Progressive censoring scheme has received considerable attention in recent years. In this paper we introduce a new type-II progressive censoring scheme for two samples. It is observed that the proposed censoring scheme is analytically more tractable than the existing joint progressive type-II censoring scheme proposed by Rasouli and Balakrishnan [12]. It has some other advantages also. We study the statistical inference of the unknown parameters based on the assumptions that the lifetime distribution of the experimental units for the two samples follow exponential distribution with different scale parameters. The maximum likelihood estimators of the unknown parameters are obtained and their exact distributions are derived. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals are also constructed. For comparison purposes we have used bootstrap confidence intervals also. It is observed that the bootstrap confidence intervals work very well and they are very easy to implement in practice. Some simulation experiments are performed to compare the performances of the proposed method with the existing one, and the performances of the proposed method are quite satisfactory. One data analysis has been performed for illustrative purposes. Finally we propose some open problems. R i + k = n. At the time of the first failure, R 1 units are chosen randomly from the remaining n − 1 units and they are removed from the experiment. Similarly at the time of the second failure, R 2 units are chosen randomly from the remaining n − R 1 − 2 units and they are removed, and so on. Finally at the time of k-th failure remaining R k units are removed, and the experiment stops. Extensive work has been done during the last ten years on various aspects of different progressive censoring schemes. Interested readers may refer to the recent book by Balakrishnan and Cramer [3] for a detailed account on different progressive censoring schemes and the related issues. See also Balakrishnan [2], Pradhan and Kundu [10] and Kundu [7], in this respect.Although extensive work has been done on different aspects of the progressive censoring schemes for one sample, not much work has been done related to two sample problems.Recently, Rasouli and Balakrishnan [12] introduced the joint progressive type-II censoring for two samples. The joint progressive censoring scheme is quite useful to compare the lifetime

The progressive censoring scheme has received a considerable amount of attention in the last 15 years. During the last few years, joint progressive censoring scheme has gained some popularity. Recently, the authors Mondal and Kundu ("A New Two Sample Type-II Progressive Censoring Scheme," Communications in Statistics-Theory and Methods) introduced a balanced two-sample type II progressive censoring scheme and provided the exact inference when the two populations are exponentially distributed. In this article, we consider the case when the two populations follow Weibull distributions with the common shape parameter and different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators cannot be obtained in explicit forms; hence, we propose approximate maximum likelihood estimators, which can be obtained in explicit forms. We construct the asymptotic and bootstrap confidence intervals of the population parameters. Further, we derive an exact joint confidence region of the unknown parameters. We propose an objective function based on the expected volume of this confidence region, and using that, we obtain the optimum progressive censoring scheme. Extensive simulations have been performed to see the performances of the proposed method, and one real data set has been analyzed for illustrative purposes. KEYWORDS approximate maximum likelihood estimator, joint confidence region, joint progressive censoring, maximum likelihood estimator, optimum censoring scheme, progressive censoring, type II censoring MSC CLASSIFICATION 62N01; 62N02; 62F10 Qual Reliab Engng Int. 2020;36:1-17.wileyonlinelibrary.com/journal/qre

The progressive censoring scheme has received a considerable amount of attention in the last 15 years. During the last few years, joint progressive censoring scheme has gained some popularity. Recently, the authors Mondal and Kundu (“A New Two Sample Type‐II Progressive Censoring Scheme,” Communications in Statistics‐Theory and Methods) introduced a balanced two‐sample type II progressive censoring scheme and provided the exact inference when the two populations are exponentially distributed. In this article, we consider the case when the two populations follow Weibull distributions with the common shape parameter and different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators cannot be obtained in explicit forms; hence, we propose approximate maximum likelihood estimators, which can be obtained in explicit forms. We construct the asymptotic and bootstrap confidence intervals of the population parameters. Further, we derive an exact joint confidence region of the unknown parameters. We propose an objective function based on the expected volume of this confidence region, and using that, we obtain the optimum progressive censoring scheme. Extensive simulations have been performed to see the performances of the proposed method, and one real data set has been analyzed for illustrative purposes.

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The analysis of progressively censored data has received considerable attention in the last few years. In this paper we consider the joint progressive censoring scheme for two populations. It is assumed that the lifetime distribution of the items from the two populations follow Weibull distribution with the same shape but different scale parameters. Based on the joint progressive censoring scheme first we consider the maximum likelihood estimators of the unknown parameters whenever they exist. We provide the Bayesian inferences of the unknown parameters under a fairly general priors on the shape and scale parameters. The Bayes estimators and the associated credible intervals cannot be obtained in closed form, and we propose to use the importance sampling technique to compute the same. Further, we consider the problem when it is known apriori that the expected lifetime of one population is smaller than the other. We provide the order restricted classical and Bayesian inferences of the unknown parameters. Monte Carlo simulations are performed to observe the performances of the different estimators and the associated confidence and credible intervals. One real data set has been analyzed for illustrative purpose.

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In statistical quality control, decision‐theoretic approach draws a significant amount of attention due to its economic considerations. In reliability life testing, decision‐theoretic approach has been used quite extensively under different censoring schemes. All these implementations are based on single sample of products coming from a particular source. In this work we study decision‐theoretic approach on two sample of products coming from two different sources under a joint censoring scheme when the life times are exponentially distributed. The major advantage of such implementation is to take decision on the acceptance or rejection of one or both the batches in a single life testing experiment. Decision making is performed based on minimizing the Bayes risk with respect to a given loss function. It is observed that under certain set‐ups, the joint censoring scheme is preferable over the two separate single sample censoring schemes in decision making.

Joint progressive censoring schemes are quite useful to conduct comparative life‐testing experiment of different competing products. Recently, Mondal and Kundu (“A New Two Sample Type‐II Progressive Censoring Scheme,” Commun Stat‐Theory Methods; 2018) introduced a joint progressive censoring scheme on two samples known as the balanced joint progressive censoring (BJPC) scheme. Optimal planning of such progressive censoring scheme is an important issue to the experimenter. This article considers optimal life‐testing plan under the BJPC scheme using the Bayesian precision and D‐optimality criteria, assuming that the lifetimes follow Weibull distribution. In order to obtain the optimal BJPC life‐testing plans, one needs to carry out an exhaustive search within the set of all admissible plans under the BJPC scheme. However, for large sample size, determination of the optimal life‐testing plan is difficult by exhaustive search technique. A metaheuristic algorithm based on the variable neighborhood search method is employed for computation of the optimal life‐testing plan. Optimal plans are provided under different scenarios. The optimal plans depend upon the values of the hyperparameters of the prior distribution. The effect of different prior information on optimal scheme is studied.