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 replacementproblem. the application is concerned with the time to replace two machines producing aspecific product; each machine doing a special operation on the product when there aremanufacturing defects because of failures. a common practice for this kind of problem is to fita single distribution to the combined defect data, usually a distribution with an increasinghazard rate. while this may be convenient, it does not adequately capture the fact that there aretwo different underlying causes of failures. a better approach is to view the defect as arisingfrom a mixture population: one due to the first machine failures and the other due to the secondone. this allows one to estimate the various parameters of interest including the mixtureproportion and the distribution of time between productions of defective products for eachmachine, separately. to do this, first we briefly introduce the data augmentation method forbayesian inferences in the context of the finite mixture models. then, we discuss the analysis oftime-to-failure data and propose an optimal decision-making procedure for machinereplacement strategy. in order to demonstrate the application of the proposed method weprovide a numerical example.