Using EWMA control schemes for monitoring wafer quality in negative binomial process

Abstract

The traditional control chart for nonconformities (called C control chart) assumes that process nonconformities follow a Poisson distribution. In actuality, however, the occurrence of nonconformities does not always observe Poisson distribution. For example, when nonconformities of wafers have clustering phenomenon in semiconductor production process, the process control based on Poisson distribution always underestimates the true average nonconformities and process variance. If the compound Poisson process is taken as the basis for process control, the quality feature could be described more accurately. When the process has minor variation, the sensitivity of the exponentially weighted moving average (EWMA) control chart is higher than the C control chart and more accurately reflects the current situation of the process on the control chart. Hence, this study considers Poisson–Gamma compound distribution for the failure mechanism, and takes the Markov chain approach to calculate the average run length produced by the EWMA control chart with different design parameters. Moreover, the EWMA control chart based on Poisson–Gamma compound distribution was constructed and actual data from a wafer plant were employed to illustrate the operation of the model. This study could be useful for detecting minor process variations in wafer plants and improving the process quality.