Abstract
This study is concerned with the transient state analysis of M/M/1 machine repairable system consisting of M operating units. F-policy is quite useful to avoid the overloading of failed machines that arrive for repair in the system. The failed machines are repaired by a server that is susceptible to failure and follows the threshold recovery while being repaired. The server leaves for a vacation if there are no machines waiting in the system for the repair. Runge-Kutta method is implemented to solve the governing equations and evaluate the system's state probabilities. Cost function is also designed to determine the system’s minimum cost. In addition, the numerical outcomes acquired by the Runge-Kutta method are compared with the results generated by adaptive neuro-fuzzy inference system (ANFIS).
Highlights
The significant contributions in varying situations to unreliable machining systems can be observed in the study by Jain and Bhagat (2013), Tan et al (2013), Yang et al (2015), Jain et al (2017)
Bhargava and Jain (2014) evaluated the use of the adaptive neuro-fuzzy inference system (ANFIS) to provide a comparative analysis of the outcomes acquired by an unreliable vacation queueing model using matrix method (MGM)
The arrival is controlled using F-policy following an exponential distribution and failed machines are permitted in the system after a start-up time with rate
Summary
The machining systems are of enormous benefit to people. Machining parts failure is quite common causing an adverse impact on reliability, efficiency and quality of the machining system. Jain and Meena (2018) examined an unreliable machining system with mixed standby support and obtained the numerical results using Runge-Kutta method. They constructed a cost function to determine the repair rate and to minimize the total system cost. Sethi and Bhagat (2019) examined a machine repair model with working vacation and used Runge-Kutta method to examine the performance indices. Bhargava and Jain (2014) evaluated the use of the ANFIS to provide a comparative analysis of the outcomes acquired by an unreliable vacation queueing model using matrix method (MGM). An unreliable machine repair model with finite capacity has been considered in the present study where the arrival of failed machines in the system is controlled using F-policy. Whenever the system is empty (i.e. no customers) the server operates with lower service rate rather than completely terminating the system entirely
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