On Monitoring Processes and Assessing Process Capability under a Hierarchical Model, Part 2
In industrial SPC-applications, it is not always appropriate to use a normal distribution with constant variance to describe the within group distribution of measurements. The common statistical properties for the basic distributions of counts, fractions and within group variance may be described by treating them as exponential dispersion families characterized by the relation of the variance to the mean. In the paper we review the theory of exponential dispersion families and discuss the use of standard conjugate distributions to model the between group distribution of means of the charted variable. We introduce a parametrization of the between group distribution by the overall mean of the charted statistic and a ‘signal to noise ratio’ describing the overdispersion as a factor to the average within group variance. The discussion is exemplified by two cases from industry, one showing overdispersion of fractions, and the other showing nonhomogeneity of within-subgroup variances.
KeywordsSubgroup Average Control Chart Variance Function Exponential Family Group Distribution
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