The random deterioration rate model with measurement error based on the inverse Gaussian distribution

In this paper, we introduce the random deterioration rate model with measurement error in order to incorporate the variability among different components. The motivation behind the random variable model is to capture the randomness in the individual differences across the population. This model incorporates only sample uncertainty of the degradation, and no temporal variability is included. The measurement error models appear to overcome this problem. The random rate analysis is based on repeated measurements of failure sizes generated by a degradation process over time in a components population. Some characteristics of the random deterioration rate model based on the inverse Gaussian distribution and subject to measurement error, are examined. We carry out simulation studies to (i) assess the performance of the maximum likelihood estimates obtained through the Gaussian quadrature along with Quasi-Newton optimization method; and (ii) examine the effects of model misspecification on the model selection criteria's performance, as well as on the lifetime prediction's accuracy and precision. The potentiality of the proposed model is illustrated through two real data sets.