An application of Gumbel's bivariate exponential distribution in estimation of warranty cost of motor cycles

In this article we present an application of Gumbel's bivariate exponential distribution model in the context of estimating warranty costs of motor cycles under a new warranty policy. The problem in question is as follows: Under the present two‐dimensional warranty policy, repair costs (termed as warranty costs) of a motorcycle during the age of first six months or within the usage of 8,000 kilometers are borne by the company. To enhance customer satisfaction, the company wanted to bear the repair costs up to an age of one year or a usage of 12,000 kilometers. The problem is to estimate the expected hike in warranty costs if the warranty policy were revised as mentioned above. Using the past data, the problem is solved by studying the underlying renewal process. Gumbel's bivariate exponential distribution function is found to be useful in approximating the renewal function. Some practical difficulties posed by the past data in the analysis are highlighted and tackled in an interesting way.