an:01078766
Zbl 0896.62105
Sen, Ananda; Fries, Arthur
Estimation in a discrete reliability growth model under an inverse sampling scheme
EN
Ann. Inst. Stat. Math. 49, No. 2, 211-229 (1997).
00043679
1997
j
62N05 62F12 62J12
asymptotics; nonhomogeneous geometric; discrete reliability growth; inverse sampling; maximum likelihood estimators
Summary: This paper develops a discrete reliability growth (RG) model for an inverse sampling scheme, e.g., for destructive tests of expensive single-shot operations systems where design changes are made only and immediately after the occurrence of failures. For \(q_i\), the probability of failure at the \(i\)-th stage, a specific parametric form is chosen which conforms to the concept of the \textit{J. T. Duane} [IEEE Trans. Aerospace Electron. Syst. 2, 563-566 (1964)] learning curve in the continuous-time RG setting. A generalized linear model approach is pursued which efficiently handles a certain non-standard situation arising in the study of large-sample properties of the maximum likelihood estimators (MLEs) of the parameters. Alternative closed-form estimators of the model parameters are proposed and compared with the MLEs through asymptotic efficiency as well as small and moderate sample size simulation studies.