Control charts based on medians

Abstract

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.

A Note on the Median Control Chart

“…, where f is the unknown density of F. The variety of the median control charts comes from a group of various consistent estimates of 1/(4 f 2 (θ)) (Nelson, 1982;Janacek and Meikle, 1997;Khoo, 2005). Park (2008Park ( , 2009 proposed several median control charts through an estimation of the variance ofθ with various bootstrap methods.…”

“…As an alternative control chart for the detection of location shift, a median control chart can also be applied when the distribution of the process may not be normal. Many median control charts have been proposed using the limit distribution of a sample median with various algorithms for the estimation of variance according to asymptotic normality (Nelson, 1982;Janacek and Meikle, 1997;Park, 2008Park, , 2009). The non-availability of exact distribution of any sample median is the main reason for the difficulty of the construction of the median control charts.…”

Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

“…This approach, presented by Chakraborti et al (2004), has been recently exploited by Balakrishnan et al (2008) to study a generalization of the classical median control chart (see Janacek and Meikle, 1997). By transforming the random variables X a:b with the use of Eq.…”

A Note on the Robustness of the X Chart to Non-Normality

“…In theory, theX-chart assumes that the quality characteristic is from normal distribution or the number of its observations is large enough for the central limit theorem to hold. As previous authors, such as Bai and Choi (1995), Roes and Does (1995), Janacek and Meikle (1997), have remarked the observations are often from a non-normal distribution and its size is not large in practice. Moreover, the control parameters such as µ and σ 2 are usually unknown and therefore estimated.…”