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Compares optimum constant‐stress and simple step‐stress ALTs for the Weibull distribution. The purpose is to quantify the advantage of using step‐stress testing in comparison to constant‐stress testing when censoring is likely to occur at the lower levels of stress. Assumes that a log‐linear relationship exists between log scale parameter and stress and that the cumulative exposure model holds for the effect of changing stress in step‐stress test. The variance of the MLE of log scale parameter at design stress is used as the criterion for comparing ALTs. The efficiency of simple step‐stress tests relative to constant‐stress with Type I censoring is studied in terms of the ratio of these variances. Results are given for asymptotic variances and for finite sample sizes using simulation to estimate variances.

To obtain an optimal simple time‐step stress accelerated life test for the case involving pre‐specified censoring time. Such a test saves time and expenses over tests at normal conditions.

Most of the available literature on step‐stress accelerated life testing deals with the exponential and weibull distribution. The log‐logistic life distribution has been found appropriate for high reliability components.

The method developed has been illustrated using the data simulated from cumulative exposure log‐logistic step‐stress model with censoring time specified.

The model suggested is appropriate in the field of high reliability components such as insulation system.

The purpose of this paper is to design a simple step-stress model under type-I censoring when the failure time has an extension of the exponential distribution.

The scale parameter of the distribution is assumed to be a log-linear function of the stress and a cumulative exposure model is hold. The maximum likelihood estimates of the parameters, as well as the corresponding Fisher information matrix are derived. Two real examples are given to show the application of an extension of the exponential distribution in reliability studies and a numerical example is presented to illustrate the method discussed here.

A simple step-stress test under cumulative exposure model and type-I censoring for an extension of the exponential distribution is presented.

The work is original.

The purpose of this paper is to forecast the reliable storage life of a certain kind of equipment under the normal stress level.

Through the stepping stress acceleration life test and the failure mechanism analysis, this paper aims to confirm the stress level for the stepping stress acceleration life test of a certain kind of equipment and establish the data processing mathematical model and storage life forecasting method.

The stress level for the stepping stress acceleration life test of a certain kind of equipment is confirmed and the data processing mathematical model and storage life forecasting method is established.

Availability of data is the main limitation affecting which model will be applied.

Useful advice for products' storage life forecasting.

The paper presents a new approach to product storage life estimation.

The step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.

A Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.

The authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.

Most of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

An alternative is proposed to the Weibull cumulative exposure model in step‐stress testing, that we call the transformed exponential model. The proposed model comes from a natural transformation of the exponential cumulative exposure model. It is as flexible as the cumulative exposure model for describing data, but its mathematical form makes it easier to obtain parameter estimates and standard errors. Inferential procedures and optimum designs are discussed for two‐step accelerated test plans with known shape parameter.

The purpose of this paper is to consider the general k level step-stress accelerated life test with the Rayleigh lifetime distribution for units subjected to stress under progressive Type-I censoring.

The parameter of this distribution is assumed to be a log-linear function of the stress, and a tampered failure rate model holds. The progressive Type-I censoring reduces the cost of testing. Due to constrained resources in practice, the test design must be optimized carefully. A numerical study is conducted to illustrate the optimum test design based on several four optimality criteria under the constraint that the total experimental cost does not exceed a pre-specified budget.

This paper compares unconstrained and constrained optimal k level step-stress test. Based on the results of the simulation study, the cost constraint reduces cost and time of the test and it also, in the most cases, increases the efficiency of the test. Also, the T-optimal design is lowest cost and time for testing and it is found more optimal in both conditions.

In this paper, various optimization criteria for selecting the stress durations have been used, and these criteria are compared together. Also, because of affecting the stress durations on the experimental cost, the author optimize under the constraint that the total experimental cost does not exceed a pre-specified budget. The efficiency of the unconstrained test in comparison with constrained test is discussed.

In this paper, the author proposed an optimization design for a step-stress accelerated life test (SSALT) with two stress variables for the generalized exponential (GE) distribution under progressive type-I censoring.

