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.

The key to excellent casthouse operation are low cost, high productivity, dry hearth and high casting rate while minimising the consumable material. The stable blast furnace operation requires proper control of drainage rate of liquid hot metal and slag from hearth. The productivity of blast furnace can be effectively increased if drainage rate is considerably increased. If the drainage rate is controlled, the periodic tapping of hot metal and slag from hearth can be made effective. This paper highlight the improvement made in casting practice by controlling the hearth liquid level in blast furnace. The improvements have made significant change in casthouse management. It is well demonstrated that various casthouse operations have migrated from one regime of operation to another regime and various consumable items are significantly reduced. The importance of increasing the drainage rate in improving the productivity of blast furnace is explained in details.

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