ANFIS computing and cost minimization of M/G/1/K fault-tolerant machining system with general startup under F -policy

In industrial settings, the ability to maintain uninterrupted operations and minimize productivity losses relies heavily on the effectiveness of a fault-tolerant machining system (FTS). The present study investigates the queueing dynamics of an M/G/1/K fault-tolerant machining system that follows a general startup mechanism under the F -policy. The F -policy is implemented to prevent system overload and ensure efficient repair processes by managing the influx of failed machines into the system. In the mathematical framework of our model, we construct the Chapman–Kolmogorov (C–K) steady-state equations by introducing supplementary variables corresponding to remaining repair and startup times. The Laplace–Stieltjes transform (LST) and a recursive method are then utilized to establish probability distributions. Using probability distributions, we develop several system performance metrics that provide insights into various aspects of the system’s behavior. To gain deeper insights, we conduct numerical experiments to analyze trends in performance metrics. The adaptive neuro-fuzzy inference system (ANFIS) technique is used to compare the results obtained from ANFIS with the results calculated through the analytical method. Moreover, the non-linear cost function is constructed with the aim of identifying the optimal control parameters, including the threshold parameter, repair rate, and startup rate. This optimization objective is achieved using two metaheuristic algorithms: particle swarm optimization (PSO) and sine cosine algorithm (SCA). The model’s practical applicability is demonstrated in optimizing forklift operations within a production system.