Statistical monitoring of polytomous logistic profiles in phase II

Abstract

In certain statistical process control applications, the quality of a process or a product can be characterized by a function commonly referred to as a profile. Some potential applications of profile monitoring are cases where the quality characteristic of interest can be modelled using dichotomous or polytomous variables. Polytomous variables, especially ordinal variables, have various applications. An ordinal (or ordered) variable is a categorical variable, whose values are related in a greater/lesser sense. In this paper, which is the first investigation on ordinal profiles, we propose four methods for monitoring a profile when the process/service output is an ordinal response variable. Ordinal Logistic Regression (OLR) provides the basis for our profile model. These four methods are: Multivariate Exponentially Weighted Moving Average (MEWMA), χ2 statistics, Exponentially Weighted Moving Average (EWMA) with R statistic, and a combination of the last two statistics that are used to monitor OLR profiles in phase II. Performances of these four methods are evaluated using An Average Run Length (ARL) criterion. Two different case studies involving customer satisfaction in the tourist industry and sensory measurements of an electronic nose are used to demonstrate application of the proposed methods in practice.