Asymptotic properties of estimators in a binomial reliability growth model and its continuous-time analog

Bhattacharyya, Gouri K. ; Ghosh, Jayanta K. (1992) Asymptotic properties of estimators in a binomial reliability growth model and its continuous-time analog Journal of Statistical Planning and Inference, 29 (1-2). pp. 43-53. ISSN 0378-3758

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/037837...

Related URL: http://dx.doi.org/10.1016/0378-3758(92)90120-H

Abstract

This article deals with a nonhomogeneous binomial (NHB) model where the probability of failure at the ith trial has the functional form μ[iβ - (i) - 1)β], 0 < μ < 1, 0 < β < 1. The model arises in the context of reliability growth of a one-shot system during the successive stages of its development, and is a discrete analog of a continuous-time growth model based on a nonhomogeneous Poisson process (NHPP) with Weibull intensity. Asymptotic properties of the 'continuous analog estimators' (CAE's) are compared with those of the maximum likelihood estimators (MLE's) in the continuous-time growth model. Unlike the NHPP model, the MLE's in the NHB model are not available in closed forms, and derivation of their asymptotic properties confronts the fundamental difficulty that the appropriately scaled information matrix is asymptotically singular. To get around this difficulty, we first link the CAE's to the maximization of a certain pseudo-likelihood, examine the corresponding Taylor expansion, and relate that to the expansion of the correct NHB likelihood. The closeness of the two expansions is then used to establish consistency and asymptotic normality of the MLE's and asymptotic equivalence with the CAE's.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Primary 62F12; Secondary 62N05; Reliability Growth; Nonhomogeneous Binomial; Poisson Process; Maximum Likelihood; Asymptotics
ID Code:22541
Deposited On:24 Nov 2010 08:22
Last Modified:02 Jun 2011 07:12

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