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Modeling and Statistical Inference of a System Degrading According to a Gamma Process

Abstract : The gamma process is known for its power to capture the temporal variability of deterioration over time. It is one of the most popular stochastic processes in reliability theory. The power law is the most common non-linear shape function for modeling degradation by the gamma process. Also, two classical estimation methods, namely the maximum likelihood method and the method of moments, have been developed in various applications of the gamma process as a degradation model. However, while some studies assumed that the exponent of the power law is known and modeled a non-homogeneous gamma process, others only considered the homogeneous gamma process. Also, the asymptotic properties of these estimators are not often studied. In particular, the maximum likelihood method. In this study, we modeled degradation by both the homogeneous and non-homogeneous gamma processes with a power law shape function. For each model, we considered two methods of parameter estimations, precisely the maximum likelihood method and the method of moments. Furthermore, we provided the theoretical and numerical results of these estimators for different sets of observations and parameters. We have shown that the estimates of the parameters are better with the maximum likelihood method than the method of moments. Further, the maximum likelihood estimator is asymptotically unbiased, consistent, and efficient, which validates the theoretical results. Also, initializing the maximum likelihood estimator with the estimates of the method of moments improves the quality of the estimates, depending on the coefficient as well as the convexity of the shape function}. Lastly, the convexity of the shape function also influences the quality of the estimates. To be more precise, the estimates are better for concave and convex shape functions than for a linear one.
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Submitted on : Wednesday, September 30, 2020 - 1:35:34 AM
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Abdul-Fatawu Majeed. Modeling and Statistical Inference of a System Degrading According to a Gamma Process. Statistics [stat]. Université de Pau et des Pays de l'Adour, 2020. English. ⟨tel-02953267⟩

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