A one-sided procedure for monitoring variables defined on contingency tables

Abstract

Nowadays the use of the multivariate statistical process control (MSPC) toolbox is efficiently generalized beyond assuring product quality through the monitoring of industrial processes in order to be used in many other non industrial fields (e.g., public health, environmental, financial monitoring, etc.). Data produced by non industrial processes usually require the development of problem-oriented monitoring procedures. In this article we develop a method for monitoring bivariate random variables defined on contingency tables and introduce an appropriate one-sided control procedure, motivated by a problem from double reading used in many medical processes. Specifically, we propose a procedure for monitoring simultaneously the measure of agreement between Cohen’s kappa defined on a contingency table associated with the process stability and one percentage associated with the process quality level, defined on the same contingency table. The procedure is based on an appropriate approximation that is assessed numerically and shows an excellent performance. Then we explore the performance of several candidate one-sided techniques for monitoring the process and we propose a new one that is based on a penalization strategy that appears to have the best performance. The new technique is very easy to implement by a non statistician, as illustrated by its application to a real case from double reading.