Reliability of degrading load sharing k-out-of-n:F system

Reliability of a degrading load sharing k out-of-n:F system is studied in which the total load on the system is shared among all the functioning components. The performance of the system is evaluated based on degradation of its components, and the system lifetime is determined accordingly. It is assumed that degradation of the functioning components follows a Gamma process, such that the shape parameter is a time dependent function and the scale parameter is constant. The effect of load sharing is modeled by considering a power law function as the shape parameter of the Gamma process. A recursive formula is obtained to calculate the reliability function, and its sensitivity is discussed with respect to the model parameters. The estimation problem of the load sharing parameter is also investigated based on degradation data measured at some pre-specified inspection times. Since the obtained formulas are complex, the reliability function is numerically computed. Further, the performance of the proposed estimator is studied using a simulation algorithm.