Lifetime Predictive Density Estimation in Accelerated Degradation Testing for Lognormal Response Distributions with an Arrhenius Rate Relationship

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Steven Michael Alferink*+ and V. A. Samaranayake
• Companies: Missouri University of Science and Technology and Missouri university of Science and Technology
• Keywords: Accelerated Degradation Model ; Maximum Likelihood Predictive Density ; Maximum Likelihood Estimation ; Lognormal Distribution ; Prediction Bounds ; Bootstrap Intervals

Abstract

A relatively simple method is proposed for obtaining a predictive density for the lifetime of a future product at the design stress level using an accelerated degradation model. The degradation model assumes the natural logarithm of the response variable has a normal distribution with a mean that follows the Arrhenius rate relationship and a standard deviation whose natural logarithm follows a linear function of the accelerating stress. The degradation model assumes each product is subjected to a constant accelerating stress, where the accelerating stress has two or more levels. The response variable for each product is measured only once, and failure is assumed to occur when the response variable crosses a predefined threshold. This method is based on the maximum likelihood predictive density approach first proposed by Lejeune and Faulkenberry. The use of the percentiles of the predictive density as prediction bounds for the lifetime of a future product at the design stress level is examined using Monte Carlo simulation. Comparisons are made with the prediction bounds obtained from the traditional maximum likelihood estimator based approach and the bootstrap technique.