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
Mechanics of deformable directed surfaces
Abstract The paper develops a simple, yet complete and consistent non-linear dynamic thermo-elastic shell theory based on the concepts of a two-dimensional directed continuum. The constitutive equations are postulated in a general form. Stress-strain relations are derived using the equation of energy balance and the two entropy production inequalities, which are rewritten in a special form. The linear theory is discussed in detail. The structure of the stress-strain relations is presented in the most general form and then specialized to concrete examples, in particular, to the classical shell theory, using their invariance properties with respective to certain symmetry groups. The elastic moduli are determined by demanding the coincidence of the frequency dispersion surfaces obtained using the two-dimensional theory with the lowest foils of the corresponding surfaces resulting from the three-dimensional theory of elasticity.