tailieunhanh - Future Manufacturing Systems Part 3

Tham khảo tài liệu 'future manufacturing systems part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Discrete event models for flexible manufacturing cells 33 for machines for MHS fm rm b Fig. 9. State process of a FMC with time-dependent failures a State process for a stateindependent failure model b Decomposed failure repair process. Because the failure repair behavior of the system components are independent the state process can be decomposed into two CTMCs as shown in Fig. 9 b. Analytically the state process is expressed by relations So 21 11 and SF 20 10 00 . For each state in SF no production is possible since the M0HS or both machines are down. In Fig. 2 b the failure repair behavior of each resource type machines or MHS is described by a unique Markov chain. Thus the transient state probabilities pij t can be obtained from relation pij t pi t Pj t 53 where pi t is the probability that i machines are working at time t for i 0 1 2. The probability pi t is obtained by solving separately the failure repair model of the machines. Pj t is the probability that j MHS load unload station and conveyor are working at instant t for j 0 1. Let fa and fm denote the failure rates of MHS and of a machine respectively. 34 Future Manufacturing Systems Operation dependent failures We assume that when the system is functional the resources are all fully utilized. Since failures occur only when the system is operational the state space is S 21 11 20 10 01 with S0 21 11 Sp 20 10 01 . The Markov chain model is shown in Fig. 10. Transitions representing failures will be allowed only when the resource is busy. Transitions rates can however be computed as the product of the failure rates and percentage utilization of the resource. If Tkij represents the average utilization of the kth resource in the state i j the transition rates are given in Fig. 10. Fig. 10. State process of a FMC with state-dependent failures A numerical example For the FMC presented in this paper in Table 1 the failure repair data of the system components are given. We notice that Tkij the system .

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