Multiple Comparisons for Exponential Median Lifetimes with the Control Based on Doubly Censored Samples

Shu-Fei Wu

doi:10.3390/math9010076

Abstract

Under doubly censoring, the one-stage multiple comparison procedures with the control in terms of exponential median lifetimes are presented. The uniformly minimum variance unbiased estimator for median lifetime is found. The upper bounds, lower bounds and two-sided confidence intervals for the difference between each median lifetimes and the median lifetime of the control population are developed. Statistical tables of critical values are constructed for the practical use of our proposed procedures. Users can use these simultaneous confidence intervals to determine whether the performance of treatment populations is better than or worse than the control population in agriculture and pharmaceutical industries. At last, one practical example is provided to illustrate the proposed procedures.

Highlights

In reliability studies, the lifetimes of some products may not have normal distribution
The exponential distribution we focus on in this study is one type of frequently used lifetime distribution and some examples can be seen in Johnson et al [1]
Wu [4] proposed one-stage multiple comparison procedures with the control for location parameter based on the doubly censored sample

Summary

Introduction

The lifetimes of some products may not have normal distribution. Wu [4] proposed one-stage multiple comparison procedures with the control for location parameter based on the doubly censored sample. Wu [11] proposed the one-stage multiple comparison procedures for exponential mean lifetimes with the control based on the doubly type II censored sample. We can generate independent random variables Ti and Ui to generate random variable Gi. By the Monte-Carlo simulation method, we can find the empirical distribution of Gi. Making use of the pivotal quantities Gi’s, we can start to develop the multiple comparison procedures for each median lifetime with the control (the kth population is regarded as the control population), i.e., δi − δk, i = 1, · · · , k − 1 based on the doubly censored samples in the following theorem: Theorem.

Example

Conclusions