The Phase I Dispersion Charts for Bivariate Process Monitoring Aamir Saghir, a * † Yousaf Ali Khan b and Subha Chakraborti c Multivariate control charts are usually implemented in statistical process control to monitor several correlated quality characteristics. Process dispersion charts are used to determine the stability of process variation (which is typically done before monitoring the process location/mean). A Phase-I study is generally used when population parameters are unknown. This article develops Phase-I |S| and |G| control charts, to monitor the dispersion of a bivariate normal process. The charting constants are determined to achieve the required nominal false alarm probability (FAP 0 ). The performance of the proposed charts is evaluated in terms of (i) the attained false rate and (ii) the probability of signaling for out-of-control situations. The analysis shows that the proposed Phase-I bivariate charts correctly control the FAP (the false alarm probability) and detect a shift occurring in the bivariate dispersion matrix with adequate probability. An example is given to explain the practical implementation of these charts. Copyright © 2015 John Wiley & Sons, Ltd. Keywords: false alarm probability; joint distribution; in-control process; process dispersion 1. Introduction I n modern statistical process control (SPC) applications, it is common to monitor several correlated quality characteristics simultaneously. Average control charts are used for monitoring process location, while dispersion charts are used for monitoring process variation. A lot of work has been done so far to extend the univariate Shewhart charts, cumulative sum (CUSUM) charts and exponentially weighted moving average (EWMA) charts to multivariate data. These include the Hotelling’s T 2 -chart, the multivariate CUSUM chart and the multivariate EWMA chart and are available in many textbooks, including Montgomery. 1 For more details on and review of multivariate control charts, see, Bersimis et al., 2 Dogu and Kocakoc, 3 Hawkins and Deng, 4 Saghir, 5 Vargas and Lagos 6 , Yeh et al. 7 and Zhang et al. 8 It is generally accepted in the literature that a control chart is implemented in two phases: Phase-I (so called retrospective phase), to establish and define the stable state of the process and to estimate any unknown parameters; and Phase-II (prospective phase), to monitor the process (Chakraborti et al., 9 Human et al., 10 Zwetsloot et al. 11 ). Jones-Farmer et al. 12 review the major issues and developments in Phase-I analysis. One major issue is the choice of the Phase-I sample. The unusual observations in Phase-I can lead to the widening of the control limits which reduces their power to detect process changes in Phase-II. Therefore a successful Phase-II analysis depends on a successful Phase-I analysis in estimating the in-control (IC) mean, variance and covariance parameters (Yahaya et al. 13 ). Other recent studies on the Phase-I control charts include Chakraborti et al., 9 Human et al., 10 Saghir, 14 Jones-Farmer et al., 12 Kumar and Chakraborti, 15 Ning et al., 16 Zwetsloot et al., 17 etc. In the context of multivariate data, process variability is summarized in the variance–covariance matrix Σ. The population generalized variance (|Σ|) is a single quantity that has been used to represent the population dispersion (Khoo and Quah 18 ). The |S| chart is popularly used in application for monitoring (|Σ|) in Phase-II analysis (Montgomery 1 ). The multivariate control charts are generally constructed based on the assumption that the underlying process follows a multivariate normal distribution. In cases when the process distribution deviates from multivariate normality, these charts lose their efficiency as discussed by Saghir. 5 In such situations, a robust control chart is preferable. Robustness is a desired property of any control chart, and a lot of work has been done to develop robust control charts for monitoring of location and dispersion of a process (Abu-Shaweish et al., 19 Adewara and Adekeye, 20 Alfaro and Ortega, 21 Alkahtani, 22 Chenouri and Variyath, 23 Saghir and Lin, 24 Variyath and Vattathoor 25 and Zwetsloot a Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan b Department of Statistics, University of Hazara, Manshera, Pakistan c Department of Information Systems, Statistics and Management Science, University of Alabama, Tuscaloosa, USA *Correspondence to: Aamir Saghir, Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan. † E-mail: aamirstat@yahoo.com Copyright © 2015 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2015 Research Article (wileyonlinelibrary.com) DOI: 10.1002/qre.1915 Published online in Wiley Online Library