Misspecification Analysis of a Gamma- with an Inverse Gaussian-Based Perturbed Degradation Model by Using a New Expectation Maximization Particle Filter Algorithm

Gamma and inverse Gaussian degradation processes are often considered equivalent, though this is not true. For this reason, the misspecification of these models is a problem of concern. The point of this paper is evaluating whether and how the presence of measurement error impacts on this model misspecification issue. Mainly due to numerical problems, simulation studies that are carried out to evaluate the performance of maximum likelihood estimators of parameters, and/or functions of parameters, of the gamma and inverse Gaussian processes in the presence of measurement error are typically performed by using a relatively small number of synthetic datasets. In fact, computing the likelihood functions of these perturbed models, which are not available in closed form, requires intensive numerical methods that, at the same time, increase the computational burden and exacerbate convergence issues of numerical algorithms used to maximize the likelihood. In this paper, we propose a new expectation maximization particle filter algorithm, which allows to drastically simplify the estimation task, and present the results of a vast Monte Carlo study carried out by taking advantage of its use. The risk of incurring in a misspecification is evaluated as the percentage of times the Akaike information criterion leads to select the wrong model. The severity of a misspecification is evaluated in terms of its impact on remaining useful life estimates.