Development of a load sharing policy by managing the residual life based on a stochastic process

In this paper, we analyze the time (viz., the number of cycles) to reach any given crack size in a fatigue life test using a gamma stochastic process. It is assumed that the time increments are nonstationary but independent for each specimen while the shape parameter of the gamma distribution is a function of the crack length. In addition, using a random effect model, the between-specimen variability is explained by modeling the scale parameter of the process with a gamma distribution. This yields explicit formulas for the marginal lifetime distributions, the associated mean and variance, which boosts computational efficiency.