On estimating the current intensity of failure for the power-law process

✍ Scribed by Ananda Sen; Ravindra Khattree

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 177 KB
• Volume: 74
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(98)00116-5

✦ Synopsis

We consider the problem of estimating the current failure intensity for the power-law (Weibull) process. Closed-form optimum estimators under the criteria of minimum risks as well as Pitmancloseness are derived for the failure truncated case. A unique Pitman-closest estimator which is also invariant of the choice of the loss function within a very wide class of loss functions is obtained. In the frequentist setup, no admissible estimator under these criteria are available for the time truncated scheme due to the lack of any pivotal quantity. We present a Bayesian approach, which circumvents this problem and provides a uniform solution. In the Bayesian framework, we provide an algorithm based on Markov Chain Monte Carlo (MCMC) technique, which facilitates the evaluation of the estimators. The theoretical ÿndings are supplemented by substantial numerical investigation.