Misspecification Analysis of Gamma with Inverse Gaussian Degradation Processes

Abstract

Degradation models are widely used to assess the lifetime information of highly reliable products. In this study, motivated by a stress relaxation data, we investigate the misspecification effect on the prediction of product’s mean time to failure (MTTF) when the degradation model is wrongly fitted. Assuming the true model comes from gamma degradation process, but wrongly treated as inverse Gaussian degradation process, we first derive an analytic expression for the asymptotic distribution of quasi maximum likelihood estimate (QMLE) of the product’s MTTF. Next, the penalty for the model misspecification is addressed comprehensively. The result demonstrates that the effect on the accuracy of the product’s MTTF prediction strongly depends on the ratio of critical value to the scale parameter of the gamma degradation process.