692 B E E TRANSACTIONS ON ROBOTICS zyxwvu AND AUTOMATION, zyxwv VOL. 11, NO. 5, OCTOBER 1995 Automated Performability Studies of Manufacturing Systems with Multiple Part Types N. Viswanadham, zyxwvutsrq Fellow, ZEEE, Krishna R. Pattipati, Fellow, ZEEE, and V. Gopalakrishna Abstract-In this paper, we consider the transient performance analysis of failure-prone manufacturing systems producing multi- ple part types. We decompose the exact monolithic model into (a) a slower time scale structure state process modeling the failure and repair and (b) a faster time scale performance model describ- ing the part processing and the material movement. We combine the solution of these two models zyxwvuts to show that the accumulated reward over a given time interval is a solution of a set of forward or adjoint multidimensional linear hyperbolic partial differential equations. This result generalizes the existing results on composite performance-dependability analysis of manufacturing systems. We also present efficient numerical methods for computing the distribution of the cumulative operational time, and the mean and variance of the cumulative production over a given time interval. Further, we bring out the signiticance of these results in the manufacturing systems context through several examples. I. INTRODUCTION A. Manufacturing Systems ODERN MANUFACTURING systems are intercon- M nections of subsystems such as numerically controlled machines, assembly stations, automated guided vehicles (AGV’s), robots, conveyors and computer control systems. These components are typically prone to failures. Usually, manual or automatic repair facilities are available to restore failed subsystems to the normal level of operation. Sometimes, reconfiguration of system resources and layout may be done, in order to cope with failures of subsystems. Failures, together with repairs and reconfigurations, constitute three basic events that we need to model for computing the performance of manufacturing systems in the presence of failures and repairs. Production rate (the number of parts produced per unit time) and manufacturing lead time (the amount of time the workpiece resides on the factory floor) are two important performance measures in a manufacturing system. Most of the literature on performance analysis of manufacturing systems and also the need to take into account failure-repair behavior of the system [24], [25]. In this paper, we conduct composite performance-dependability analysis of manufacturing systems producing multiple part types to determine the distribution and moments of performance measures such as the accumulated production over a time interval using Markov reward models. In this paper, we consider the transient performance analysis of failure-prone manufacturing systems producing multiple part types. We decompose the exact monolithic model into: (a) a slower time scale structure state process modeling the failure and repair events, and (b) a faster time scale performance model describing the part processing and the material move- ment events. We combine the solution of these two models to show that the accumulated reward over a given time interval is a solution of a set of forward or adjoint multidimensional linear hyperbolic partial differential equations. We also derive the differential equations satisfied by the nth moment of each of the part types. These results generalize the existing results on composite performance-dependability analysis of manufacturing systems. We illustrate all the results through examples. The main contributions of this paper are the following: Composite performance-reliability analysis for systems producing multiple part types. Derivation of multidimensional hyperbolic partial dif- ferential equations for the distribution of accumulated production over [0, t]. Efficient numerical method for solving the first and sec- ond moments of the distribution of accumulated produc- tion over [0, t] for each part type. Several analytical and numerical examples of manufac- turing systems producing multiple part types. B. Earlier Work deals with computation of average performance measures of failure-free systems. However, there is recent awareness production rates and neglecting the variance of production [9] There are several papers in the dealing with performance analysis of automated manufacturing systems. [23], with queuing networks [4] and stochastic Petri nets regarding the Pitfalls that arise in just dealing with the mean Markov chains constitute the most fundamental analytical tool [22] serving as higher level models. Discrete event simulation is another POpdX tool. Literature dealing with combined performance-reliability (performability) analysis is relatively Manuscript received January 15, 1994; revised December 1994. This work was supported by AFOSR under Grant ~49620-92-j-0150, the b pment of Economic Development of the State of Connecticut, and the Department of Science and Technology of Govemment of India. Automation, Indian Institute of Science, Bangalore 560 012, India. ing, University of Connecticut, Storrs, CT 06269 USA. 001, India. sparse. Also, most authors focus on determining the mean values. There is a recent awareness in manufacturing literature regarding the pitfalls that arise in just dealing with first moments of the distribution and neglecting the higher ones 191. Literature on performability modeling of fault-tolerant com- puter systems is abundant. Beaudry [ l ] introduced perfor- N. Viswanadham is with the Department of Computer, Science, and K. R. Pattipati is with the Department of Electrical and Systems Engineer- V. Gopalakrishna is with Integra Micro Systems Pvt. Ltd., Bangalore 560 IEEE Log Number 9411926. 1042-296W95$04.00 zyxwvuts 0 1995 IEEE