This thesis involves exploring enhancement of estimating the probability of a critical station blackout in nuclear power plant operations by the use of direct numerical evaluation of multidimensional nonrecovery integrals. This requires development of computational methods with data provided from South Texas Project Nuclear Operating Company (STPNOC). Several methods that are currently used in the industry to estimate such probabilities often overestimate the value substantially. The computational integral method developed in the thesis will reduce excess conservatism while maintaining plant safety standards. This computational integral is calculated using a MATLAB research code referred to generally as "STP-TAMIL" which is for South Texas Project --Texas A&M Improved LOOP. The code itself (along with the user manual) was developed in conjunction with this Thesis. STP-TAMIL is successful in reducing the estimated probability of critical station blackout by a significant amount (about 88.47 percent ) with the incorporation of recovery of offsite and onsite power for South Texas Project̕ s nuclear plants, and results were verified. This thesis also describes an asymptotic justification for to the non-recovery integral used. Applications to the industry, or STPNOC, which will use the "TAMIL" code are addressed. Some assumptions used throughout the problem suggest that if more dynamic rates or distributions are used then more recovery can be obtained, which will decrease the probability of critical station blackout. Methodology developed in this thesis will be used in future work to develop this STP-TAMIL research code into a model used industry wide in commercial nuclear power plants.