Short run spc based upon the second order dynamic linear model for trend detection

Abstract

Recently, several new applications of control chart procedures for short production runs have been introduced. Bothe (1989) and Burr (1989) proposed the use of control chart statistics which are obtained by scaling the quality characteristic by target values or process estimates of a location and scale parameter. The performance of these control charts can be significantly affected by the use of incorrect scaling parameters, resulting in either an excessive "false alarm rate," or insensitivity to the detection of moderate shifts in the process. To correct for these deficiencies, Quesenberry (1990, 1991) has developed the Q-Chart which is formed from running process estimates of the sample mean and variance. For the case where both the process mean and variance are unknown, the Q-chaxt statistic is formed from the standard inverse Z-transformation of a t-statistic. Q-charts do not perform correctly, however, in the presence of special cause disturbances at process startup. This has recently been supported by results published by Del Castillo and Montgomery (1992), who recommend the use of an alternative control chart procedure which is based upon a first-order adaptive Kalman filter model Consistent with the recommendations by Castillo and Montgomery, we propose an alternative short run control chart procedure which is based upon the second order dynamic linear model (DLM). The control chart is shown to be useful for the early detection of unwanted process trends. Model and control chart parameters are updated sequentially in a Bayesian estimation framework, providing the greatest degree of flexibility in the level of prior information which is incorporated into the model. The result is a weighted moving average control chart statistic which can be used to provide running estimates of process capability. The average run length performance of the control chart is compared to the optimal performance of the exponentially weighted moving average (EWMA) chart, as reported by Gan (1991). Using a simulation approach, the second order DLM control chart is shown to provide better overall performance than the EWMA for short production run applications

Keywords:

• dynamic
• linear model
• short run statistical process control (SPC)
• Bayesian estimation
• adaptive
• Kalman filter