Aggregate modeling in semiconductor manufacturing using effective process times

Transcription

1 Aggregate modeling in semiconductor manufacturing using effective process times C.P.L. Veeger 1, L.F.P. Etman 1, A.A.J. Lefeber 1, I.J.B.F. Adan 2, J. van Herk 3, and J.E. Rooda 1 1 Systems Engineering Group, Department of Mechanical Engineering, TU/e 2 Stochastic Operations Research Group, Department of Mathematics and Computing Science, TU/e 3 NXP Semiconductors Nijmegen Eindhoven, June 24, 21 1 / 19

2 1 Background 2 EPT-based aggregate modeling 3 Objective and contributions 4 Single-server aggregate model with overtaking 5 Aggregate modeling of networks of workstations 6 Conclusions and recommendation 2 / 19

3 Motivation Performance analysis: high throughput versus low cycle times 3 / 19

4 Modeling of semiconductor manufacturing systems Modeling challenge: complexity versus accuracy Aggregate modeling concept: combine several factory floor aspects into a single EPT distribution 4 / 19

5 Estimating the EPT distribution Reconstruct EPT realizations from measured arrivals and departures 5 / 19

6 Example Time EPT 1 EPT 2 EPT 3 EPT 4 Legend Processing Queueing Machine breakdown Setup Waiting for operator 6 / 19

7 Objective and contributions Objective: Develop EPT-based aggregate models for semiconductor manufacturing Contributions: Single-server aggregate model with overtaking has been developed Aggregate model has been validated for a lithography workstation, using a simulation and an industry case Experiments are performed to model a network of workstations 7 / 19

8 Workstation abstraction Workstation is modeled as a single server (timer) with an EPT distribution and a distribution for overtaking of lots 8 / 19

9 Simulation case 9 / 19 The proposed aggregate model is illustrated using a simulation model of a four-machine lithography workstation: Each machine has three sequential processing steps and a one-place buffer Process step 2 is the bottleneck process Machines have recipe qualification Workstation operates at δ/δ max =.8

10 Measured EPT and overtaking distribution 2.5 Mean EPT as function of w 1 CV of EPT as function of w Overtaking distribution 1 Mean EPT CV of EPT Work in Process (w) w w = 1 w = 5 w = 1.2 w = Number of overtaken lots Cumulative probability 1 / 19

11 Predictions of the cycle time distribution.25.2 Throughput ratio =.6 observed predicted.25.2 Throughput ratio =.8 Throughput ratio = Probability Cycle time Cycle time Cycle time Observation: The tail of the cycle time distributions is accurately predicted, also at throughput other than the working point (δ/δ max =.8) 11 / 19

12 Crolles2 case Lithography workstation in Crolles2 wafer fab consisting of 14 track-scanner machines: Raw data extracted from Manufacturing Execution System (MES) Process MES data to deal with hold lots, and merging lots ±4 arrivals and departures obtained from processed MES data EPT and overtaking realizations calculated EPT and overtaking distribution parameters determined Cycle time distribution predicted by aggregate model 12 / 19

13 Model parameters Mean EPT Measured Fitted curve Work in Process (w) CV of EPT Measured Fitted curve w w = 1 w = 5.2 w = 15 w = Number of overtaken lots 1 Cumulative probability Curve fit for mean EPT and coefficient of variability of EPT Overtaking distribution function without fit 13 / 19

14 Results Throughput working point Measured Predicted.9 * throughput w.p..8 * throughput w.p. Probability Cycle time Cycle time Cycle time Tail of cycle time distribution accurately predicted at the working point Simulation case suggests that accurate predictions for the tail of the distribution can be made for throughput levels other than the working point 14 / 19

15 Network abstraction Model re-entrant flow line by a single-server aggregate model 15 / 19

16 Simulation case Simulation case of a re-entrant flow line, in which we vary: Length of the flow line Number of parallel servers Coefficient of variability of process and inter-arrival time Number of re-entrant cycles Number of measured EPT realizations 16 / 19

17 Measured mean EPT workstations Measured Fitted Curve workstations workstations Mean EPT Work in process Work in process Work in process Challenge: find a fitting procedure that fits the available data and extrapolates for other WIP levels 17 / 19

18 Mean cycle time predictions Mean cycle time workstations Measured Predicted working point workstations workstations Throughput ratio Throughput ratio Throughput ratio Accurate cycle time prediction in region around the working point 18 / 19

19 Conclusions Conclusions: A single-server aggregate model with overtaking has been developed to predict the cycle time distribution in semiconductor manufacturing Single-server aggregate model has been validated using simulation cases and an industry case First results of EPT-based aggregate modeling of networks are promising Recommendation: investigate a fitting procedure to estimate the mean and CV of the EPT as a function of the WIP, in particular for growing network size. 19 / 19