Multiple Comparison Procedures for Exponential Mean Lifetimes Compared with Several Controls

Shu-Fei Wu

doi:10.3390/math10040609

Abstract

Under heteroscedasticity, we propose one-stage multiple comparison procedures for several treatment groups compared with several control groups in terms of exponential mean lifetimes. The simultaneous confidence intervals including one-sided and two-sided confidence intervals for the difference between the mean lifetime from the i-th treatment group and the mean lifetime from the j-th control group are developed in this research. The required critical values are obtained and tabulated for the practical use of users. The experimenters can use these simultaneous confidence intervals to determine whether the treatment mean lifetimes are better than several controls or worse than several controls under a specified confidence level. Finally, one example of comparing the mean duration of remission using four drugs for treating leukemia is used for the aims of illustrations.

Highlights

Our research is related to the field of ranking and selection
Exponential distributions are widely used to model the lifetimes of products
Let Xi1, · · ·, Xim be the random sample of size m from the i-th treatment group πi, I = 1, . . . , k, where πi follows a two-parameter exponential distribution denoted by E(θi, σi ), I = 1, . . . , k

Summary

Introduction

Our research is related to the field of ranking and selection. For normal distributions, Bechhofer [1] and Gupta [2] are the pioneers in this field. When scale parameters for exponential distributions are unknown and possibly unequal, Lam and Ng [3] proposed the design-oriented two-stage multiple comparisons with the control. Based on the one-stage sample from k populations, Wu et al [4] developed the multiple comparison procedures for exponential location parameters with the control when scale parameters are unknown and unequal. Instead of comparing with the control, Wu [5] proposed one-stage multiple comparisons with the average for exponential location parameters. Instead of comparing the location parameters for exponential distributions, the one-stage multiple comparisons with the average in terms of mean lifetimes are proposed by Wu [8].

Comparing with Several Controls for Exponential Mean Lifetimes

Example

Conclusions