Variation transmission in multi-stage industrial processes

Abstract

The subject of variation analysis is of interest in manufacturing processes where items are being produced in large quantity and pass through many operations or stages before they are completed. After the final operation, they must meet certain specifications. The issue is to discover how variation in the product characteristics at the final stage of the process can be reduced. With that goal in mind, it is useful to understand how the variation is conveyed through the process.

Multivariate normality is assumed as the underlying model for the measured product. Methods are given for analysing variance transmission under this model, both when a general multivariate normal holds, and in a more restricted case, when a first order autoregressive structure is appropriate.

Inevitably, there will be measurement error in the data collected on the process. It is shown that this measurement error can severely hinder attempts to characterize the process, and should be incorporated explicitly in an analysis. A naive estimation method is introduced and shown to work well.

It may be less expensive, in some instances, to collect large amounts of sample data after each stage, and then track only a few items through the process. Methods are given of incorporating cross-sectional data into the analysis. Also discussed is how to do this when the problem is compounded by measurement error.

Finally, some consideration is given to the issue of multivariate data.