose of this paper is to deal with the problem of designing an ADT. By using the criterion of minimizing the mean‐squared error of the estimated 100$p$th percentile of the product's lifetime distribution at the use condition subject to the constraint that the total experimental cost does not exceed a predetermined budget, a nonlinear integer programming problem is built to derive the optimal combination of the sample size, inspection frequency and the termination time at each stress level. A numerical example is provided to illustrate the proposed method. Copyright © 2003 John Wiley &amp; Sons, Ltd.

In an accelerated life test, inferences on extreme quantiles of the lifetime distribution at the use condition are obtained via extrapolation in two directions: in time, and in stress levels. Extrapolation is known to highly depend on the working model, and ignoring model uncertainty can result in over-confidence. This paper explores the use of Bayesian model averaging for estimating quantiles in an accelerated life test. Two of the most commonly used lifetime regression models, lognormal, and Weibull log-location-scale regression models, are considered in this paper as candidate models. To illustrate, we analyse complementary metal-oxide semiconductor integrated circuit data. We also construct a simulation study to compare the performance of the Bayesian model averaging -credibility intervals with other exiting interval estimators. The simulation study shows that, for estimating extreme quantiles, both the standard Bayesian and the maximum likelihood approaches can lead to an over-confident result, and Bayesian model averaging provides a -credibility interval with a wider average length, but a more accurate coverage probability.

The optimal plan of a time-censored accelerated life test (ALT) depends on unknown parameters in the ALT model. The general strategy for coping with this problem is to replace the unknown parameters with their a priori estimated values, after which we can design test plans that are robust to deviations of the estimated values. In an ALT with log-location-scale lifetime distribution and linear acceleration relation function, the slope parameter of the acceleration relation function usually has the highest uncertainty. Instead of prespecifying the slope parameter in the ALT design, in this article, we propose a new design criterion that minimizes the risk of misclassifying whether the product's pth quantile meets the design specification. Through a case study of a circular electric connector, we illustrate the proposed method, and compare it with other test criteria. The comparison result shows that the proposed plan exhibits good performance in both estimating and s-testing the product's pth quantile.

The accelerated life testing is the key methodology of evaluating product reliability rapidly. This paper presents statistical inference of Gompertz distribution based on unified hybrid censored data under constant-stress partially accelerated life test (CSPALT) model. We apply the stochastic expectation-maximization algorithm to estimate the CSPALT parameters and to reduce computational complexity. It is shown that the maximum likelihood estimates exist uniquely. Asymptotic confidence intervals and confidence intervals using bootstrap-p and bootstrap-t methods are constructed. Moreover the maximum product of spacing (MPS) and maximum a posteriori (MAP) estimates of the model parameters and accelerated factor are discussed. The performances of the various estimators of the CSPALT parameters are compared through the simulation study. In summary, the MAP estimates perform superior than MLEs (or MPSs) with respect to the smallest MSE values.

One may think that the design of bivariate accelerated life tests (ALTs) with one main effect and one interaction effect can be extended directly from the design proposed by Escobar and Meeker (1995) for bivariate ALTs with no interaction between the two variables. However, it can be shown that the “split” method, which is used in pursuing bivariate ALTs designs with no interaction term, can not be used here directly since it is found that the standardized test region is now a trapezoid instead of a square. In this article, this problem is solved. Test plans are developed to determine test conditions and allocate test units for constant-stress ALTs with Type-I censoring. The test criterion is to minimize , which is the asymptotic variance of the maximum likelihood estimator of the 100pth quantile of the lifetime distribution. An example is presented to illustrate the proposed approach.

The traditional constant‐stress accelerated life test may encounter the problem of no or a few failures at the low stress level, if the test is stopped after a fixed period. Insufficient failures usually make it difficult to estimate reliability characteristics and to discover design deficiencies of the product. To mitigate the problem, the adaptive plan is designed based on Bayesian methods in this study. Under the constraints of test facilities, test units, time, and cost, the adaptive plan is optimized according to the criterion of minimizing the preposterior variance of the logarithm of a quantile of the lifetime distribution at the use condition. Large‐sample approximation is applied to reduce the computational burden. Genetic algorithm is adopted to determine the optimal design of the adaptive plan. Finally, a numerical example is given to demonstrate the advantages of the proposed adaptive plan.

In this paper, the estimation for the bivariate generalized exponential (BVGE) distribution under type-I censored with constant stress accelerated life testing (CSALT) are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The unknown parameters are estimated by the maximum likelihood approach and their approximate variance-covariance matrix is obtained. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the bivariate generalized exponential distribution. Keywords : Accelerated life testing, Bivariate generalized exponential distribution, Constant stress, Type-I censoring, Maximum likelihood estimation.

Accelerated life testing is a method for estimating the reliability of products at normal use conditions from the failure data obtained at the severe conditions. In this paper, constant-stress accelerated life testing is considered when the lifetime of a product follows a two- parameter Birnbaum-Saunders distribution. Based on type-II censoring. A certain conditions (stress) are assumed to affect the scale parameter through the inverse power law model. Maximum likelihood estimators (MLEs) of an accelerated life tests model are derived. Prediction of the scale parameter under usual conditions is obtained. Moreover, the reliability function at a certain mission time under the same conditions is also predicted. Simulation results are carried out to study the precision of the MLEs for the parameters involved.

Optimal design of accelerated life tests for the Weibull distribution under periodic inspection and type I censoring

With the increasing marketplace demand for decreasing test time and cost, constant‐stress accelerated life testing (CSALT) is widely used for reliability demonstration in practice. The existing accelerated acceptance sampling plans (AASPs) do not consider the uncertainty of accelerated factor (AF), which makes it difficult to accurately describe the producer's and consumer's risks. Previous AASP studies on CSALT were mainly carried out under a fixed accelerated stress level, and the influence of accelerated stress level is not concerned. Therefore, considering the uncertainty of AF and taking the lognormal distribution as an example, the AASP design method with time‐censoring is proposed, where the life‐stress relationship between the location parameter and stress level is expressed by an inverse power law model. First, considering the uncertainty of AF expressed by a distribution, the acceptance probability can be obtained by the mathematic expectation of conditional acceptance probability, and the producer's and consumer's risks can be accurately expressed. Then, to reduce the total cost furtherly, the accelerated stress level is considered as a new decision variable, the optimum AASP including the sampling plan and the decision‐making criterion can be designed by minimizing the total cost and solving the risk constraint equations of both sides. A real case study of white organic light‐emitting diodes is carried out to verify the effectiveness of the proposed method.

This paper deals with non-Bayesian estimation problem of constant-stress Accelerated Life Tests (ALTs) when the lifetime of the items follow truncated Generalized Logistic Distribution (GLD). Some considerations on inference based on the use of asymptotically normality of the ML estimators are presented considering the stress effects on the two scale parameters of the truncated GLD with a k-level constant-stress ALT under progressive type-I censored grouped data. The EM algorithm method is used to obtain the estimators of the unknown parameters. In addition, estimator of the two scale parameters, reliability function under usual conditions and Fisher information matrix of the estimators are given. Finally, we present a Simulation Study to illustrate the proposed procedure.

Inference on adaptive progressive hybrid censored accelerated life test for Gompertz distribution and its evaluation for virus-containing micro droplets data

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