QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, VOL. zyxwvu 11, 101-105 (1995) zyxw A KALMAN FILTERING PROCESS CONTROL SCHEME WITH AN APPLICATION IN SEMICONDUCTOR SHORT RUN MANUFACTURING ENRIQUE DEL CASTILLO zyxwvutsr Department of Industrial Engineering, University of Texas at Arlington, Arlington TX 7601 zyxw 9-001 7, zyxw US. A. AND DOUGLAS C. MONTGOMERY Department of Industrial Engineering, Arizona State University, Tempe, A Z 85287, U.S.A. SUMMARY A quality control chart for monitoring a short run process during the start-up phase is presented in this article. The chart is based on the Kalman filter recursive equations being applied to a stable process where the process variance is unknown prior to the start of the production run. The run length properties of this control scheme are discussed. It is shown that for the proposed scheme the run length properties are independent of the unknown process variance and that these properties are appropriate for monitoring a stable process during start-up. An economic model for the optimal design of the control scheme is presented and illustrated with a wet etching process used in semiconductor manufacturing. zyxwvuts KEY WORDS: short runs; Kalman filtering; quality control charts; semiconductor manufacturing INTRODUCTION In a short-run manufacturing environment, a com- mon approach for monitoring the quality of the products is to monitor the deviations from target. This is in contrast to traditional quality control charts, where the chart scheme should discriminate between common or random variation and assign- able causes of variation (see Reference 1, for example) without any reference to specifications. In a short-run environment, estimates of the process mean and variance may not be available prior to starting production, and setting control limits at the early stages of production is very difficult due to the lack of process data. Instead of testing for a ‘lack of control’, short run control charts test for a significant deviation from target. This corresponds to the third case studied by Quesenberry2 and Del Castillo and M~ntgomery.~ Short run processes are frequently found in sem- iconductor manufacturing where batch sizes of sili- con VLSI wafers can be smaller than 50 units in some custom applications. We define a batch of product as a single production run of wafers. Wafers may be processed individually, but they are returned to the batch after the operation is complete. We assume in this paper that the quality charac- teristic follows a stable process of the form Y, zyxwvuts = po + E, where E, is a normal random variable with mean 60 and variance a2, or equivalently, CCC 0748-8017/95/020101-05 zyxwvut 0 1995 by John Wiley & Sons, Ltd. x, = Y, - po = E, (1) where X, represents the deviation from target at time t and 6 is the size of the shift in the process level measured in standard deviations u. The process variance, u2, is assumed unknown, and the sample size is assumed equal to one, which is common practice in many short-run manufacturing environ- ments. We assume a stable process during the start- up phase. This is likely to be encountered in well- established processes. In this paper we present a Kalman filtering approach for monitoring process (1). After describing the Kalman procedure and control chart, we present an economic approach for designing the chart. Finally, we apply the economic model to a short-run manufacturing process from the semiconductor industry. DESCRIPTION OF THE KALMAN CONTROL SCHEME A control scheme can be developed for a stable process using the Kalman filter recursive equations applied to process (1) expressed in the simple state- space form: p, = krp1, system equation X, = kr + E,, observation equation The recursive equations to estimate p,, the system’s level at time t, are given by Received 11 April 1994 Revised 11 November 1994