Supriya Maheshwari et. al. / International Journal of Engineering Science and Technology Vol. 2(9), 2010, 4701-4716 UNRELIABLE FLEXIBLE MANUFACTURING CELL WITH COMMON CAUSE FAILURE SUPRIYA MAHESHWARI Department of Mathematics, St. John’s College, Agra (India) supmaheshwari@rediffmail.com PANKAJ SHARMA Department of Mathematics, St. John’s College, Agra (India) pankajsharma2007_s@rediffmail.com MADHU JAIN Department of Mathematics, I.I.T. Roorkee (India) madhujain@yahoomail.com Abstract: A mathematical model is developed for unreliable flexible manufacturing cell (FMC) which operates under stochastic environment and produces a variety of parts by utilizing computer controlled machines, a robot and an automated pallet system. FMC is served by the pallet system which delivers blanks into the cell and moves finished parts out of the cell. The robot acts as a mediator between pallet system and the machines i.e. it takes the blanks from the pallet to load them on the machines and places manufactured parts again on the pallet after unloading them from the machines. The operation times, loading/unloading times and material handling times by the pallet are assumed to be exponentially distributed. Using birth death process, the differential difference equations governing the Markov model have been constructed. By using Runge-Kutta method, the probabilities for different system states have been evaluated. Various performance measures viz. machine utilization, robot utilization, pallet handling system utilization, production rate, etc. are established. The model has been compared with that of earlier existing models with reliable/unreliable machines/robot; such models can be treated as special cases of our model. The sensitivity analysis is also performed to explore the effects of different parameters on the various system performance indices, which have been displayed with the help of tables and graphs. Keywords: Unreliable FMC; Common cause failure; Runge-Kutta method. 1. Introduction Flexible manufacturing system (FMS) is advanced production system, which has evolved in parallel to the developments in computers and automation technology over past three decades. The system is best suited for low to medium volume industries, which work under the unpredictable market environments that demand low cost solutions for fast and effective adaptation to frequently changing demands and designs. An FMS is a highly versatile production system consisting of an integrated computer controlled configuration of numerically controlled (NC) machines with an automated material handling system. The multifunctional machines in FMS can perform a variety of operations simultaneously when provided with the required range of tools. Thus tool management is a significant issue that should necessarily be taken care of in such systems. Many researchers have offered various sophisticated models related to FMC which are capable to mould themselves according to rapidly changing market patterns and customers demand. Numerous contributors working in the area of queueing modeling also paid their attention in this specific area (cf. Vinod [23]; Sharifria and Hildebrant [21]; Vinod and Solberg [24]; Dallery [8]; Chan and Bedwarth [5]; Wang [26] ). Wang and Wilson [27] explored the effect of the cell structures on the means and variances of the cell throughput. Cogun and Savsar [7] have done performance evaluation of a flexible manufacturing cell by computer simulation. Savsar [16] performed reliability analysis of a flexible manufacturing cell and compared it to that of a fully reliable flexible manufacturing cell. A longitudinal study of a flexible manufacturing cell was presented by Sohal et al. [22]. Jain et al. [12] studied flexible manufacturing system with ISSN: 0975-5462 4701