Using Latent Variables to Estimate Parameters of Inverse Gaussian Distribution Based on Time-Censored Wiener Degradation Data

• Activity Number: 254
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Ming-Yung Lee*+
• Companies: Providence University
• Keywords: inverse Gaussian distribution ; latent variable ; modified maximum likelihood estimator ; Wiener process ; time-censored

Abstract

How to effectively assess the lifetime distribution of a highly reliability product during the product development stage in a timely manner is an important issue for a manufacturer. The traditional accelerated life testing, where samples are tested under higher stress to accelerate failures, may not be the most effective way in this context. On the other hand, if we could measure the degradationof a critical product characteristic over time, these measurements may provide useful information for estimating the lifetime without observing the failure of the product. Tseng, Tang, and Ku (2003) proposed a (time-transformed) Wiener process for the degradation of the brightness of LED bulbs in a scanner (CIS). Under their model, Lee and Tang (2007) proposed a modified EM algorithm to obtain modified MLEs (MMLEs) for both location and scale parameters of the lifetime distribution of LEDs. Due to time-censoring, the MMLE of the scale parameter was asymptotically biased. In this paper, we propose a method based on the latent variable technique to obtain a new estimate (LVE) of the scale parameter, and prove that this LVE is a consistent estimate with a smaller deviation than the MMLE.