Boolean algebra method to calculate network system reliability indices in terms of a proposed FMEA

Abstract As different MC's or MP's (minimal cuts or paths) may have common components, we cannot apply the product rule to evaluate the system reliability through the RBD (reliability block diagram) of MC's. However, for a non-oriented network, the series of MC's up to order 2 can be transformed into the series of independent parallel-series, i.e. having no common components between each other. Hence, for a very reliable network such as a power station, such a series can be approximately regarded as its RBD so that the product rule, that the system availability is the product of those of independent blocks, applies. For a highly reliable network such as a power transmission and distribution system, more MC's up to an order say 3,4 or even the upmost one should be taken into account. The product rule still applies if we further apply the pivotal decomposition formulas. The method to calculate the system failure frequency is developed in parallel. In terms of the similar ‘differential and integral’ relationship between the failure frequency and the availability, we can easily derive the failure frequency from the availability. For a network with a few oriented arcs, we have to pivot on such arcs first.

[1]  Chanan Singh,et al.  A New Method to Determine the Failure Frequency of a Complex System , 1974 .

[2]  K. K. Aggarwal,et al.  A new method for system reliability evaluation , 1973 .

[3]  C. Singh,et al.  Rules for Calculating the Time-Specific Frequency of System Failure , 1981, IEEE Transactions on Reliability.

[4]  Roy Jensen,et al.  Reliability Modeling in Electric Power Systems , 1979 .

[5]  D. Shi General Formulas for Calculating the Steady-State Frequency of System Failure , 1981, IEEE Transactions on Reliability.

[6]  C. Singh Calculating the Time-Specific Frequency of System Failure , 1979, IEEE Transactions on Reliability.

[7]  Hayao Nakazawa A Decomposition Method for Computing System Reliability by a Boolean Expression , 1977, IEEE Transactions on Reliability.

[8]  K.B. Misra,et al.  A Fast Algorithm for Reliability Evaluation , 1975, IEEE Transactions on Reliability.

[9]  J. Abraham An Improved Algorithm for Network Reliability , 1979, IEEE Transactions on Reliability.

[10]  S. Rai,et al.  An Efficient Method for Reliability Evaluation of a General Network , 1978, IEEE Transactions on Reliability.

[11]  W. Schneeweiss,et al.  Computing Failure Frequency, MTBF & MTTR via Mixed Products of Availabilities and Unavailabilities , 1981, IEEE Transactions on Reliability.

[12]  Avinash Agrawal,et al.  A Survey of Network Reliability and Domination Theory , 1984, Oper. Res..

[13]  Ernest J. Henley,et al.  Reliability engineering and risk assessment , 1981 .

[14]  Mark K. Chang,et al.  Network reliability and the factoring theorem , 1983, Networks.