Exact Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censored Competing Risks Data

Youngseuk Cho,Kyeongjun Lee

doi:10.3390/sym12122005

Abstract

It is known that the lifetimes of items may not be recorded exactly. In addition, it is known that more than one risk factor (RisF) may be present at the same time. In this paper, we discuss exact likelihood inference for competing risk model (CoRiM) with generalized adaptive progressive hybrid censored exponential data. We derive the conditional moment generating function (ConMGF) of the maximum likelihood estimators of scale parameters of exponential distribution (ExpD) and the resulting lower confidence bound under generalized adaptive progressive hybrid censoring scheme (GeAdPHCS). From the example data, it can be seen that the PDF of MLE is almost symmetrical.

Highlights

Let us consider a lifetime test where items are kept under observation until failure
It is known that the lifetimes of items may not be recorded exactly
It is known that more than one risk factor (RisF) may be present at the same time

Summary

Introduction

Let us consider a lifetime test where items are kept under observation until failure. For Weibull distribution, Author1 [4] developed a CoRiM under progressive Type II censoring scheme (Pr2CS) with binomial removals. For this reason, Author1 [12] suggested a GeAdPHCS in which the test is assured to end at a pre-assigned time. If the mth failure is observed before the pre-assigned time T1 (Xm:m:n < T1 ), terminate the test at Xm:m:n (Case I). If T1 < Xm:m:n < T2 , instead of terminating the test by removing all survival units at pre-assigned time T1 , continue to observe failures, without any removals, up to the mth failure (Case II). If T2 < Xm:m:n , and terminate the test at pre-assigned time T2 (Case III).

Model and Conditional MLEs

Exact Conditional Inference for MLE

Simulation Results

Data Analysis

Conclusions