SEQUENTIAL LIFE TESTING WITH UNDERLYING WEIBULL AND INVERSE WEIBULL SAMPLING DISTRIBUTIONS

摘要

The sequential life testing approach is a hypothesis testing situation in which a decision is made about accepting, rejecting or continuing sampling as observations become available. The Inverse Weibull distribution was derived by Pascoal Erto [1]. It has been used in Bayesian reliability estimation to represent the information available about the shape parameter of an underlying Weibull sampling distribution (Erto [1]; De Souza & Lamberson [2]). It has a location, a scale and a shape parameter. It has been also used before in a sequential life testing situation by De Souza [3]. The Weibull distribution is widely used as a failure model, particularly for metallurgical and mechanical components (De Souza 1997 [4], 1999 [5], 2000 [6] and 2001 [7]). It also has a location, a scale and a shape parameter. It happens that when its shape parameter value is greater than 7, the Weibull curve becomes highly pointed, resulting in some computational difficulty (accuracy) in calculating the component's characteristic of interest values. In situations where the shape parameter values of the Weibull distribution are above 7, the Inverse Weibull distribution seems to have a better answer to the accuracy problem presented by the Weibull model. In this work we will analyze this possibility and we will apply sequential life testing approaches derived before by De Souza [7] and [6], in which the underlying sampling distributions were, respectively, the Inverse Weibull and Weibull models. An example will illustrate the application of a sequential life testing approach when the underlying sampling distributions are the Inverse Weibull and Weibull models.