Common cause failure (CCF) is analyzed as a manifestation of the probabilistic characteristics of component failure rate:probability stemming from stochastic environment load. CCF revolved concepts, such as 'root cause' and 'coupling mechanism' are interpreted mathematically from the viewpoint of random environment load bringing about failure dependency. Opinions about 'inherent CCF' and 'additional CCF', 'absolute CCF' and 'relative CCF' are presented and discussed. An easy-to-use CCF model is developed through multi-dimension environment load-component strength interference analysis and knowledge based parameter discretization. Owing to its strict statistical foundation, such a model has the ability of estimating component failure rate:probability and common cause failure rates: probabilities consistently, dealing with low redundancy system CCF and high redundancy system CCF uniformly, and predicting high multiplicity failure rate:probability based on low multiplicity failure data satisfactorily.

In order to demonstrate the role of multi-crack growth:coalescence in the leak-before-break concept, Monte Carlo method is applied to simulate multiple crack growth:coalescence behavior which are quite common to component vulnerable zone such as weld. For the multi-crack behavior simulation, typical component vulnerable zone is postulated to have randomly distributed initial cracks. The parameters such as crack number, crack location and crack length are all treated as random variables. The crack distribution parameters are assumed according to generic knowledge available. For single crack situation, the crack size with detectable leak and the critical crack size with unstable propagation are cited from literature. For the multi-crack situation, an equivalent crack-opening area is used to identify the detectable leak. The simulation results show that, for LBB concept related components, the existence of multiple cracks might lead to much shorter leak-free time and much shorter allowable response time compared with those in single crack situation.

The growth/coalescence behavior of multiple cracks is investigated through computer simulation to present the effects of multiple cracks on the pipe leak-before-break (LBB) case. For the multiple crack behavior simulation, randomly distributed initial cracks are postulated in a typical vulnerable zone (such as weld) of pipe. The parameters such as the initial crack number, initial crack ocations, initial crack lengths and the growth rates of the cracks are taken as random variables. Different crack distribution parameters, different crack growth laws, and different crack interaction rules are adopted to examine the sensitivity of the LBB case to these factors. The simulation results show that the effects of multiple cracks on the LBB case are different for different failure mechanisms, while the general trend is that multiple cracks always lead to shorter leak-free lifetimes and shorter allowable response time. Moreover, the undesired situation of sudden catastrophic break without previous leak may also be derived in the cases where the amount of initial cracks is large and the degree of crack interaction is strong.

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The present paper is mainly concerned with pipe system failure probability estimation. For this purpose, a multiple component dependent failure (MCDF) model is introduced to deal with dependency among pipe segment failures. The MCDF model is directly derived from load-strength interference analysis with the underlying notion that stochastic environment load brings about failure dependency. The influence of pipe segment failure dependency on pipe system failure probability is addressed and a modified system failure probability model is presented. It is also shown that, with regard to a pipe system, the multiple failures of pipe segment leaks might lead to a pipe system disabling leak or even to a break. The probability of pipe system disabling leak or break induced by the imultaneous failures of multiple segment leaks is estimated by means of the MCDF model. The estimation results indicate that pipe system failure probability depends not only on the mean values of the respective segment failure probability random variables, but also on other distribution parameters (e.g., the standard deviations) of them. Pipe system failure probability estimated by means of the modified model is sometimes several times lower than that estimated by the conventional system failure probability model.