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Estimation in a discrete reliability growth model under an inverse sampling scheme. (English) Zbl 0896.62105
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 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.

MSC:
62N05 Reliability and life testing
62F12 Asymptotic properties of parametric estimators
62J12 Generalized linear models (logistic models)
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