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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.

Estimation based on sequential order statistics with random removals

Esmailian M., Doostparast M.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 1

81--95

Suppose that n individuals are scrutinized in an experiment. Each failure is accompanied by a fixed number of removals. The experiment terminates after r (≤ n) failures. An explicit expression for the likelihood function of the available progressive sequential order statistics (PSOS) data is proposed. Under the conditional proportional hazard rate (CPHR) model, the maximum likelihood (ML) estimates of parameters are derived. Under the CPHR model and the assumption that the baseline distribution belongs to the Weibull family of distributions, the existence and uniqueness of the ML estimates are investigated. Moreover, two general classes of lifetime distributions, as an extension of theWeibull distribution, are studied in more detail. An algorithm for generating PSOS data under the CPHR model is proposed. Finally, some concluding remarks are given.