Waiting time distribution for an exchangeable item repair system with up to two failed components

• DOI: 10.1007/s10479-017-2614-0
• Publication Date: 2017-08-30T01:50:57Z
• Authors: Michael Dreyfuss; Alan Stulman
• Keywords: Component (thermodynamics); Theory of computation

Models involving exchangeable component repair systems are widely treated in the literature. In such systems a customer arrives at a repair queue with a failed component which is replaced from stocks of previously repaired components and spares. Various strategies and service measures have been discussed. The waiting time distribution for a single failed component has also been developed. Most customers who arrive at a repair facility will arrive with a single failed component type. They will be referred to an appropriate service queue which will ultimately exchange that particular failed component. Due to its complexity the development of the waiting time distribution for a single queue servicing multiple simultaneous component failures has been generally neglected. In a previous paper we found the waiting time distribution for the case where an item arrives with exactly two simultaneously failed components. In this paper we will consider a much more general case where either one or both of the components have failed. Finding the waiting time distribution is important because it can lead to better facility planning and new realistic service measures. For example, how many extra spares should be allocated to the system so that the probability of waiting more than an acceptable amount of time (the window fill rate) could be kept to within a predefined limit?