Abstract
When the additional sample for the second stage may not be available, one-stage multiple comparisons for exponential median lifetimes with the control under heteroscedasticity including one-sided and two-sided confidence intervals are proposed in this paper since the median is a more robust measure of central tendency compared to the mean. These intervals can be used to identify treatment populations that are better than the control or worse than the control in terms of median lifetimes in agriculture, stock market, pharmaceutical industries. Tables of critical values are obtained for practical use. An example of comparing the survival days for four categories of lung cancer in a standard chemotherapeutic agent is given to demonstrate the proposed procedures.
Highlights
In the lifetime test problems, the lifetime of some products follows an exponential distribution
As the lifetime of products possesses a two-parameter exponential distribution, this research focuses on the development of multiple comparison procedures with the control population in terms of median lifetime
When the lifetime of products follows a two-parameter exponential distribution, this theorem can be used to find the upper confidence bounds and the lower confidence bounds for the parameters of δ0.5,i − δ0.5,k, i = 1, . . . , k − 1, where δ0.5,k represents the median lifetime of the control population
Summary
In the lifetime test problems, the lifetime of some products follows an exponential distribution (see Lawless [1]). We propose one-stage multiple comparison procedures for exponential median lifetimes with the control as follows: Take a random sample of size m (≥ 2) from πi denoted by Xi1 , · · · , Xim for the one-stage procedures. Based on these pivotal quantities, we propose the one-stage multiple comparison procedures with the control in terms of median lifetimes in Theorem 1. K − 1, where δ0.5,k represents the median lifetime of the control population This theorem can be used to find the two-sided simultaneous confidence intervals for parameters δ0.5,i − δ0.5,k , i = 1, . L1 increases when P∗ increases for fixed k and m or when k increases for fixed P∗ and m
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