Combining risk and uncertainty in technical systems

The risk matrix is tool for making decision about technical system such as prioritising of maintenance. It is used in methods such as FMEA (failure mode and effect analysis) and it is based on the definition of risk as the product of the probability of a certain failure and its consequence. The problem with the standard formulation is that the probability is not always completely known. The uncertainty of the probability can be estimated by its variance. %We suggest that the the mean value plus the standard deviation times a factor could be used instead of just the mean value. Instead of a specific value for the probability of failure, a beta distribution is used for the probability. The main point is to find a trade-off between mean and variance. In this case we want to avoid probabilities larger than the mean. We use a loss function taking into account only the right tail starting at a factor times the mean. The exponent of the deviation is 0. We have calculated how much a decreasing variance should compensate for an increasing mean. We get an approximate relation between the quotient of variances and the quotient of means. The conclusion is that this model should be investigated further.
QC 20170928
RCAM