On the performance of different control charting rules

Abstract

On the performance of different control charting rules Riaz, M.; Mehmood, R.; Does, R.J.M.M. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. In the literature a number of control charting rules are proposed to decide whether a process is in control or out of control. Some issues with these rules will be highlighted in this article. By redefining and listing a set of rules we will evaluate their performance on theX, R, S and S 2 charts. Also we will compare the performance of these rules using their power curves to figure out the superior ones. Application of a few of these rules with real data sets will show their detection ability and use for practitioners.

Control charts for location based on different sampling schemes

“…In case of SRS, a number of authors have defined sensitizing rules and runs rules schemes for different control charts to improve the detecting ability for small and moderate shifts. These rules are described and evaluated in the Western Electric Statistical Quality Control Handbook [31], and in the articles of Khoo [11], Khoo and Ariffin [12], Acosta-Mejia [3], Koutras et al [13], Antzoulakos and Rakitzis [6], Acosta-Mejia and Pignatiello [4] and Riaz et al [25], among others.…”

Efficient power computation for r out of m runs rules schemes

“…In order to overcome these issues with the runs rules Riaz et al (2011) provided an extended and compact form of the runs rules and recommended their application in industrial processes for efficient process monitoring.…”

“…Therefore, some efficient code is needed which addresses and overcomes these complications and is flexible for a variety of distributions useful for practical purposes. In this study we develop an efficient code for different normal and non-normal distributions in the R language which addresses issues (i) through (v), particularly with reference to Riaz et al (2011). The choice of the R language is made due to its friendly environment, easy access, interactive software environment for statistical computations and graphics, its de-facto standard behavior and implementation link with the S programming language, and its wide application among statisticians and researchers of other fields.…”

“…Before discussing the said code in the R language we review first the methodological details of all the rules and procedures of Riaz et al (2011).…”

“…In this set of rules the phrase "at least" is in fact the suggested modification for these runs rules schemes which helps to overcome the above mentioned problems (ii), (iii) and (v) and gives an attractive independence to each rule. The signaling limit h r/m is set according to a pre-specified value of false alarm rate for a given value of n and it is obtained using the mathematical (m−r ) , where α is the pre-specified false alarm rate and p is the probability of a single point falling outside the respective signaling limits depending upon r and m. For more details the interested reader is referred to Riaz et al (2011).…”