Title: A TSST of the reliability function for exponential failure model using type II censored data with minimum cost of experimentations

Authors: Zuhair A. Al-Hemyari; Alla K. Jiheel

Addresses: University of Nizwa, P.O. Box 33, PC 616, Nizwa, Oman ' Mathematics Department, Theqar University, Iraq

Abstract: This paper considers a class of an efficient 'two-stage shrinkage testimator' (TSST) of 'reliability function' of 'exponential distribution', and the class uses additional information which can be obtained from the past practices, and in the form of past initial estimates (λ0) about the unknown parameter λ. The TSST is dependent upon a convenient shrinking factor, conventional estimators, the 'right censored plan' of sj 'ordered observations' of a variable sample of 'size' Sj and by developing five 'testing regions' for screening the 'closeness' of λ0 to λ by different 'criteria'. The computations of 'bias', 'mean squared error', 'expected sample size' and 'relative efficiency' show that the behaviour of the class of 'TSST' is almost similar to existing testimators and better than classical and similar estimators in several properties, for different constants and variables involved in it. Throughout the paper an application to a 'life time' problem is provided to illustrate applicability of the 'TSST' and expressions that are obtained from it. The behaviour of the developed 'TSST' and the significant comparative results offer some useful and sufficient insights for researchers to continue in the 'TSST' direction, and give adequate reasons for experimenters/practitioners to use 'TSST' in their applications.

Keywords: reliability function; Bessel's function; exponential failure model; two-stage shrinkage; minimum experimentation; type II censored data; efficiency.

DOI: 10.1504/IJRS.2019.101320

International Journal of Reliability and Safety, 2019 Vol.13 No.3, pp.211 - 234

Received: 01 Jun 2018
Accepted: 31 Oct 2018

Published online: 30 Apr 2019 *

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