A risk index for ordinal variables and its statistical properties: A priority of intervention indicator in quality control framework

Measuring risk when data are available only on an ordinal scale is not an easy task. The most common approach of risk modeling is a quantitative approach. In this paper, we propose the Criticality Index: a risk index suitable for studies where data are collected on ordinal scales, defined on the relative frequencies of the considered ordinal variables. Exact and asymptotic distributions of the index estimator are derived, and its statistical properties are studied. Moreover, the confidence intervals using the asymptotic normality are defined. The proposed index may be used as an initial view of the level of risk, for comparisons among environments, to indicate how risk changes over time, and to identify interventions in control systems. An application in quality control framework to data on severity, detection, and the occurrence of product defects of a multinational manufacturer is also presented.