Cost benefit analysis of series systems with warm standby components
This paper deals with the cost benefit analysis of series systems with warm standby components. The time-to-repair and the time-to-failure for each of the primary and warm standby components is assumed to have the negative exponential distribution. We develop the explicit expressions for the mean time-to-failure, MTTF, and the steady-state availability, AT(∞) for three configurations and perform a comparative analysis. Under the cost/benefit (C/B) criterion, comparisons are made based on assumed numerical values given to the distribution parameters, and to the cost of the components. The configurations are ranked based on: MTTF, AT(∞), and C/B where B is either MTTF or AT(∞).
Machine Repair Problem with K-Type Warm Spares, Multiple Vacations for Repairmen and Reneging
In this paper, a multi-repairmen machine repair problem comprising of M operating units together with k type of warm spares has been investigated. The failed units are immediately attended by repairmen if available. When there are no failed units in the queue for repair, the repairmen leave for a vacation of random length. When the vacation period is terminated, the repairmen return and check for any failed unit in the queue. If the queue is non-empty, the repairmen start repairing of failed units until the queue becomes empty, and again they leave for another vacation. The repair rate of the repairmen depends upon the workload. The caretaker of the failed machines may renege on finding all repairmen busy. The steady state queue size distribution and other important performance measures have been derived using matrix recursive approach. Furthermore, a numerical example provides a profound understanding of the sensitivity of parameters with
Technical Note - Probabilistic Analysis of a Single-Server n-unit System with (n - 1) Warm Standbys
This paper deals with the availability and reliability of an n-unit system with (n − 1) warm standbys and a single repair facility. The failure times of the operating unit and of a standby are assumed 1o be exponentially distributed with parameters λ1 and λ2 respectively. Initially, a unit is switched on and the other units are kept as warm standbys. The system breaks down when the last operating unit foils. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes, and employs the Laplace-transform technique to solve these equations. It obtains the mean down-time of the system during (0, t) and the mean time to system failure explicitly. Finally it discusses the cases n = 2 and 3.