Phase I Statistical Process Control Charts: An Overview and Some Results

ABSTRACT

In practice, Phase I analysis constitutes an integral part of an overall SPC program in which control charts play a crucial role. An overview of the literature on Phase I parametric control charts for univariate variables data is presented. Since the Phase I signaling events are dependent and multiple signaling events are to be dealt with simultaneously in making an in-control or out-of-control decision, the joint distribution of the charting statistics is used to control the false alarm probability, which is defined as the probability of at least one false alarm, while designing the charts. An example is given. Concluding remarks include suggestions regarding future research problems.

KEYWORDS:

• change-point
• exponential distribution
• false alarm probability (FAP)
• false alarm rate (FAR)
• mean
• normal distribution
• Phase II
• prospective
• retrospective
• variance

ACKNOWLEDGEMENTS

We thank the referees and the editor for their constructive comments and suggestions. The second and third authors would also like to thank the Department of Statistics and STATOMET of the University of Pretoria for support.