Evaluating the KTI Monte Carlo Method for System Reliability Calculations

This paper describes and analyses the Kumamoto, Tanaka, Inoue (KTI) Monte Carlo method for estimating the reliability R of an s-coherent system by bracketing it between deterministic lower and upper bounds, and then positioning R between the bounds as a weighted average of the structure functions of Monte Carlo generated k-vectors. The procedure is illustrated with both a 2-out-of-3 system and a larger example. Some known alternatives are discussed: bracketing R as in KTI, but without Monte Carlo; exact methods; the Esary-Proschan min-cut lower bounds; and Monte Carlo that samples component reliabilities instead of successes or failures. Although KTI has interesting set-theoretic features and is apparently both variance reducing and s-unbiased, each of the alternatives mentioned above is more useful than KTI because it is easier to develop and uses existing general purpose software.