A Sequential life-testing applied to an accelerated life-testing: using a maximum likelihood approach to estimate the three parameters of an underlying Weibull model

Abstract

The sequential life-testing approach is an attractive alternative to that of predetermined, fixed sample size hypothesis testing because of the fewer observations required for its use, especially when the underlying sampling distribution is the three-parameter Weibull model. It happens that sometimes the amount of time available for testing could be considerably less than the expected lifetime of the component. To overcome such a problem, there is the accelerated life-testing alternative aimed at forcing components to fail by testing them at much higher-than-intended application conditions. One possible way to translate test results obtained under accelerated conditions to normal using conditions could be through the application of the "Maxwell Distribution Law.� In this work we will be life-testing a new industrial product. To estimate the three parameters of the Weibull model we will use a maximum likelihood approach for censored failure data. We will be assuming a linear acceleration condition. To evaluate the accuracy (significance) of the parameter values obtained under normal conditions for the underlying Weibull model we will apply to the expected normal failure times a sequential life testing using a truncation mechanism developed by De Souza [1]. An example will illustrate the application of this procedure. Keywords: Accelerated Models, Sequential Test, Acceleration, Maxwell Distribution Law, Maximum Likelihood.