Identification of Statistical Distributions for Cycle Time in Wafer Fabrication

Abstract

Wafer fabrication is characterized with complex production processes, advanced equipment, and high variability. Cycle time (CT) is a key performance measure in fab operations affecting other measures, such as throughput and cost. Previous studies use analytical and empirical methods in investigating CT. Theoretical statistical distribution of CT have seldom been studied, while in other scientific fields they have been frequently used for analysis and modeling, for example, in economics and medicine. This work investigates the theoretical statistical distribution of CT of a wafer lot in a production step, based on actual data originating at various processes and equipment types of a wafer fab. The data is evaluated with goodness of fit methods for ten distributions describing time. The evaluation results with suggesting Burr and Dagum as the best fitted distributions, known in economics for income. This conclusion differs from the common distributions assumed for CT, as Gamma, Weibull, and their special cases. The results are strengthened with additional analysis of their hazard functions. Log-logistic and lognormal can also be used for mathematical simplicity. The identification of theoretical distributions for CT enables improved statistical analysis and system modeling of fab operation.