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An important goal for the producers is to stimulate the purchase intention of consumers so that the profit can be increased. An attractive warranty policy can not only represent the quality of prod...

In this paper, we investigate some inference and design problems related to multiple constant-stress accelerated life test with progressive type-I interval censoring. A Weibull lifetime dis...

In this article, we investigate the optimization problem when the competing risks data come from a progressive type II censoring in an accelerated life test with multiple levels of constant stress. The failure times of the individual causes are assumed to be independent and exponentially distributed with different parameters. We propose three criteria related to the Fisher's information matrix to determine the optimal stress level as well as the optimal sample allocation at each stress level. A real data set is studied to illustrate the application of the proposed criteria.

In this article, we study the optimization problem of sample size allocation when the competing risks data are from a progressive type-II censoring in a constant-stress accelerated life test with multiple levels. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher information matrix. We propose three optimization criteria and two search scenarios to obtain the sample size allocation at each stress level. Some numerical results are studied to illustrate the usage of the proposed methods.

In this paper, we investigate some statistical inference, optimal design, and reliability sampling plan problems related to multiple constant-stress accelerated life test with one-shot device testing. At each stress-level combination, a generalized exponential lifetime distribution is considered. The scale parameter of the proposed distribution is assumed to be a log-linear function of stresses. To conduct a one-shot device accelerated life test more efficiently, one has to address the problem of determining optimal setting that produces the best estimation results. In practice, the experimental budget is always limited. The size of budget usually influences the decision of experimental setting and hence, influences the precision of estimation. Therefore, this paper is to determine the optimal experimental setting under D-optimality criterion with cost constraint. In addition, reliability sampling plan is an important statistical tool in the area of quality control. This paper is also to explore the optimal reliability sampling plan which minimizes the total experimental cost of a one-shot device accelerated life test with specified producer’s risk and consumer’s risk.

In this article, we investigate some reliability and quality problems when the competing risks data are progressive type-I interval censored with binomial removals. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher's information matrix. The optimal lengths of the inspection intervals are determined under two different criteria. The reliability sampling plans are established under given producer's and customer's risks. A Monte Carlo simulation is conducted to evaluate the performance of the estimators, and also some numerical results are presented.

This article presents the statistical inferences on Weibull parameters with the data that are progressively type II censored. The maximum likelihood estimators are derived. For incorporation of previous information with current data, the Bayesian approach is considered. We obtain the Bayes estimators under squared error loss with a bivariate prior distribution, and derive the credible intervals for the parameters of Weibull distribution. Also, the Bayes prediction intervals for future observations are obtained in the one- and two-sample cases. The method is shown to be practical, although a computer program is required for its implementation. A numerical example is presented for illustration and some simulation study are performed.

In this article, reliability sampling plans are developed for the Weibull distribution when the life test is progressively first-failure censored. We use the maximum likelihood method to obtain the point estimators of the model parameters. We propose an approach to establish reliability sampling plans which minimize three different objective functions under the constraint of total cost of experiment and given consumer's and producer's risks. The results are tabulated for selected specifications under progressive first-failure censoring scheme, and the sensitivity analysis is also studied. A Monte Carlo simulation is performed to study the accuracy of large-sample approximation.

In this paper, a reliability sampling plan under progressively type-1 interval censoring is proposed when the lifetime of products follows the Pareto distribution of second kind. We use the maximum likelihood estimator for the median life and its asymptotic distribution. The cost model is proposed and the design parameters are determined such that the given producer's and the consumer's risks are satisfied. Tables are given and the results are explained with examples.

This article discusses a life test under progressive type-I group-censoring. We use maximum likelihood method to obtain the point and interval estimators of the parameter of lifetime distribution. In order to obtain a precise estimate of mean life, one needs to design an optimal life test. Thus, this article proposes an approach to determine the number of test units, number of inspections, and length of inspection interval of a life test under a pre-determined budget of experiment such that the asymptotic variance of estimator of mean life is minimum. The method will be applied to two numerical examples and the sensitivity analysis will be investigated.

This paper considers a life test under progressive type I group censoring with a Weibull failure time distribution. The maximum likelihood method is used to derive the estimators of the parameters of the failure time distribution. In practice, several variables, such as the number of test units, the number of inspections, and the length of inspection interval are related to the precision of estimation and the cost of experiment. An inappropriate setting of these decision variables not only wastes the resources of the experiment but also reduces the precision of estimation. One problem arising from designing a life test is the restricted budget of experiment. Therefore, under the constraint that the total cost of experiment does not exceed a pre-determined budget, this paper provides an algorithm to solve the optimal decision variables by considering three different criteria. An example is discussed to illustrate the proposed method. The sensitivity analysis is also studied.

This paper gives a reliability sampling plan for progressively type I interval censored life tests when the lifetime follows the exponential distribution. We use the maximum likelihood method to obtain the point estimation of the parameter of failure time distribution. We provide an approach to establish reliability sampling plans which minimize the total cost of life testing under given consumer's and producer's risks. Some numerical studies are investigated to illustrate the proposed approach.