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A risk index for ordinal variables and its statistical properties: A priority of intervention indicator in quality control framework
Author(s) -
Facchinetti Silvia,
Osmetti Silvia Angela
Publication year - 2018
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2254
Subject(s) - ordinal data , estimator , index (typography) , statistics , ordinal scale , ordinal regression , econometrics , mathematics , confidence interval , computer science , data mining , world wide web
Abstract 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.