Simulating state-dependent systems with partial aging in standby

We analyze a two-component standby system with failures in standby (2SBS). Typically, such a system is interpreted as a state-dependent system with time-dependent failure rates. When the backup component is aging in standby as if it is working, the 2SBS is denoted as 2SBS with full aging. Such a system can be modelled with a system of ODEs and may have a numerical solution. Alternatively, simulation modelling can generate the probability of the system and estimate the important reliability characteristics. However, when the backup component does not age in standby (2SBS with no aging), or when the backup component ages in standby slower than in operation (2SBS with partial aging), then there is no system of ODEs because the system is not state dependent. We develop simulation algorithms to solve the 2SBS with no aging and with partial aging. The partial aging model assumes that the aging uses reliability as a proxy variable for aging and introduces the equivalent aging time T* as the starting time for the conditional reliability function of the backup component in standby. An extensive numerical example is provided.