Parameters estimation for weibull distributed lifetimes under progressive censoring with random removeals

Abstract

This paper considers the estimation problem when lifetimes are Weibull distributed and are collected under a Type-I1 progressive censoring with random removals, where the number of units removed at each failure time follows a uniform discrete distribution. The expected time of this censoring plan is discussed and compared numerically to that under a Type I1 censoring without removal. Maximum likelihood estimator of the parameters and their asymptotic variances are derived.

Estimations of the parameters of generalised exponential distribution under progressive interval type-I censoring scheme with random removals

“…It seems more logical and natural to consider these p i as random variables for the risk of dropping at the i th stage. Perhaps, keeping a similar thought in mind, Yuen and Tse (1996) and Tse, Yang, and Yuen (2000) discussed progressive censoring scheme with binomial removal. Ashour and Afify (2007) have used PITI censoring scheme with binomial removals assuming that the exact value of the lifetimes of the units are observable.…”

On Estimating Flexible Weibull Parameters with Type I Progressive Interval Censoring with Random Removal Using Data of Cancerous Tumors in Blood

“…In practice, it is impossible to pre-determine the removal pattern. Thus, Yuen & Tse [4] and Yang et al [5] considered the estimation problem when lifetimes collected under a Type II progressive censoring with random removals and Kendell & Anderson [6] point out that the expected duration under grouped data. Progressive type-I interval censored sampling is an important practical problem that has received considerable attention in the past several years.…”

Statistical inference for generalized Pareto distribution based on progressive Type-II censored data with random removals

“…There have been several references about the statistical inference on lifetime distributions under progressive censoring with random removals; for example, we refer to Yuen and Tse [2], Tse and Yuen [5], Tse et al [10], Shuo and Tao [12], Wu [11], Wu and Chang [4] and Wu et al [9].…”

“…for example, in some reliability experiments, an experimenter may decide that it is inappropriate or too dangerous to carry on the testing on some of the tested units even though these units have not failed. In such cases, the pattern of removal at each failure is random (Zeinab [3], Yen and Tse [2]). This leads to progressive censoring with random removals (illustrated by " Table 1").…”