Convolution correction factor adjustments on static PRA models for event assessment

Current probabilistic risk assessment (PRA) models contain cut sets that have time-constrained basic events such as switched components, recovery of failed components, and failures in time. For these cut sets that have multiple time-constrained events that interact (e.g., offsite power recover at the same time as multiple diesel generators fail to run), there is the possibility that the minimal cut set quantified result is either conservative or non-conservative. Since current PRA models typically assume that the accident scenario starts at �time zero,� the fails-to-run basic events use this starting time as the basis for their respective reliability models. Over time, the standard practice was to recognize this issue and accept it as part of the approximations built into the event tree/fault tree PRA models. However, now that these same PRA models are being used in a regulatory forum, this approximation needs to be addressed. Further, this issue exists not only for the baseline PRA results, but for deficiencies that have been observed or those that have the potential of occurrence, whether the deficiency is complete failure or just a degraded condition. It is found that this approximation becomes very important when evaluating scenarios such as station blackout sequences and other loss of offsite power sequences. This paper will address the theory and implemented process used by the Systems Analysis Programs for Hands-on Integrated Reliability Evaluations (SAPHIRE) PRA software. Starting with SAPHIRE version 8, the process that was developed is to calculate a �convolution correction factor� based on three distinct calculations. The first calculation is the cut set based frequency calculated via the standard event tree/fault tree PRA model (assuming all run failures start at time equal to zero). The second calculation is to perform the exact time-constrained calculation by integrating the component failure models over the time period of interest (e.g., time to recover, a mission time). For example, this exact calculation for the case of the diesel generators is to convolve their failure models with the offsite power recovery model to obtain the exact probability. The third calculation is to produce the convolution correction factor by dividing the exact probability calculation by the standard cut set probability. This convolution correction factor is then applied to the PRA cut sets in order to remove the time-constrained conservatism. The process used to obtain the convolution correction factor for the baseline PRA is important; however, in this paper also describe what happens when there is degradation of a component or a potential deficiency. These issues become very important in order to ensure that the convolution correction factor is re-calculated correctly. If the correction factor does not get re-calculated and the same baseline convolution correction factor is used, the final analysis result could be over conservative or under conservative. This paper will discuss how these issues are addressed and provide examples on how SAPHIRE automatically makes the necessary adjustments. MathCad verification results can be computed using the provided equations and input data.