Modelling a general standby system and evaluation of its performance

Abstract

SUMMARYRedundancy or standby is a technique that has been widely applied to improving system reliability and availability in system design. In this paper, a general method for modelling standby system is proposed and system performance measures are derived. It is shown that the proposed general standby system includes the cases of cold, hot and warm standby systems with units of exponential distribution, which were studied in the literature, as special cases. An optimal allocation problem for a standby system is also discussed.

Optimal Allocation of Active Redundancies to k-out-of-n Systems with Heterogeneous Components

“…Generally, the following two types of allocation are commonly used: (i) active redundancy (hot standby), in which the redundancies are put in parallel to components of the system and start functioning at the same time as the components are initiated; (ii) standby redundancy (cold standby), in which redundancies are put in standby and start functioning once components fail. Recently, Cha et al (2008) considered the so-called general standby, in which the redundancy works in a milder environment in the standby state and, hence, the failure rate is nonzero and smaller than that in the usual environment; therefore, it is just an intermediate stage between the cold and the hot stages. This paper will focus only on the active redundancy.…”

“…This paper will focus only on the active redundancy. For more on general standby, we refer the reader to Cha et al (2008) and Li et al (2009). Shaked and Shanthikumar (1992) were among the first to study the problem of allocating m active redundancies to a series system with n components in the situation that lifetimes of components and redundancies are independent and identically distributed.…”

Some new results involving general standby systems

“…These three kinds of standby redundancy are first unified as the so-called general standby in Cha et al [8]. Unless stated otherwise, the term 'standby' stands for the general standby in this paper.…”

A comparison between two switching policies for two-unit standby system

“…Hence, the distinction between the two switching policies may be ascribed to that which unit is activated for the two-unit standby system [18]. The similar observation is considered as the allocation problem in [14]. Cha et al [14] pointed out that if the time-to-failure of units follow the exponential distribution and w t ð Þ is a linear function of t, the optimal allocation means using the weaker unit with larger failure rate as the active one and the stronger unit with smaller failure rate as the standby one.…”

“…To describe the lifetimes under different environments, Cha et al [14] proposed a general model according to the ideas in accelerated life tests and the concept of equivalent age. In this section, this general model is introduced briefly.…”