Assessing the Capability of a Manufacturing Process Using Nonparametric Bayesian Density Estimation

The capability of a manufacturing process refers to the ability of the process to produce items that are within set specifications. The determination of the capability of a stable manufacturing process with a multivariate quality characteristic using standard methods usually requires the assumption that the quality characteristic of interest follows a multivariate normal distribution, an assumption that is difficult to assess in practice. Departures from this assumption can result in erroneous conclusions, which can be costly to the manufacturer. In this paper, we propose assessing the capability of a process using a nonparametric Bayesian framework. This framework relies on using mixtures of Dirichlet processes to elicit a prior on the multivariate distribution of the quality characteristic. The posterior distribution of the distribution of the quality characteristic can then be used to induce a posterior distribution on the process fallout rate, the mean distance between the quality characteristic and a specified target value, or on an associated process capability index. The methodology is demonstrated through three examples using real-world data. Particular emphasis in these examples is given toward specifying the parameter values required to specify the prior distribution and on interpretation of the results.