Bayesian Reasoning in Managerial Decisions on the Choice of Equipment for the Prevention of Industrial Accidents

Abstract

The managerial problem of the choice among alternative protective equipment used to prevent industrial (technological) accidents is considered. The choice takes into account potential failures of the equipment or, conversely, the equipment reliability. Such failures can substantiate contributors to escalations of industrial accidents. The problem of the choice is formulated in the form of a multi-attribute selection. The probability of failure of alternative equipment sets is used as an attribute of the selection problem. An estimation of this probability by means of Bayesian statistical theory is considered. Bayesian prior and posterior distributions are applied as an estimate of failure probability. These distributions are incorporated in the selection problem as uncertain attributes. Development of prior distributions of individual alternatives is discussed in detail. The prior and posterior distributions are treated as measures of the epistemic uncertainty (state-of-knowledge) related to unknown values of failure probabilities. The modelling of uncertainty related to the failure probability corresponds to the classical Bayesian approach to risk assessment. It is suggested to apply the uncertain failure probabilities to developing risk profile for each of the alternative equipments and to incorporate the risk profile to the multi-attribute decision making. The epistemic uncertainty in the failure probabilities and elements of risk profile is quantified by means of Bayesian statistical theory. It is shown that this uncertainty can be reduced by applying Bayesian updating procedure when new data on equipment failures is obtained. Probable cases of the application of this procedure are discussed. This discussion relates the acquisition of the new statistical evidence used for Bayesian updating to the moments, at which managerial decisions are made. It is suggested to solve the problem of the multiattribute selection with uncertain attributes by means of uncertainty propagation. This propagation is accomplished by means of Monte Carlo simulation. The epistemic uncertainty related to the attributes is transformed into a discrete distribution of epistemic uncertainty. Probability masses of this distribution express the chance of individual alternatives to be selected as the best one. The result of this selection will be the alternative with the largest epistemic weight. The potential field of the application of the proposed approach is the management of technological risks present in many industrial facilities and non-industrial installations (dwellings, offices, public places) which are subjected to the hazard of accidents. The approach proposed in the paper allows to make managerial decisions which take into account the reliability of protective equipment. In addition, this approach will allow to utilize data on equipment failures encountered in the past. Such data is usually scarce and expensive. The Bayesian framework is best suited for the application of such data.