Abstract
This study analyzes three availability systems with warm standby units, fault detection delay, and general repair times. The failure times and repair times of failed components were assumed to follow exponential and general distributions, respectively. The detection delay times were assumed to be exponentially distributed. This study exploited the supplementary variable technique to develop a recursive method for deriving the steady-state availability for three systems. By using extensive numerical computations, we compared three systems in terms of system availability based on specific values given to the system parameters. The state transition rate diagrams of the three systems revealed the symmetry property approximately. The three systems were ranked based on the system availability and the cost/benefit for the three various repair time distributions: exponential, three-stage Erlang, and deterministic, where the benefit was system availability.
Highlights
System availability plays an increasingly important role in many real-world systems, such as manufacturing systems, computer systems, and power plants
This study proposes a form of steady-state availability analysis of repairable systems with warm standby components, a detection delay, and general repair times
We demonstrated that the first system generalized Trivedi’s two-component system with a fault detection delay
Summary
System availability plays an increasingly important role in many real-world systems, such as manufacturing systems, computer systems, and power plants. This study proposes a form of steady-state availability analysis of repairable systems with warm standby components, a detection delay, and general repair times. Wang and Pearn [11] studied the cost–benefit analysis of series systems with warm standbys They derived explicit expressions for the mean time to first system failure and system availability for three systems. Wang and Chiu [12] presented the cost–benefit analysis of queueing systems with warm standby components and imperfect coverage. They explored a comparative analysis associated with numerical results to verify the effects of parameters on the cost/benefit ratios.
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