Optimal periodic replacement policy for a warranted product subject to multi modes failure process

A complex product subjects to multiple failure modes such as minor and catastrophic failure with some probability.This paper investigates the effects of minor failure and catastrophic failure on the periodic replacement policy for a complex product supported by a warranty period.Cost models are developed and the expected optimal replacement policies are developed analytically such that long run expected life-cycle cost rate is minimized.Structural properties of the optimal replacement policies are derived for a product which fails with multiple failure modes and the failure rate is an increasing function of time.Finally,a numerical experiment is performed to show the important features of our study.