Misspecification analysis of degradation models for tweedie exponential dispersion process with random effects

Degradation models are the basis for reliability analysis of products whose performance deteriorates over time. The choice of degradation model is often based on information criteria such as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). However, the direct influence of model misspecification on the accuracy of the reliability assessment is rarely quantified. This paper focuses on models based on the Tweedie exponential dispersion (TED) process, chosen for the excellent versatility it demonstrates, and wish to study the problem of model misspecification for the TED process with random effects (TEDR). First, we derive the asymptotic distribution of the quasi-maximum likelihood estimator (QMLE) of the mean time to failure (MTTF). when the model is mis-specified. Then, we quantitatively analyze the influence of the misspecification by calculating the relative bias and variability. Finally, we apply the theoretical elements developed to the case of wear data of a civil aircraft flap and the GaAs laser data, for verification purposes. The results observed through the case study confirm that the misspecification of the TED process model will have a significant impact on the assessment of the average product lifetime. This impact will be more pronounced in the case of small samples. It also shows that the TEDR model is robust. In this paper, we therefore provide theoretical elements to enrich reliability studies of products whose performance deteriorates over time by associating and quantifying the effects of a misspecification of the degradation model.