In this paper, two stress variables were considered. Progressive censoring and accelerated life testing were used to reduce the time and cost of testing. It was assumed that the lifetimes of the test units followed a GE distribution. The effects of changing stress were considered as a cumulative exposure model. A log-linear relationship between the scale parameter of the GE distribution and the stress was proposed. The maximum likelihood estimators and approximate and bootstrap confidence intervals (CIs) for the model parameters were obtained. An optimum test plan was developed using minimization of the asymptotic variance (AV) of the percentile life under the usual operating condition.

According to the simulation results, the bootstrap CIs of the model parameters gave more accurate results than approximate CIs through the length of CIs. The sensitivity analysis was performed to illustrate the effect of initial estimates on optimal values that has been studied. Simulation results also indicated that the optimal times were not too sensitive to the initial values of parameters; thus, the proposed design was robust.

In most studies, only one accelerating stress variable is used. Sometimes accelerating one stress variable does not yield enough failure data. Thus, two stress variables may be needed for additional acceleration. In this paper, two stress variables are considered. The inclusion of two stress variables in a test design will lead to a better understanding of the effect of two simultaneously operating stress variables. Also, the author assumes that the failure time of the test units follows a GE distribution. It is observed that the GE distribution can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. Also, most studies in this field have focused on the derivation of optimum test plans. In this paper, the author examined the estimation of model parameters and the optimization of the test design. In this paper, the asymptotic and bootstrap CIs for the model parameters are calculated. In addition, a sensitivity analysis is performed to examine the effect of the changes in the pre-estimated parameters on the optimal hold times. For determining the optimal test plan, due to nonlinearity and complexity of the objective function, the particle swarm optimization (PSO) algorithm is developed to calculate the optimal hold times. In this method, the research speed is very fast and optimization ability is more.

Accelerated life test is undertaken to induce early failure in high-reliability products likely to last for several years. Most of these products are exposed to several fatal risk factors and fail due to one of them. Examples include solar lighting device with two failure modes: capacitor failure, and controller failure. It is necessary to assess each risk factor in the presence of other risk factors as each one cannot be studied in isolation. The purpose of this paper is to explore formulation of optimum time-censored accelerated life test model under modified ramp-stress loading when different failure causes have independent exponential life distributions.

The modified ramp-stress uses one test chamber in place of the various chambers used in the normal ramp-stress accelerate life test thus saving experimental cost. The stress-life relationship is modeled by inverse power law, and for each failure cause, a cumulative exposure model is assumed. The method of maximum likelihood is used for estimating design parameters. The optimal plan consists in finding out relevant experimental variables, namely, stress rate and stress rate change point(s).

The optimal plan is devised using D-optimality criterion which consists in finding out optimal stress rate and optimal stress rate change point by maximizing logarithm of determinant of Fisher information matrix to the base 10. This criterion is motivated by the fact that the volume of joint confidence region of model parameters is inversely proportional to square root of determinant of Fisher information matrix. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.

The model formulated can help reliability engineers obtain reliability estimates quickly of high-reliability products that are likely to last for several years.

Accelerated life tests (ALTs) are used to make timely assessments of the lifetime distribution of highly reliable materials and components. Life test under accelerated environmental conditions may be fully accelerated or partially accelerated. In fully accelerated life testing, all the test units are run at accelerated condition, while in partially accelerated life testing, they are both run at normal and accelerated conditions. The products can fail due to one of the several possible causes of failure which need not be independent. The purpose of this paper is to design constant-stress PALT with dependent competing causes of failure using the tampered failure rate model.

Gumbel–Hougaard copula is used to model and measure the dependence between the life times of competing causes of failure. The use of the copula simplifies the model specification and gives a general class of distributions with the same dependent structure and arbitrary marginal distributions.

The optimal plan consists in finding optimum allocation of test units in different chambers by minimizing the reciprocal of the determinant of Fisher Information Matrix. The confidence interval for the estimated values of the design parameters has been obtained and sensitivity analysis carried out. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.

The model formulated can help reliability engineers obtain reliability estimates quickly of high reliability products that are likely to last for several years.