Progressive censoring methodology: an appraisal

Abstract

Progressive censoring, Order statistics, Life-testing experiment, Bounds, Generalized order statistics, Characterizations, Markov property, Likelihood inference, Reliability sampling plans, Goodness-of-fit tests, Prediction, Competing risks, Step-stress test, Hybrid censoring, Permanents, Outliers, Robustness, 62G30, 62E99, 62F10, 62N01, 62N05,

On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints

“…More specifically, for any u ∈ (0, 1), we have lim θ↑∞ F r ((n − 1 + u)T ; θ|D 1) = u when r > 1 and lim θ↑∞ F r (nuT ; θ|D 1) = u when r = 1 which means that the problem of nonexistence of a solution to the equation F r (y; θ|D 1) = u for particular values y is also present here. The same situation arises under type-I hybrid progressive censoring introduced by Childs et al (2008) (see also Cramer and Balakrishnan, 2013), generalized type-II hybrid censoring (Chandrasekar et al, 2004), progressive type-I censoring (Balakrishnan, 2007;Balakrishnan et al, 2011) and some other life-testing scenarios as well.…”

Estimation of Stress-Strength Reliability for the Generalized Pareto Distribution Based on Progressively Censored Samples

“…The parameter α is a shape parameter and λ is a scale parameter. We shall write X ∼ GP(α, λ) if X has the pdf and cdf specified by (2) and (3), respectively. Let X ∼ GP (α, λ 1 ) and Y ∼ GP (β, λ 2 ) be independent random variables.…”

“…It can be described as follows: Let N items be put in a life time study and n(< N ) items be completely observed; At the time of the first failure, r 1 surviving units are removed from the N − 1 remaining items; At the time of the next failure, r 2 items are randomly withdrawn from the N − r 1 − 2 remaining items; When the nth failure occurs all the remaining N − n − r 1 − · · · − r n−1 items are removed. See [2] for more details.…”

Inference for the Rayleigh Distribution Based on Progressive Type-II Fuzzy Censored Data

“…Pradhan and Kundu (2009) considered the statistical inference of the unknown parameters of the generalized exponential distribution in presence of progressive censoring. A recent account on progressive censoring schemes can be obtained in the monograph by Balakrishnan and Aggarwala (2000) or in the excellent review article by Balakrishnan (2007).…”