Equivalence of Risk : A Mathematical Approach

Naval engineers express risk in terms of probability, severity, and risk acceptance authority. Currently, Naval Sea Systems Command Instruction (NAVSEAINST) 5000.8 specifies the typical format for reporting risk probability, severity, and acceptance authority. NAVSEAINST 5100.12 provides a chart whereby given a probability and severity, the risk can be found. Although risk can be quantified, the human perception of risk often influences how risk is addressed. Risk perception does not necessarily map directly to probability and severity in a linear fashion. This paper proposes a Composite Risk Index (CRI) based on probability and severity that takes into account the human perception of equivalent risk. This paper also answers questions as to why the NAVSEAINST 5100.12 risk chart is logarithmic with respect to probability and proposes changes supporting the next NAVSEAINST 5100.12 revision. Background Risk is the potential for mishaps or other adverse variation in the cost, schedule, or performance of a program or its products (ref. 1). Safety risk is the potential for mishaps that result in injury, illness, death, equipment damage or loss, or environmental damage. All safety programs desire accurate risk quantification in order to provide a meaningful expression of risk. One factor complicating risk quantification is never having one single risk associated with a program. Safety engineers define a program’s multitude of risks in terms of probability and severity for acceptance by the appropriate authority. To accept the total safety risk of a system, these authorities typically desire a composite risk estimate. Current methods of obtaining this composite risk estimate use summing techniques to add the individual risks associated with the system and produce a single number (ref. 2). This method seems intuitive; however, it is often difficult to determine particular probabilities or quantify severity. Accepted methods of quantifying severity include dollar amounts or severity of injury (ref. 3). Expressing severity in terms of cost establishes consistency, but it is still difficult to put a dollar amount on human injuries. For example, how many broken backs are equivalent to death? Furthermore, perception of what constitutes “high” risk may vary from project to project. Discussion This paper discloses methods to address these issues. Beginning with an analysis of the typical risk acceptance chart, let us investigate how the various Mishap Risk Indices (MRIs) relate to one another. Figure 1 shows the typical MRI chart. This chart helps evaluate the level of risk as “high,” “serious,” “medium,” or “low” based on probability and severity. The authority qualified to accept the safety risk increases from the Program Manager (PM), to the Program Executive Office (PEO), to the Component Acquisition Executive as the level of risk increases. In Figure 1 severity is categorized in general terms of loss. This type of chart assigns a higher priority (lower number) to the more severe incidents. There is not a clear mapping of one severity to another in Figure 1. This paper proposes an approach to relate the severity categories to one another; whereby, there would be a relationship between the different severity categories.