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Phase I Control of Simple Linear Profiles with Individual Observations


Correspondence to: Arthur Yeh, Department of Applied Statistics and Operations Research, Bowling Green State University, Bowling Green, OH 43403, USA.



Most of the existing literature on phase I control of simple linear profiles requires multiple observations because the profile parameters need to be estimated given each subgroup of observations. Such a requirement may not be attainable in practical applications in that the observations collected in phase I for assessing whether the process is in control and estimating the profile parameters may not necessarily follow what is prescribed by the existing phase I methods. This is particularly the case for processes in which only few observations or a single observation per subgroup can be obtained for phase I control. In this work, a control charting mechanism based on a change-point model is proposed for phase I control of simple linear profiles with individual observations. The proposed charting mechanism consists of two control charts. The first control chart, which is essentially based on a likelihood ratio test, is used to monitor the profile parameters. The error standard deviation is monitored using a second control chart, which is constructed on the basis of the recursive residuals. Simulation results show that the control charting mechanism is effective in detecting sustained changes in the profile parameters and/or error standard deviation. The proposed phase I control charting mechanism is used in an application to demonstrate how the proposed control charts can be applied in practice. Copyright © 2012 John Wiley & Sons, Ltd.