A general X-factor determination model for wafer fabrication

Shorten cycle time and maximum output are the major concerns of highly competitive industry, wafer fabrication in particular. X-factor theory presents the relationship between normalized cycle times and tools utilization. Using X-factor to identify the capacity constraint machine and its impact on overall cycle time performance is an effective way for shop floor control. Unfortunately, there is no any consideration about the batching process in pervious studies. In addition, the different arrival pattern of un-batching process will also lead to different model of X-factor determination. Thus, the purpose of this paper is to establish a general model to determine the X-factor for all types of machines in wafer fabrication. In this X-factor determination model, GI/G/m queuing theory is applied for the aggregated cycle time estimation. The machine downtime variability, lot arrival variability, batching processing, and un-batching processing are taken into account. Besides, regarding to the waiting time estimation of batching process, we define two types of queues in front of these processes. The first queue is to form a batch and the second one is to wait for processing separately. The same definition is applied to the un-batching process except the first queue is to wait for un-batch. By using the completed cycle time estimation, the general X-factor determination model is established. Finally, the measurement was tested by simulation to demonstrate its feasibility.