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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.

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