Accelerated life testing and the Burr XII distribution.

This thesis looks at extending previous work in the field of accelerated life testing experiments. Hitherto, much investigation in this field has centred on a few standard statistical lifetime distributions, the Weibull being particularly popular. We consider a more flexible distribution, the Burr XII, and compare theoretical and simulated results; we also examine a number of examples. This comparison is interesting particularly since there is a limiting relationship between the two distributions, a property that is exploited in this thesis. Having laid down the necessary groundwork, we then proceed to fit the Weibull and Burr XH models to completely failed, published data sets and compare results. In order to assess our ability to make small sample theoretical inspections, we then establish the expected Fisher information matrices for the accelerated and non-accelerated Burr XH models, validating our results through simulations. The limiting link between the two distributions is then investigated, where we see that we can determine whether the Burr XH distribution will provide a better fit to a given data set than the Weibull, by fitting the Weibull distribution and then calculating a simple discriminating function. Type I censoring for the accelerated models is then considered. As for complete data, we formulate the expected Fisher information matrices. We then examine theoretical agreement between these results and those obtained for completely failed data. We also examine the agreement between Type I simulated and theoretical results. Finally, we investigate the practical applications of our work, and consider in particular extrapolations to lower operating stresses and the expected lifetimes of items tested at those stresses. Our investigations, although based on limited parameter values, illustrate useful conclusions on the conduct of such experiments and, consequently, are of potential value to a practitioner who, prior to carrying out an experiment, would like to know what combination of stresses and sample sizes would return the most information about the running time of items at the normal operating stress. After summarising our results and conclusions, some ideas for future research are detailed