Two Dimensional Warranted Products Protected by Lemon Laws Considering Mutual Failure Interaction

We study a warranty cost analysis for a product sold with a two-dimensional warranty. During the warranty, the product is also protected by lemon laws for a period which is less than or equal to the warranty period. The product is considered as a multi-component system consisting of two types of components – i.e., critical and non-critical components. Failure of either a critical component or a non-critical component can cause the product to fail. The lemon laws protect the consumer from recurrent failures. In this, we consider that the product turns to be a lemon only due to the number of failures is equal to or greater than the threshold, (e.g., k). This happens either the number of critical or non-critical component failures reaches k in the lemon law period. The failed product under warranty is always fixed by a minimal repair. We consider that there is a mutual failure interaction (or two-way interaction) between critical and non-critical components. Hence, the number of failures of each component type is the sum of natural and induced failures. We obtain the expected warranty cost and the optimal lemon law period minimizing the expected warranty cost rate. Numerical examples are provided to illustrate the expected warranty cost and the optimal lemon law period.