The median chart with estimated parameters

Philippe Castagliola · Fernanda Figueiredo

38 citations0/0 files storedEuropean J of Industrial Engineering

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

A modified median chart with estimated control limits is proposed for monitoring the mean value of a normal process. The estimates for the nominal process parameters used to set up the control limits in Phase I are the average of the sample medians and the average of the sample ranges of m initial subgroups of size n. The run length properties of the chart are examined, and the obtained results lead us to conclude the proposed chart present an interesting RL performance (at least for an adequate choice of the chart parameter used to determine the control limits). Control chart parameters are provided for a specific in-control average run length of 370.4 for several combinations of n and m, which facilitates the use of the chart by practitioners, and an illustrative example of implementation of the chart is presented. Some recommendations are also given about the minimum number of initial subgroups m that must be considered to implement the chart with the constant parameter used in the case of known nominal values, and in order to obtain the expected performance.

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References

2006Effects of Parameter Estimation on Control Chart Properties: A Literature Review 1993The Effect of Sample Size on Estimated Limits forXandXControl Charts 2001The Performance of Exponentially Weighted Moving Average Charts With Estimated Parameters 1991SPCQCharts for Start-Up Processes and Short or Long Runs 1987Self-Starting Cusum Charts for Location and Scale 1969X- and R-Chart Control Limits Based on a Small Number of Subgroups 2002The Statistical Design of EWMA Control Charts with Estimated Parameters 2009An EWMA chart for monitoring the process standard deviation when parameters are estimated

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2017Run Rules median control charts for monitoring process mean in manufacturing 2019A Synthetic median control chart for monitoring the process mean with measurement errors 2017The performance of EWMA median and CUSUM median control charts for a normal process with measurement errors 2018The performance of the adaptive EWMA median chart in the presence of measurement error 2017Guaranteed conditional design of the median chart with estimated parameters

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