A One-Stage Two-Machine Replacement Strategy Based on the Bayesian Inference Method

In this research, we consider an application of the Bayesian Inferences in machine replacement problem. The application is concerned with the time to replace two machines producing a specific product; each machine doing a special operation on the product when there are manufacturing defects because of failures. A common practice for this kind of problem is to fit a single distribution to the combined defect data, usually a distribution with an increasing hazard rate. While this may be convenient, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defect as arising from a mixture population: one due to the first machine failures and the other due to the second one. This allows one to estimate the various parameters of interest including the mixture proportion and the distribution of time between productions of defective products for each machine, separately. To do this, first we briefly introduce the data augmentation method for Bayesian inferences in the context of the finite mixture models. Then, we discuss the analysis of time-to-failure data and propose an optimal decision-making procedure for machine replacement strategy. In order to demonstrate the application of the proposed method we provide a numerical example.