Simultaneous process control of several independent quality variables
A method for multivariate quality control with the dual objectives of providing a true level of sampling error probabilities for the joint control of several quality variables while also giving problem diagnoses for the quality variables individually. The method is comprised of an afine transformation of the multiple quality variables which creates a univariate test statistic used to monitor the quality and provide problem diagnoses. In practice, realized values of this statistic would be plotted as a time series on a control chart with multiple diagnosis intervals. For the analysis of the method’s effectiveness, the quality variables are assumed to be independent and normally distributed.
The method is shown to be successful in achieving desired sampling error probabilities for any m quality variables in the case of positive shifts in the means of the variables. A second transformed variable is added for the diagnosis of shifts of unrestricted direction, and its effectiveness is analyzed. The sample size requirement of the afine transformation method is compared to the total sample size necessary when a separate Shewhart chart for the mean is maintained for each quality variable with the same overall sampling plan objectives. The power of the method to detect quality problems in general while disregarding specific diagnoses is compared to the power of Hotelling’s T² test for multivariate quality control. A comprehensive evaluation of the relative worth of the two methods is not possible since the T² statistic does not consider diagnoses of the individual quality variables.