A new two sample type-II progressive censoring scheme

Abstract

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

Inference on Weibull parameters under a balanced two‐sample type II progressive censoring scheme

“…Censoring Scheme E(Vol 0.1 ) ETOT m = 25, k = 20, R = (5, 0 (18) ) 49.927 1.523 m = 25, k = 20, R = (0, 5, 0 (17) ) 50.653 1.522 m = 25, k = 20, R = (0 (2) , 5, 0 (16) ) 51.265 1.515 m = 25, k = 20, R = (0 (3) , 5, 0 (15) ) 51.578 1.512 m = 25, k = 20, R = (0 (4) , 5, 0 (14) ) 52.719 1.508 m = 25, k = 20, R = (0 (8) , 5, 0 (10) ) 57.245 1.492 m = 25, k = 20, R = (0 (14) , 5, 0 (4) ) 67.359 1.424 m = 25, k = 20, R = (0 (16) = 2, 1 = 0.5, 2 = 1…”

“…The expected time of test (ETOT) and E(D( †)) for m = 22, k = 20, = 2, 1 = 0.5, 2 = 1, where s1 ∶ R = (5, 0 (18) ), s2 ∶ R = (0 (4 )5, 0 (14) ), s3 ∶ R = (0 (8) , 5, 0 (10) ), s4 ∶ R = (0 (14) , 5, 0 (4) ), s5 ∶ R = (0 (16) , 5, 0 (2) ), s6 ∶ R = (0 (18) , 5)…”

Prediction for Modified Topp Leone-Chen Distribution Based on Progressive Type-II Censoring Scheme

“…Lifetime distributions under progressive Type-II censored scheme have been attracting great interest due to their wide application in the fields of science, engineering, social sciences and medicine [see, El-Sagheer and Ahsanullah [2], Dey et al [3], Almetwaly and Almongy [4], Karakoca and Pekgör [5], Mondal and Kundu [6], Xiuyun et al [7], Li and Gui [8] and others].…”

Optimal decision‐theoretic sampling plan for two exponential distributions under joint censoring scheme

“…Joint censoring scheme is quite useful to conduct comparative life testing experiment of different products. Mondal and Kundu 9,10 have introduced a joint progressive censoring scheme applied on two or multiple samples called the balanced joint progressive censoring (BJPC) scheme. Here we briefly discuss the BJPC scheme on two samples.…”

“…On the other hand under certain set‐up, this joint censoring scheme, provides better estimation than conventional progressive Type‐II censoring schemes applied on two samples separately. For detail study see Mondal and Kundu 9‐11 . Due to these factors, application of the acceptance sampling plan under the BJPC scheme, can be regarded very beneficial and convenient in statistical quality control.…”