Showing papers by "Palaniappan Vellaisamy published in 2002"
01 Apr 2002
TL;DR: In this paper, a class of improved estimators that dominate the natural estimator is presented and their risks are shown to be O(kn-2) for the squared error loss.
Abstract: Let πi, i = 1, 2, ..., k be k independent exponential populations with different unknown location parameters θi, i = 1, 2, ..., k and common known scale parameter σ. Let Yidenote the smallest observation based on a random sample of size n from the i-th population. Suppose a subset of the given k populations is selected using the subset selection procedure according to which the population πi, is selected iff Yi ≥ Y(1) - d, where Y(1) is the largest of the Yi’s and d is some suitable constant. The estimation of the location parameters associated with the selected populations is considered for the squared error loss. It is observed that the natural estimator dominates the unbiased estimator. It is also shown that the natural estimator itself is inadmissible and a class of improved estimators that dominate the natural estimator is obtained. The improved estimators are consistent and their risks are shown to be O(kn-2). As a special case, we obtain the corresponding results for the estimation of θ(1), the parameter associated with Y(1).
14 citations
TL;DR: In this article, a two-stage component test plan is proposed for series systems with n components, where the lifetime of the i-th component follows exponential distribution with parameter λi. Assuming test costs for the components are different, the authors develop an efficient algorithm to design a two stage test plan that satisfies the usual probability requirements on the system reliability and in addition minimizes the maximum expected cost.
Abstract: A system reliability is often evaluated by individual tests of components that constitute the system. These component test plans have advantages over complete system based tests in terms of time and cost. In this paper, we consider the series system with n components, where the lifetime of the i-th component follows exponential distribution with parameter λi. Assuming test costs for the components are different, we develop an efficient algorithm to design a two-stage component test plan that satisfies the usual probability requirements on the system reliability and in addition minimizes the maximum expected cost. For the case of prior information in the form of upper bounds on λi's, we use the genetic algorithm to solve the associated optimization problems which are otherwise difficult to solve using mathematical programming techniques. The two-stage component test plans are cost effective compared to single-stage plans developed by Rajgopal and Mazumdar. We demonstrate through several numerical examples that our approach has the potential to reduce the overall testing costs significantly. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 95–116, 2002; DOI 10.1002/nav.1051
4 citations