Two-level burn-in for reliability and economy in repairable series systems having incompatibility

When a system is assembled from components, incompatibility often occurs as a result of the assembly process. The ability to quantify incompatibility is very important for making burn-in decisions because the goal of system burn-in is to minimize the incompatibility factor. In the past, incompatibility has been only partially represented in the system prediction models because it was assumed that assembly had no effect on the components. This paper presents a more accurate model for system prediction by allowing for the possibility that, in some cases, assembly adversely affects the components. After applying a superposition of delayed renewal processes and a nonhomogeneous Poisson process for modeling times between system failures, we derive and analyze the effects of component and system burn-in on the system cost and performance. Examples are included to demonstrate how to determine optimal component and system burn-in times simultaneously based on an equivalent problem formation and nonlinear programming.