RELIABILITY ANALYSIS AND SETTING RELIABILITY REQUIREMENTS BASED ON THE COST OF FAILURE

Abstract

A theoretical framework and models are proposed for reliability analysis and setting reliability requirements based on the cost of failure. It is demonstrated that a high availability target does not necessarily limit the risk of failure or minimize the total losses. The proposed models include: (i) models for determining the value from the reliability investment, (ii) optimization models for minimizing the total losses, (iii) models for limiting the risk of failure below a maximum acceptable level, (iv) a model for guaranteeing an availability target and (v) a model for guaranteeing a minimum failure-free operating interval before each random failure in a finite time interval. The models related to the value from the reliability investment can be used to determine the effect from reducing early-life failures on the financial revenue. On the basis of a counterexample it is demonstrated that altering the hazard rates of the components may lead to decreasing the probability of failure of the system and a simultaneous increase of the risk of failure, which shows that the cost-of-failure reliability analysis requires new reliability tools, different from the conventional tools. A new closed-form relationship has been derived related to reliability associated with an overstress failure mechanism. On its basis, a method for setting reliability requirements has been proposed, which limits the risk of impact failure within a maximum acceptable level. On the basis of counterexamples, it has also been demonstrated that for a load and strength not following a normal distribution, the standard reliability measures "reliability index" and "loading roughness" can be misleading. A new reliability integral has been proposed, based on integration performed only within the region of the upper tail of the load distribution and the lower tail of the strength distribution.