A risk index to evaluate the criticality of a product defectiveness

We propose a risk index naturally suitable in quality-control framework characterized by data often collected on ordinal scale, to measure the risk of failure of a product. A so-called Severity Index is defined on the basis of the relative frequencies of the ordinal variables. We examine the distribution and the statistical properties of its estimator. We apply the index to real data concerning the severity and the occurrence of defectiveness of the products of a multinational corporation manufacturer. Our index may be employed to communicate the level of risk, to compare among different risks and to identify interventions in the production system.