Stochastic Analysis of an Industrial System with Preparation Time Repair under Warranty Policy

The main purpose of this study is to examine the behavior of certain industrial systems under the conditions of product warranty policy. Given this policy, we are interested in considering all the parameters of the system in order to study them and show their impact on the proposed system. In order to increase the efficiency of the system and activate the product warranty policy, the system will undergo a preliminary examination for any system failure occurrence to determine the reasons that led to the failure. After completing the initial inspection, the mechanic will decide whether it is a user-caused failure or a manufacturing defect to determine whether or not the repair of the broken appliance is covered by the manufacturer’s contractual warranty policy. All times in the system are assumed as a negative exponential distribution. The expressions for some measures of system effectiveness such as reliability, mean time to system failure (MTSF), and availability are derived using the supplementary variable technique and Laplace transform. Sensitivity analysis and a relative sensitivity are then carried out in order to recognize how each system parameter affects performance measures. Finally, some numerical examples are designed and performed to show how the change of each system parameter affects system performance.