Approximation of partial distribution in renewal function calculation

A renewal process with waiting time being the life span of a product is widely used as a statistical model in the analysis of product failures. The renewal function is often the expected number of warranty services for the product. This paper proposes approximation of partial distribution method in renewal function computations. The feasibility of the approach and the use of applets that can draw graphics and do calculations are explored. It is demonstrated in a case study that a partial gamma approximation achieves remarkable accuracy for k-out-of-n product system with exponential component life.