Mis-Specification Analysis of gamma and Inverse Gaussian Degradation Models
Sheng-T. Tseng
Institute of Statistics, National Tsing-Hua University, Hsin-Chu, Taiwan

Degradation models are widely used these days to assess the lifetime information of highly reliable products if there exist some quality characteristics (QC) whose degradation over time can be related to the reliability of products. In this study, motivated by a laser data, we investigated the model mis-specification effect on the prediction of product's mean-time-to-failure (MTTF) when the degradation is wrongly fitted. More specifically, we derive an expression for the asymptotic distribution of quasi maximum likelihood estimate (QMLE) of the product's MTTF when the true model comes from gamma process, but is wrongly treated as inverse Gaussian process. The penalty for the model mis-specification can be addressed sequentially. The results demonstrate the effect on the accuracy of the product's MTTF prediction strongly depends on the ratio of critical value to scale parameter of the gamma process, while the effects on the precision of the product's MTTF prediction are serious when the shape and scale parameters of the gamma process are large. We also carry out a simulation study to evaluate the penalty of the model-specification. It demonstrates that the simulation results are quite close to the theoretical one even when the sample size and termination time are not moderately large. For the reverse mis-specification problem, i.e., when the true degradation is an inverse Guassian process, but is wrongly assumed to be a gamma degradation process, we carry out a Monte Carlo simulation study to examine the effect of the corresponding model mis-specification. The obtained results reveal that the effect of this model mis-specification is negligible.

Keywords: Degradation models; model mis-specification analysis; gamma process; inverse-Gaussian process

Biography: Prof. Tseng got a B.S. in Business Mathematics from Soochow University, an M.S. in Applied Mathematics from Tsing-Hua University, and a Ph.D. in Management Science from Tamkang University, Taiwan. Currently, he is a professor in the Institute of Statistics at Tsing-Hua University, Taiwan. His research interests include quality and productivity improvement, reliability lifetime analysis and statistical decision methodology. Currently, he is an Associate Editor of Journal of Statistical Planning and Inference, an elected member of ISI, and member of the IEEE and ASQ.