This paper investigated the stochastic analysis of twodissimilar unit cold standby system considering repair, inspection, post repair under Poisson shocks. The serverman, is called when the operative unit fails. The shocks can attack the operative unit. The repaired unit is sent for inspection to decide whether the repair is satisfactory. If the repair is found unsatisfactory, then the unit is again sent for post repair. Some reliability measures of the system such as system reliability, mean time to system failure (MTSF) and steady state availability are derived. Graphical representations are presented to illustrate the theoretical results.
The purpose of this study is to analyze the behavior of some industrial systems in light of the cost-free warranty policy. According to this policy, we assume that the repairman is not always present in the system. When the active unit fails, the repairman will be called to visit the system; however, administrative procedures may delay the visit for some time. Once on the system, the repairman first inspects whether the fault is caused by the user or not and whether it is repairable or not. According to product warranty laws, the repairman carries out the repair or replacement of the faulty unit. The failure time, administrative delay time, inspection time, and repair time are assumed taken as a negative exponential distribution. The system model is analyzed by the supplementary variable technique and Laplace transform, as various performance metrics of system efficiency have been obtained. The sensitivity and relative sensitivity analyses for the system parameters have also been performed. Finally, an illustrative example is taken to illustrate the efficiency of the system.
In this article, we study the impact of some system parameters on an industrial system consisting of two nonidentical parallel units with one repairer. The active unit may fail due to essential factors such as aging or deterioration, or due to external phenomena such as Poisson shocks occurring at different time periods. Whenever the value of a shock is greater than the specified threshold of the active unit, the active unit fails. The article assumes that the repairman can make one of two decisions at the beginning of system operation: either he takes a vacation when the two units are operating normally, or he remains in the system to monitor it until the first failure of the system. If a failure occurs in either unit during the repairman’s absence, the failed unit must wait until the repairman is called back to work. We assume that the value of each shock is i.i.d. with a known distribution. The length of the repairman’s vacation, the repair time, and the recall time are arbitrary distributions. Various reliability measures were calculated using the supplementary variable technique and the theory of Markov vector processes. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, numerical calculations and graphical analyses were performed to validate the derived indices.
This article examines the impact of some system parameters on an industrial system composed of two dissimilar parallel units with one repairman. The active unit may fail due to essential factors like aging or deteriorating, or exterior phenomena such as Poisson shocks that occur at various time periods. Whenever the value of a shock is larger than the specified threshold of the active unit, the active unit will fail. The article assumes that the repairman has the right to take any of two decisions at the beginning of the system operation: either a takes a vacation if the two units work in a normal way, or stay in the system to monitor the system until the first system failure. In case of having a failure in any of the two units during the absence of the repairman, the failing unit will have to wait until the repairman is called back to work. We suppose that the value of every shock is assumed to be i.i.d. with some known distribution. The length of the repairman’s vacation, repair time, and recall time are arbitrary distributions. Various reliability measures have been calculated by the supplementary variable technique and the Markov’s vector process theory. At last, numerical computation and graphical analysis have been given for a particular case to validate the derived indices.
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