ESTIMATION IN A DISCRETE RELIABILITY GROWTH MODEL UNDER AN INVERSE SAMPLING SCHEME

ANANDA SEN^{1} AND ARTHUR FRIES^{2}

1Department of Mathematical Sciences, Oakland University, Rochester, MI 48309, U.S.A.

2Institute for Defense Analyses, Operational Evaluation Division, Alexandria, VA 22311, U.S.A.

(Received March 16, 1995; revised March 4, 1996)

Abstract. 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 Duane (1964, IEEE Trans. Aerospace Electron. Systems, 2, 563–566) 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.

Key words and phrases: Asymptotics, generalized linear model, maximum likelihood, nonhomogeneous geometric, reliability growth.