A Smooth Nonparametric Approach to Multivariate Process Capability

The determination of the capability of a stable process with a multivariate quality characteristic using standard methods usually requires the assumption that the quality characteristic of interest follows a multivariate normal distribution. Unfortunately, multivariate normality is a difficult assumption to assess. Further, departures from this assumption can result in erroneous conclusions. In this article, I propose assessing the capability of a process using a nonparametric estimator. This estimator is based on a kernel estimate of an integral of a multivariate density. Bandwidth selection for this method is based on a smoothed bootstrap estimate of the mean squared error of the estimator. I also address the issue of constructing approximate confidence intervals. An example is presented that applies the proposed method to bivariate nonnormal process data. The performance of the resulting estimator is then compared to the sample proportion and a normal parametric estimate in a simulation study.