Redundancy Optimization Problems with Uncertain Lifetimes

Abstract

Component redundancy plays a key role in engineering design and can be effectively used to increase system performances. Often two underlying component redundancy techniques are considered. One is parallel redundancy where all redundant units are in parallel and working simultaneously. This method is usually employed when the system is required to operate for a long period of time without interruption. The other is standby redundancy where one of redundant units (i.e., spares) begins to work only when the active one failed. This method is usually employed when the replacement takes a negligible amount of time and does not cause system failure. The problem of determining the number of redundant units for improving the system performances under some constraints such as cost constraint is well known as the redundancy optimization problem. It has been addressed in much research work on redundancy optimization theory such as Coit (2001), Coit and Smith (1998), Kuo and Prasad (2000), Levitin et al. (1998), Prasad et al. (1999) and Zhao and Liu (2003). In a classical redundancy optimization model, the lifetimes of system and components have been basically assumed to be random variables, and system performances such as system reliability are evaluated using the probability measure. Although this assumption has been adopted and accorded with the facts in widespread cases, it is not reasonable in a vast range of situations. For many systems such as space shuttle system, the estimations of probability distributions of lifetimes of systems and components are very difficult due to uncertainties and imprecision of data (Cai et al. (1991)). Instead, fuzzy theory can be employed to handle this case.