Using Latent Variable to Estimate Parameters of Inverse Gaussian Distribution Based on Time-Censored Wiener Degradation Data

Abstract

To effectively assess the lifetime distribution of a highly reliability product, a degradation test is used if the product’s lifetime is highly related to a critical product characteristic degrading over time. The failure times, as well as the degradation values, provide useful information for estimating the lifetime in a short test duration. The Wiener process model has been successfully used for describing degradation paths of many modern products such as LED light lamps. Based on this model, the lifetime of a product would follow the Inverse Gaussian (IG) distribution with two parameters. To estimate the parameters, we propose a method using the latent variables to obtain Latent Variable Estimates (LVE) of the parameters of the IG lifetime distribution. The proposed LVEs have simple closed functional form and thus they are easy to interpret and implement. Moreover, we prove the LVEs are consistent estimates. Via simulation studies, we show that the LVEs have smaller bias and mean square error than existing estimates in the literature.