In pressure vessels and piping the leak-before-break (LBB) assessment method is employed to avoid any catastrophic failure prior to a detectable leakage. One of the most important parameters, the leak rate, is investigated in the present paper by means of the Monte Carlo method. A brief reviewed is carried out with emphasis on aspects such as crack growth, crack size with detectable leakage, crack opening area and leak rate. Issues concerning the property and behavior of multiple cracks are also covered along with a review of the characteristics of leak rate through distributed multiple cracks using a statistical simulation method. The simulation results show that, the effect of multiple cracks is quite significant to the LBB concept. Both the relationship between leak rate and crack length (or time) and the statistical characteristics of the leak rate are considerably different for different initial crack conditions.

For s-dependent systems, reliability models capable of reflecting the effect of failure dependence, i.e. the so called "common cause failure" are in demand, since the system reliability depends not only on the reliabilities of the individual components but also on the interactions among the component failures. Based on the attribute of system failure, the meaning of order statistics, as well as the mechanism of failure dependence, this paper developed s-dependent system reliability models by incorporating order statistics of component strength into load-strength interference model. The models simply characterize the fact that series system fails as long as the applied load exceeds the first (the minimum) order statistic of component strength, parallel system (with n i.i.d. components) fails when and only when load exceeds the nth (the maximum) order statistic of component strength, and k-out-of-n (F) system fails if load exceeds the kth order statistic of component strength. Since no assumption about s-independent failure was applied, the models are in a position to reflect the effect of failure dependence which may bring about common cause failures. To evaluate the reliability of general system comprising of non-i.i.d. components, an extended load - strength order statistics interference model was presented, too.

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.

The Leak-Before-Break (LBB) case of pressure vessels and piping is achieved with the sufficient margin between detectable leak and catastrophic break. Therefore, the respective characteristic crack sizes, i.e. leak size (the crack size at which leakage amount is great enough to be detected) and the break size (the crack size at which crack propagation becomes unstable) are two important governing parameters for the LBB case. In multiple crack situations, the initial crack distribution and crack coalescence behavior are also LBB governing factors. The multiple crack condition related parameters would affect the LBB margin with the characteristic crack sizes together. The effects of multiple cracks on the LBB case, with respect to the different characteristic crack sizes are investigated in the present article by means of computer simulation. The simulation results show that, in multiple crack situation, the LBB margin is not so sensitive to characteristic crack sizes as in single crack situation.

The issue of information loss in the process of system reliability modeling through conventional load-strength interference analysis is discussed first, and the reason why it is impossible to construct dependent system reliability model simply by means of component reliability index is demonstrated. Then, an approach to modeling the reliability of dependent system with common cause failure (CCF) is presented. The approach is based on system-level load-strength interference analysis and a concept of 'conditional failure probability of component' as well. With the opinion that load randomness is the direct cause of failure dependence, a discrete type system reliability model is developed via the conditional component failure probability concept. At last, the model' s capabilities to estimate system reliability with CCF effect and to predict high multiplicity failure probability based on low multiplicity failure event data are proved.