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ESTIMATION IN A DISCRETE RELIABILITY GROWTH MODEL

UNDER AN INVERSE SAMPLING SCHEME

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

^{1} *Department of Mathematical Sciences, Oakland
University, Rochester, MI 48309, U.S.A.*

^{2} *Institute 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.

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