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Record-based inference and associated cost analysis for the Weibull distribution

Doostparast M.

Control and Cybernetics

2015

Vol. 44, no. 1

163--177

In statistical process control, record schemes are used to reduce the total time on test for the inspection inquiry. In these schemes, units are examined sequentially and successive minimum values are recorded. On the basis of record data, Samaniego and Whitaker (1986) obtained the maximum likelihood (ML) estimate of the mean for an exponential distribution. Since the two parameter Weibull model, as an extension of the exponential distribution, has a wide range of application, Hoinkes and Padgett (1994) derived the record-based ML estimators for the parameters of interest in this model. This paper shows that the ML estimates of the Weibull parameters do not always exist for the basis of records. Thus, a new scheme is proposed, in which the ML estimates of the parameters always exist. An analytic cost-based comparison between the usual and the New scheme is also carried out. Finally, some concluding remarks and open problems are formulated.