Lower Prediction and Tolerance Bounds in Accelerated Life Testing for the Rayleigh Distribution

• Activity Number: 243
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Ananda Jayawardhana*+ and Yang Song
• Companies: Pittsburg State University and Department of Statistics, University of Illinois Urbana-Champagne
• Keywords: Tolerance Intervals ; Rayleigh Distribution ; Maximum Likelihood Predictive Density

Abstract

The problem of obtaining lower prediction and tolerance bounds for a future observation from a Rayleigh population at field use (design) level of stress, using Type II censored accelerated life test data from higher than design stress levels is considered. Maximum Likelihood Predictive Density method to derive a predictive density for a future observation as described by Jayawardhana and Samaranayake (2003) is used for this study. The mean life of the Rayleigh distribution is assumed to have an inverse power relationship with the level of stress. The use of lower percentile points of the predictive density as a lower prediction and tolerance bounds is investigated using Monte Carlo simulation. The results show that reasonable prediction and tolerance bounds can be provided using the predictive density.