A Distribution‐free Control Chart for the Joint Monitoring of Location and Scale

Abstract

Traditional statistical process control for variables data often involves the use of a separate mean and a standard deviation chart. Several proposals have been published recently, where a single (combination) chart that is simpler and may have performance advantages, is used. The assumption of normality is crucial for the validity of these charts. In this article, a single distribution‐free Shewhart‐type chart is proposed for monitoring the location and the scale parameters of a continuous distribution when both of these parameters are unknown. The plotting statistic combines two popular nonparametric test statistics: the Wilcoxon rank sum test for location and the Ansari–Bradley test for scale. Being nonparametric, all in‐control properties of the proposed chart remain the same and known for all continuous distributions. Control limits are tabulated for implementation in practice. The in‐control and the out‐of‐control performance properties of the chart are investigated in simulation studies in terms of the mean, the standard deviation, the median, and some percentiles of the run length distribution. The influence of the reference sample size is examined. A numerical example is given for illustration. Summary and conclusions are offered. Copyright © 2011 John Wiley & Sons, Ltd.

Performance evaluation of joint monitoring control charts

“…Moreover, a traditional approach used in SPC is to monitor each parameter separately; however, simultaneous monitoring of more than one parameter is also becoming popular in industry. Chowdhury et al [5], McCracken and Chakraborti [6], Mukherjee and Chakraborti [7], and Mukherjee et al [8] and the references therein may be seen in literature on simultaneous charts.…”

“…Recently, Mukherjee and Chakraborti [7] have proposed a Shewhart-type distribution-free chart for joint monitoring of the process parameters. It is based on the Lepage test, a combination of Wilcoxon rank sum test for location and Ansari Bradley test for scale (cf.…”

Optimal design of a nonparametric Shewhart-Lepage control chart

“…When using these control charts for variables data, estimating in-control parameters and checking the normality assumption are the very important step. Nonparametric Shewhart-Lepage chart, proposed by Mukherjee and Chakraborti (2012), is an attractive option, because this chart uses only a single control statistic, and does not require the in-control parameters and the underlying continuous distribution. In this paper, we introduce the Shewhart-Lepage chart, and propose the design procedure to find the optimal diagnosis limits when the location and the scale parameters change simultaneously.…”

“…In this paper, we introduce the Shewhart-Lepage chart, and propose the design procedure to find the optimal diagnosis limits when the location and the scale parameters change simultaneously. We also compare the efficiency of the proposed method with that of Mukherjee and Chakraborti (2012 …”

Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts

“…They noted a nearly 200% growth on research in nonparametric process control charts in the first half of the current decade. Interested readers may see Chakraborti and Graham (2007), Chakraborti et al (2011), Graham et al (2012Graham et al ( , 2014, Mukherjee and Chakraborti (2012), Mukherjee et al (2013), Balakrishnan et al (2015) Mukherjee and Sen (2015), Li et al (2016) and Mukherjee and Marozzi (2016b) among others for various aspects of nonparametric control charts. Some other recent works include Hawkins and Deng (2010) who considered a nonparametric control chart under a change-point set-up and Abbasi et al (2013) who considered a nonparametric control chart for the progressive mean.…”