Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme

Abstract

In this paper a mixture of Type-I censoring and Type-II progressive censoring schemes, called an adaptive Type-II progressive censoring scheme, is introduced for life testing or reliability experiments. For this censoring scheme, the effective sample size m is fixed in advance and the progressive censoring scheme is provided but the number of items progressively removed from the experiment upon failure may change during the experiment.If the experimental time exceeds a prefixed time T but the number of observed failures does not reach m, we terminate the experiment as soon as possible by adjusting the number of items progressively removed from the experiment upon failure. Computational formulae for the expected total test time are provided. Point and interval estimation of the failure rate for exponentially distributed failure times are discussed for this censoring scheme. The various methods are compared using Monte Carlo simulation.

Bayesian Prediction based on an Adaptive Type-II Progressive Censored Data from the Generalized Exponential Distribution

“…If the failure times of the items are from a continuous population with cumulative distribution function (CDF) F (x) and probability density function (PDF) f (x). Then, the joint density function of the adaptive Type-II progressively censored sample X = (X 1,m,n , ..., X m,m,n ) with censoring scheme R = (R 1 , ..., R m ) is then given by (see Ng et al, 2009) …”

“…For extensive reviews of the literature on progressive censoring, readers may refer to Balakrishnan and Aggarwala (2000), Balakrishnan (2007), Ng and Chan (2007), and Mohie El-Din and Shafay (2013). Recently, Ng et al (2009) have suggested an adaptive Type-II progressive censoring which is a mixture of Type-I and Type-II progressive censoring schemes. In this censoring scheme, we allow R 1 − R 2 − · · · − R m to depend on the failure times so that the effective sample size is always m which is fixed in advance.…”

Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

“…Balakrishnan and Aggarwala (2000) provided a comprehensive reference on the subject of progressive censoring and its applications. For further reading, the readers are referred to Kundu (2008), Kundu andPradhan (2009), Ng, Kundu, andChan (2009) and the references cited therein. A schematic representation of progressively Type-II right censored sample is depicted in Figure 1.1 (Cramer and Iliopoulos 2010).…”

Analysis of Generalized Exponential Distribution Under Adaptive Type-II Progressive Hybrid Censored Competing Risks Data

“…The drawback of the T-II PHCS is that the effective number of failures is random and it can be a very small number (even equal to zero), so that usual statistical inference procedures will not be applicable or they will have low efficiency. For this reason, Ng et al [14] suggested an adaptive type-II progressive hybrid censoring scheme in which the effective number of failures m is fixed in advance and the progressive censoring scheme 12 , ,..., m R R R is provided, but the values of some of the i R may be change accordingly during the experiment. Suppose the experimenter provides a time T, which is an ideal total test, but the experimental time is allowed to run over time T. If the m-th progressively censored observed failures occurs before time T (i.e.…”

“…We should mention here that many authors studied the statistical properties of some life time models under AT-II PHCS in the presence of one and two causes of failures. Ng et al [14] developed inferential methods for the case when the lifetime distribution is exponential. They observed that the MLE always exists in this case.…”