Inventory modeling yields significant cycle-time improvements
01/01/1999
CYCLE TIME
Inventory modeling yields significant cycle-time improvements
Dr. Donald W. Collins, Arizona State University East, Mesa, Arizona
Heuristic simulation modeling, specifically the 1-Step Ahead Minimum Inventory Variability Resource Scheduling Policy (MIVP),* has demonstrated productivity-improving reductions in cycle time in a wafer fab. Such fundamental and incremental improvements, while often difficult, can be extremely beneficial: an increase in production as small as 1% can potentially result in increased sales of $200,000-$300,000/month for a semiconductor manufacturer. The difficulty is that changing normal strategies in what is already a productive fab requires substantial supporting evidence that any change will be successful.
Briefly described, the theory behind our approach uses two basic laws:
Little`s Law, better known as the law of inventory in queuing theory, equates inventory to the product of mean arrival rate of products for processing and total processing time plus the total waiting time involved.
Kingman`s Formula accounts for random variations in arrival and processing times due to variability, where inventory depends on input variability, capacity variability, and input and processing rates.
Implemented in MIVP, this approach uses scheduling and release policies to introduce maximum correlation between wafer-lot inter-arrival times and service times, thereby reducing total wait times throughout the fab. Dynamic inventory will stay close to the long-term historical average inventory in a stable factory and cause the historical average to improve over time. This leads to a reduction of scheduling variability, reduction in total inventory, and reduction in mean cycle time.
Without proper scheduling, large queues at wafer processing operations cause an unbalanced fab line: Some stations are overloaded and some are starved. The mean cycle time will rise due to local starvation even though the total system inventory stays approximately the same, and it will rise due to the waiting time in the queue for those overloaded processing stations. The goal is to balance the production line to reduce work-in-progress (WIP) variability.
With MIVP, we dynamically applied a decision set of rules in parallel throughout the fab. This distributed processing balances the total production line and keeps the compute time for the schedule to a minimum. For example, if four process steps may require system "A," which feeds the next system (i.e., the "bleeder system") in the process flow, which process step should we choose? One of the software`s many objectives is to look at the next downstream queue and select the lot that will leave its instantaneous queue length below its historical average. The selected lot is processed and when machine "A" becomes available again, the MIVP rules are invoked and another optimum choice is made in relation to historical queues.
Understanding fab dynamics
Modeling a wafer fab first requires a clear understanding of its dynamics. In manufacturing, companies use process resource schedulers and product release policies that agree with common sense and can be implemented on the factory floor. Any improvements must provide some combination of meeting delivery schedules, reducing product cycle times, increasing product yield and throughput, optimizing equipment utilization, and increasing confidence for on-time delivery and profits. Demonstrable success is key.
A global understanding of all the complexities in wafer fabrication, from raw wafer arrival through shipping a wafer, is required to improve scheduling and release policies. The re-entrant nature of certain critical processes - variations in recipes for processing when there are multiple products, the random nature of tool failures and repairs, and labor - introduce a high level of complexity. Any fab simulation model must accurately include this large number of variables.
To minimize cycle time, one must reduce inventory or increase capacity, according to Little`s Law. Kingman`s Formula shows that a reduction of variability can also affect cycle time and reduce inventory. A balanced production line is one where, given a fixed input and output schedule, the mean WIP does not increase over time due to randomness of tool failures and repairs. Fab section managers will often introduce a safety factor in their tool capacity numbers that considers this randomness; they attempt to protect against this variability to maintain a certain WIP and cycle time objective through their section of the fab. One of the greatest obstacles to fab modeling is the understandable resistance to introducing new scheduling policies that reduce cycle time and increase capacity at the same time.
Unbalancing of a production line can be caused by such unpredictable disturbances as equipment failures and repairs, personnel decisions, and power failures. These disrupt the stable flow of product and may result in large queues for some tools while others are idle. Large queues, no matter what the cause, are "bottlenecks," requiring days or weeks to rebalance the production line. Bottlenecks cause product to wait for service, thereby increasing cycle time. (We define cycle time as the sum of total processing time - all the raw processing times for each step in a production flow - and the total queueing time - all queue waiting times for resource service for each step in a production flow.)
Often millions of dollars are spent on equipment to increase capacity at a critical bottleneck, reducing cycle time locally, but overall cycle time may not decrease. Local improvement may simply move the bottleneck to another location in the fab - a crucially important point.
Our target fab used a product release policy based on customer orders and a WIP chart. Scheduling of fab tools was based on first-in-first-out (FIFO) at high-speed tools and due-date-first (DDF) at bottleneck tools, except for high priority lots (MAXIs). Stochastic discrete event simulation modeling is valuable for comparing FIFO to MIVP-based scheduling and release policies. Company-specific decision rules, relying on company management and operators` experience, can be integrated with MIVP to obtain the best performance. The rules can be easily implemented by operators on a factory floor.
The development of the baseline fab simulation model is a long and tedious process, but if done with care and flexibility for future updates, it will serve as an additional tool for management decisions. The validated fab simulation model compares baseline data of FIFO, DDF, and MAXI lots with MIVP.
Application to a fab
The specific fab produces 73 different products on 55 different production flows using 185 to 395 individual processing steps (263 average). Ten products are on the factory floor at any given time, involving 485 wafer-processing systems in 132 machine groups. A product can re-enter a specific group between six and 14 times. Adding in the variability of system failure and repair, short interval scheduling based on knowledge of the global process is important.
Our objective was to reduce cycle time to 29 days on average and 32 days with 95% confidence, within a certain time frame. To apply simulation modeling, we conducted weekly seminars for section managers to introduce cycle time reduction and MIVP
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Cycle time reduction achieved at a semiconductor fab.
implementation procedures. We formulated a fab model using feedback from all these individuals. Finally, we collected fab data for all devices manufactured in the last two years. This included 34 production flows for 55 devices.
Once we had validated the fab model, we ran it to simulate three years of production. (This took two weeks using a 100-MHz Intel Pentium PC!) The first year was discarded due to model ramp-up bias; the remaining years provided historical queue data using FIFO and DDF as a baseline.
With the FIFO baseline data collected, we switched to MIVP resource scheduling and again ran the three-year production simulation, again truncating the data to the last two years. The dramatic result was that average cycle time with MIVP was 35% lower than with FIFO.
We implemented the new method maintaining MAXI priority schedules because of commitment to certain customers, but the FIFO and DDF procedures were changed to incorporate the MIVP resource scheduler when variability required a change. Implementation was done under close supervision of Prof. Collins, the developer of the method. For example, when problems occurred in the fab, such as equipment failures at bottlenecks, he instructed section managers and operators on how to use MIVP`s WIP charts and priority matrix to get around the problem. Typically, this involved slowing down wafers headed for downed equipment while speeding up the wafers headed for the up equipment. The only exceptions were the small percentage of MAXI lots in production.
We accomplished and even surpassed our 29-day objective, hitting a 26.34-day cycle time - a 29.7% reduction (see figure). We achieved our 32-day, 95% confidence objective, hitting 31.61 days for a 32.9% reduction in cycle time. Over this same period, we decreased wafer starts only 1.9% and increased wafers shipped 2.3%. Wafer yields increased 0.15%, and wafer scrap decreased 23%. In the longer term, these methods have been applied in three production fabs with 15-45% reductions in cycle time.
DONALD COLLINS is a professor in the department of manufacturing and aeronautical engineering technology in the College of Technology and Applied Sciences at Arizona State University East, Mesa, AZ . 85206; ph 602/727-1187; fax 602/727-1549; e-mail [email protected] or [email protected].