Bayesian Analysis in Industrial Applications using Markov Chain Monte Carlo Simulations

Abstract

Hierarchical modeling is often used a tool which, as an interdisciplinary effort, combines the estimation technique and data mining techniques to model reliability systems. The reliability of the model is measured in terms of how much sufficiently accurate model is over the entire input range and the level of confidence in predictions. WinBUGS is Windows based software which provides researchers, especially in production process engineering, with a very useful data analytical tool. WinBUGS has ability to fit complex statistical models which express interdependence among several response variables based on Bayesian methods of inference and Markov Chain Monte Carlo (MCMC) simulation. In this paper, we present a short description of WinBUGS and discuss implementation of WinBUGS programs by analyzing real data sets from two industrial applications. First application undertakes the analysis of the behavior of the overhead-costs with the number of machine-hours operated and the number of production-runs in a production process. In the second illustration, we analyze the relative importance of between fluxes variability versus sampling variation in a weld experiment which considers welding fluxes with differing chemical compositions.