Premium
A Robust X ¯ Control Chart
Author(s) -
Schoonhoven Marit,
Does Ronald J. M. M.
Publication year - 2013
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1447
Subject(s) - control chart , estimator , standard deviation , statistics , chart , control limits , standard error , robust statistics , x bar chart , mathematics , normality , computer science , process (computing) , operating system
This article studies alternative standard deviation estimators that serve as a basis to determine the X ¯ control chart limits used for real‐time process monitoring (phase II). Several existing (robust) estimation methods are considered. In addition, we propose a new estimation method based on a phase I analysis, that is, the use of a control chart to identify disturbances in a data set retrospectively. The method constructs a phase I control chart derived from the trimmed mean of the sample interquartile ranges, which is used to identify out‐of‐control data. An efficient estimator, namely the mean of the sample standard deviations, is used to obtain the final standard deviation estimate from the remaining data. The estimation methods are evaluated in terms of their mean squared errors and their effects on the performance of the X ¯ phase II control chart. It is shown that the newly proposed estimation method is efficient under normality and performs substantially better than standard methods when disturbances are present in phase I. Copyright © 2012 John Wiley & Sons, Ltd.