The Performance of Hazard Plotting in Estimating the Parameters of a Weibull Life Distribution in the Presence of an Independent Competing Weibull Failure Mode

• Activity Number: 457
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): John I. McCool*+ and Edward Romanowski
• Companies: Pennsylvania State Great Valley and QVC, Inc.
• Keywords: Competing Risk ; Hazard Plotting ; Multiple Censoring ; Weibull Distribution

Abstract

A simulation study was performed to determine the distribution of the estimates of the parameters and selected percentiles of a Weibull primary failure mode when the data is censored by failure due to a competing Weibull failure mode. For each simulated sample, Nelson's hazard plotting technique was used to estimate the cumulative hazard function for the designated primary mode. Linear regression was then used to estimate the slope and intercept of the linear relation between the log of the primary mode failure times and the log of the estimated primary mode cumulative hazard function. The Weibull parameters were computed in terms of the estimated slope and intercept. These parameter estimates were used to compute the 1, 5, 10 and 50-th percentiles of the primary failure distribution. The simulation was run for 10,000 iterations with simulated sample sizes ranging from 10 to 100 and with the scale parameters of the primary and competing failure distributions chosen so the expected proportion of primary mode failures ranged from 0.2 to 1.0. The amount of bias in the estimated parameters was determined as a function of the sample size and proportion of primary mode failures.