Testing for Dependency of Failure Times in Life Testing

• Activity Number: 313
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical & Engineering Sciences*
• Author(s): John McCool*+
• Affiliation(s): Pennsylvania State University, Great Valley
• Keywords: Life Testing ; Weibull Distribution ; Failure Dependence ; Monte Carlo

Abstract

In life testing, a possible problem arises with some test configurations, that the failure of one test item shortens the life of others and, thus, leads to an underestimate of the reliability. The purpose of this paper is to describe a statistical test of the hypothesis that the failure times within the test machines are independent. It is assumed that the time to failure follows a two-parameter Weibull distribution. At the completion of testing, two estimates of the Weibull shape parameter are computed. One estimate is based on the first failure times within each test unit. The second estimate is based on the ratios of the second failure time to the first failure time within each test unit. If the second failure within each unit fails prematurely, the second shape parameter estimate will tend to be larger than the first. The proposed test for dependence is based on the null distribution of the ratio of these shape parameter estimates and was determined by Monte Carlo sampling for a range of sample sizes for the case that the testers have capacity for two test items.