Considering risk profiles in design optimization for series-parallel systems

The objective of the redundancy allocation problem is to select the parts to be used and a design configuration to optimize some objective function without violating system level constraints. In this paper, the problem was formulated in a more general framework than has previously been accomplished, allowing for the explicit consideration of the risk-profile of system designers and users. Risk is related to the probability that a randomly selected system will be less reliable than a predicted or specified value. Previous formulations of the problem involved a maximization of the expected value of system reliability or the mean-time-to-failure, which implies that designers are risk-neutral. In this paper, both component reliability and time-to-failure are considered as random variables, and lower-bound limits are used in the optimization problem. The extent of the risk associated with a particular system design project was included in the problem formulations and influenced the final design decisions. These formulations were intended to more faithfully address the actual concerns and considerations of the engineering design community. The problems were then solved using genetic algorithms (GAs). Several illustrative examples are provided which show different design configurations depending on the risk profile.