IEOR 130 Methods of Manufacturing Improvement Fall, 2018, Prof. Leachman Homework Assignment 8, Due Tuesday Nov. 13

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1 IEOR 130 Methods of Manufacturing Improvement Fall, 2018, Prof. Leachman Homework Assignment 8, Due Tuesday Nov Consider a factory operating at a steady production rate. Suppose the target WIP level is 200 lots. The average cycle time per lot from release to factory output is 50 days. (a) On average, how many lots leave the factory each day, and how many new ones are released into the factory? (Hint: Apply Little's Law.). (b) Suppose photo is the bottleneck work center and it is visited 5 times by each lot as it moves through the process flow. The processing time at each photo step is 5 hours per lot. There are five identical machines in the photo work center averaging 90% availability. What is the utilization of total time and the utilization of available time in the bottleneck work center? Assume the factory operates 24 hours per day, seven days per week. (c) The standard deviations of the cycle times between each photo exposure operation have been computed as follows: Fab-in to Layer days Layer 1 to Layer days Layer 2 to Layer days Layer 3 to Layer days Layer 4 to Layer days The sum of standard cycle times for the process steps in each layer are as follows: Layer 1-2 days Layer 3-4 days Layer 5-4 days Layer 2-4 days Layer 4-4 days Layer 6-2 days For a target cycle time of 50 days, determine the target WIP level in each layer. (d) For a 50-day target cycle time, what is the multiplier of standard cycle time? What is the value of the multiplier in the various layers? Why is the multiplier different in different layers? (e) What target cycle time would be equal to 2 times standard cycle time? 2. Consider a factory producing high-volume products. A particular type of processing machine performs several recipes with the following data:! 1

2 Actual Target Target Avg. Process On-hand WIP Recipe Downstream Downstream Fab Outs Time per and WIP arriving WIP WIP per shift Wafer (mins) this shift A B C D (a) Assuming the line yields are 100%, calculate the ideal production quantity (IPQ) for each recipe. (The IPQ is defined as the production quantity needed to bring the actual downstream WIP up to the target WIP level by the end of the shift, considering that one more shift's worth of fab outs must be added to the downstream WIP to replace the fab outs due in the current shift.) (b) Calculate the schedule score for each recipe. (The schedule score is defined as the IPQ divided by the average fab out rate over the cycle time from recipe start to fab out.) According to the schedule score, what is the priority ordering of the recipes? (c) The fab line has 2 machines of the type used to process recipes A, B, C and D. Considering the available WIP and the IPQ's, how many lots of each recipe should be allocated to each machine to be processed this shift? Assume all lots have 25 wafers, a shift lasts 8 hours, machine number one will be available all shift, and machine number two is due to receive a PM during the shift lasting 1.5 hours and will be otherwise available. 3. A wafer fab has a single process flow with five masking layers. The standard deviation of the cycle time between photo exposure operations has been computed as follows: Fab-in to Layer 1 exposure shifts (where one shift equals 8 hours) Layer 1 exposure to Layer 2 exposure shifts Layer 2 exposure to Layer 3 exposure shifts Layer 3 exposure to Layer 4 exposure shifts Layer 4 exposure to Layer 5 exposure shifts Layer 5 exposure to fab-out shifts The sum of standard cycle times for the process steps in each layer has been computed as follows: Layer 1-2 shifts Layer 3-4 shifts Layer 2-4 shifts Layer 4-4 shifts! 2

3 Layer 5-4 shifts Layer 6-2 shifts (a) The target cycle time for the entire fab process is 40 shifts. The target production rate is 10 lots per shift. Determine the target WIP level for each layer. (b) Currently, layer 5 has a WIP level of 110 lots. The photo stepper machines each can process two lots per hour when they are up; average availability of these machines is 90%. If two steppers are qualified to perform the layer 5 exposure, estimate how long it will take to reduce the WIP in layer 5 to the target level. (c) How many steppers would need to be qualified for layer 5 if the recovery time is to be within two hours, i.e., less than 0.25 shifts? (d) Now suppose at the start of a shift the actual WIP levels (expressed in lots) are as follows: Layer Total WIP WIP On-Hand Qualified in Layer at Photo step Steppers A,B,C,D C,D A,B,C,D D B Assuming fab-outs up until the start of the shift are exactly on time, determine the ideal production quantity (IPQ) and schedule score (SS) for each photo operation. (Each photo operation is the last operation in its layer.) (e) The fab has four total steppers (A, B, C, D). Each stepper is qualified to perform only certain photo operations, as specified in the table above. Assume that all four steppers will be available all 8 hours during the shift, and that the process time per lot is 0.5 hours for all photo operations. Suggest an efficient shift schedule for the four steppers. Assume that only WIP on-hand at photo may be scheduled for processing by the steppers. 4. A wafer fab operates a single process flow that has a photo step at the end of layers one through five. Layer six includes the remaining process steps after the last photo step. A detailed simulation of the fab has been run and stable steady-state statistics were collected as follows: Layer Avg. Wait time Std. Dev. Of Wait time Avg. No. of Lots! 3

4 in the layer (days) in the layer (days) in the layer The average output rate in the steady-state statistics of the simulation is 20 lots per day. (a) What was the steady-state average total cycle time in the simulation? (b) Suppose management sets the target cycle time for the process flow to be equal to the simulated average total cycle time. For an output rate of 20 lots per day, recommend target WIP levels in each layer. (c) Suppose fab outs to date are on time, and suppose the target output rate of 20 lots per day will be maintained for many weeks. The fab operates two 12-hour shifts per day. Suppose it is the start of a shift and the current WIP levels in each layer are as follows: Layer WIP (no. of lots) Calculate IPQs and Schedule Scores for each photo step. What is the priority order for scheduling the photo steps? (d) In the etch area of the fab, the process time per lot is 1 hour for all etch steps. There are two etch machines, M1 and M2. Each machine can perform any etch step. At the start of the shift, the etch area has the following data: Step IPQ (lots) Available WIP (lots) A 6 4 B 2 4 C D 2 8 The following shift schedule has been prepared by the etch area supervisor:! 4

5 Machine M1: Run 4 lots of A, then run 2 lots of B, then run 6 lots of C Machine M2: Run 8 lots of C, then run 4 lots of D Can this schedule be improved upon? If so, suggest the best schedule you can, and briefly note the reason why your schedule should be preferred over the schedule above.! 5