Discounted costs for repairable units under hybrid warranty

In the present investigation, we propose a hybrid warranty model for the renewing pro-rata warranty, in which the failure rate of units, cost of preventive maintenance and cost of replacement are assumed to be constant. The expected total discounted maintenance cost has been derived in explicit form for different life time distributions, viz. exponential, Rayleigh and Weibull distributions. We determine the optimal number and optimal period for preventive maintenance after the expiry of the warranty. Numerical illustrations are provided to check the validity of the analytical results.