A Novel Modeling Method for Both Steady-State and Transient Analyses of Serial Bernoulli Production Systems

Conventionally, production system modeling (PSM) has been conducted for the purpose of steady-state analysis, which only facilitates characterizing the long-term performance of production systems. More recently, there has been a rising concern regarding analyzing production system transients, which depict the system behavior before reaching the steady state. Transients are generally undesirable because the performance measures can be quite different from those of the steady state, and such differences will cause substantial production loss. Compared to the rich knowledge on steady-state analysis of production systems, PSM for transient performance analysis is much less studied. In this paper, a novel analytical method has been established to model the production system for both steady-state and transient analyses. This research has overcome the restrictions of existing methods on the number of machines and the capacity of buffers. That is, it has greatly advanced PSM for both steady-state and transient analyses by directly dealing with general serial production systems with multiple unreliable Bernoulli machines and finite buffer capacities. The proposed PSM is a method derived based on probability theory and fixed-point theory. The solvability of the method is proved theoretically. The transient performance metrics, such as second largest eigenvalue modulus, duration of the transients (t_ITER), settling time of work-in-process (t_WIP) and production rate (t_PR), and percent loss of production (L_PR) have been investigated numerically based on the proposed PSM method. This research can serve as an atomic model for more complex optimization problems in production system design and operation.