Lifetime prediction and confidence bounds in accelerated degradation testing for lognormal response distributions with an Arrhenius rate relationship

Determining the lifetime of a product is an important component of quality assurance. Traditional life testing methods are infeasible for products that have been designed to have a very long lifetime because they require a lengthy testing period. An alternative method is accelerated degradation testing, where a response variable determining the usability of the product is measured over time under multiple accelerating stress levels. The resulting data are then used to predict the life distribution of the product under the design stress level. In this dissertation, several methods are proposed and studied for obtaining prediction bounds for the lifetime of a future product and confidence bounds for the mean lifetime of a product using accelerated degradation testing.;The proposed model assumes that products are subjected to a constant accelerating stress. The response variable is measured once for each product, and failure occurs when the response variable crosses a predefined threshold. The model assumes the natural logarithm of the response variable has a normal distribution with a mean that follows an Arrhenius rate relationship and a standard deviation whose natural logarithm follows a quadratic function of the time.;Three methods are presented for obtaining prediction bounds for the lifetime of a future product at the design stress level. These methods use the maximum likelihood, model-based bootstrap, and maximum likelihood predictive density approaches. Two methods are presented for obtaining confidence bounds for the mean lifetime of a product at the design stress level. These techniques represent the delta method and three different variations of the model-based nonparametric bootstrap approach.;The performance of the various methods for obtaining lifetime prediction and confidence bounds are studied using a Monte Carlo simulation study. The results identify several promising approaches.