Deficiencies in Safety Schemes which Rely on Stochastically Failing Protective Equipment

Probability theory is used to assess the deficiencies of safetyschemes which rely on devices which can fail either in an undetectedmanner only, or in both undetected and detected ways. Threequantities are used to express the deficiencies of these schemes;the mean period during which devices are ineffective, the proportionof time for which they are ineffective and the distributionof the durations of their ineffective periods. Analytical expressionsare derived for these quantities for a scheme in which onlyundetected failures occur and devices are replaced at regularintervals. Monte Carlo simulation techniques are used to estimatethe measures of deficiency for situations in which both typesof failure are possible. Consideration is given to the "cost-benefit"aspects of safety schemes in simple circumstances in which therate of occurrence of the hazards involved, and the penaltyto be paid in the event of a catastrophe, are known.