Reliability analysis of discrete time series-parallel systems with uncertain parameters

Reliability is an important index to describe the quality of an individual unit or a complex system. In practice, it is possible that lifetimes of the system units can estimate their probability distributions by previous experience, however, there may be only few or no samples to ascertain their distribution parameters. In order to deal with this case, this paper proposes a discrete time series-parallel system with uncertain parameters, which is studied based on both probability theory and uncertainty theory. Besides, redundant standby methods of improving the system reliability are provided, including cold, warm and hot. The lifetimes of units in redundant systems are assumed to be independent and non-identical discrete distributions, which distribution parameters are uncertain variables. Some formulas are given to calculate the reliability and mean time to failure of these systems. In addition, some numerical examples are given to illustrate different system models.