The inverse Gaussian process with a skew-normal distribution as a degradation model

Abstract

This article incorporates a skew-normal distribution into an inverse Gaussian (IG) process to represent the unit-to-unit variability of the degradation rate, while a symmetrical distribution or approximately symmetrical distribution is commonly adopted in the IG process. Then we derive the corresponding lifetime distribution and mean-time-to-failure including two special cases under the condition that the skew-normal distribution reduces to an half-normal distribution or a normal distribution. Moreover, an improved EM-type algorithm is presented to overcome the difficulties in estimating parameters. Finally, two simulation studies and a case application are used to illustrate the advantages of the proposed model.