Title: A subset selection procedure for selecting the exponential population having the longest mean lifetime when the guarantee times are the same
Authors: Misra, Neeraj ×
Kumar, Sanjay
van der Meulen, Edward
Tripathi, YM #
Issue Date: 2005
Publisher: Marcel Dekker
Series Title: Communications in Statistics: Theory and Methods vol:34 issue:7 pages:1555-1569
Abstract: Consider k (>= 2) independent exponential populations Pi(1), Pi(2),...,Pi(k), having the common unknown location parameter mu is an element of (-infinity, infinity) (also called the guarantee time) and unknown scale parameters sigma(1), sigma(2), ... sigma(k) respectively (also called the remaining mean lifetimes after the completion of guarantee times), sigma(i) > 0, i = 1, 2,..., k. Assume that the correct ordering between sigma(1), sigma(2), ... , sigma(k) is not known apriori and let sigma([i]), i = 1, 2 ,..., k, denote the ith smallest of sigma(j)s, so that sigma([1]) <= sigma([2]) ... <= sigma([k]). Then theta(i) = mu + sigma(i) is the mean lifetime of Pi(i), i = 1, 2,..., k. Let theta([1]) <= theta([2]) ... <= theta([k]) denote the ranked values of the theta(j)s, so that theta([i]) = mu + sigma([i]), i = 1, 2 ,.., k, and let Pi((i)) denote the unknown population associated with the ith smallest mean lifetime theta([i]) = mu + sigma([i]), i = 1, 2 ,..., k. Based on independent random samples from the k populations, we propose a selection procedure for the goal of selecting the population having the longest mean lifetime theta([k]) (called the "best" population), under the subset selection formulation. Tables for the implementation of the proposed selection procedure are provided. It is established that the proposed subset selection procedure is monotone for a general k (>= 2). For k = 2, we consider the loss measured by the size of the selected subset and establish that the proposed subset selection procedure is minimax among selection procedures that satisfy a certain probability requirement (called the P*-condition) for the inclusion of the best population in the selected subset.
ISSN: 0361-0926
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Statistics Section
Production Engineering, Machine Design and Automation (PMA) Section
Mathematics - miscellaneous
× corresponding author
# (joint) last author

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