Control charts based on medians By G. J. JANACEK University of East Anglia, Norwich, UK and S. E. MEIKLE British Aluminium Extrusions, Banbury, UK [Received August 1993. Final revision August 1996] SUMMARY Control charts are widely accepted and used in manufacturing industry. However, surprisingly often the data sets that they are used to analyse come from markedly non-normal populations. A modification of the control charts based on medians is proposed which overcomes non-normality problems. These median charts keep the traditional format and have reasonable power. The format is vital, for if the charts are to be used on the shop-floor then they must be acceptable and as we mimic accepted practice our proposals fulfil this requirement. Keywords: Control charts; Medians; Non-normality; Order statistics; Statistical process control 1. Introduction The basic idea of a control chart is very simple. Suppose that we manufacture items and there is some dimension or feature which it is important to control. To monitor the manufacturing process samples of say n items are drawn from the process at regular intervals and the important feature measured. The presence of a source of non-random variation in the measured feature is assumed to show up in the samples as a variation in the measurements which is outside the range of a normal variate. This variation is attributed to a change in the mean μ or the variance σ 2 and to detect such changes we use estimated values of μ and σ 2 from our samples. A sequence of graphical tests for changes in mean or variance can thus be conducted; see for example Wetherill (1977). Unfortunately, if our populations are markedly non-normal then using simple ideas based on testing means may give rise to inappropriate charts that will either fail to detect real changes in the process or which will generate spurious warnings when the process has not changed. To circumvent this problem and yet to keep the essential structure of traditional control charts we suggest modifications based on simple distribution-free methods. For different approaches see Ferrell (1964) and Von Osinski (1962). An obvious question that might be asked at this point is do sufficiently non-normal distributions occur in practice to warrant an alternative to accepted control chart practice? The customary answer among practitioners is no (see for example Dale and Shaw (1991)) and to assume that either variation is normal or that the central limit theorem will sort out the problem. We believe that this is a mistake. There are production situations where the variation of interest cannot possibly be normal, e.g. when measuring some deviation from nominal, where an absolute value is required. More importantly, it is our experience that non-normal 1997 Royal Statistical Society 0039–0526/97/46019 The Statistician (1997) 46, No. 1, pp. 19–31 Address for correspondence: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK. E-mail: G.Janacek@uea.ac.uk