Title: Estimation of the threshold parameter of a wear-out failure period in the case of a three-parameter Weibull distribution

Authors: Takatoshi Sugiyama; Toru Ogura; Takakazu Sugiyama

Addresses: Department of applied Mathematics, Science Graduate School of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan ' Clinical Research Support Center, Mie University Hospital, 2-174, Edobashi, Tsu-Shi, Mie, 514-8507, Japan ' Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

Abstract: We aimed to estimate the threshold parameter for the wear-out failure period of a three-parameter Weibull distribution. In this paper, we propose the minimum-variance linear unbiased estimator based on order statistics, which is denoted by 'T_BEST'. In Section 2, we verify the validity of T_BEST by comparing it with the existing threshold parameter estimator, based on simulation studies of bias and mean squared error (MSE). Our results show that T_BEST requires all order statistics, except for the case of an exponential distribution, in which T_BEST is reduced to an unbiased estimator based on the smallest observation only. In Section 3, by simulation studies, we compare T_BEST and other estimators known to have good performances. In the simulation results, bias and MSE of T_BEST were the smallest in most cases. We also show a numerical example to measure fatigue lives in hours of ten bearings from McCool (1974).

Keywords: estimation; threshold parameter; minimum-variance linear unbiased estimator; MVLUE; Weibull distribution.

DOI: 10.1504/IJKESDP.2019.102818

International Journal of Knowledge Engineering and Soft Data Paradigms, 2019 Vol.6 No.2, pp.110 - 119

Received: 23 Dec 2017
Accepted: 04 Jul 2018
Published online: 08 Oct 2019 *

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