Updated hazard rate equations for dual safeguard systems

A previous paper by this author [M.J. Rothschild, Updated hazard rate equation for single safeguards, J. Hazard. Mater. 130 (1-2) (2006) 15-20] showed that commonly used analytical methods for quantifying failure rates overestimates the risk in some circumstances. This can lead the analyst to mistakenly believe that a given operation presents an unacceptable risk. For a single safeguard system, a formula was presented in that paper that accurately evaluates the risk over a wide range of conditions. This paper expands on that analysis by evaluating the failure rate for dual safeguard systems. The safeguards can be activated at the same time or at staggered times, and the safeguard may provide an indication whether it was successful upon a challenge, or its status may go undetected. These combinations were evaluated using a Monte Carlo simulation. Empirical formulas for evaluating the hazard rate were developed from this analysis. It is shown that having the safeguards activate at the same time while providing positive feedback of their individual actions is the most effective arrangement in reducing the hazard rate. The hazard rate can also be reduced by staggering the testing schedules of the safeguards.