Degradation modeling based on gamma process models with random effects

Abstract

The random effects in a gamma process are introduced in terms of its scale parameter. However, the scale parameter affects both its mean and variance. Hence, the variation of the degradation rates and the within degradation increments are expected to be large. For some products, the random effects affect just the rate or just the volatility of the process. Thus, two modifications of the parameters' structure of the gamma process are proposed. One implies that the random effects affect just the volatility and the second just the rate. A Bayesian estimation approach is provided and implemented in two case studies.