Variables control chart limits and tests for special causes

Quality & Reliability Eng

et al. 2003

Several control charts for individual observations are compared. Traditional ones are the well-known Shewhart individuals control charts based on moving ranges. Alternative ones are non-parametric control charts based on empirical quantiles, on kernel estimators, and on extreme-value theory. Their in-control and out-of-control performance are studied by simulation combined with computation. It turns out that the alternative control charts are not only quite robust against deviations from normality but also perform reasonably well under normality of the observations. The performance of the Empirical Quantile control chart is excellent for all distributions considered, if the Phase I sample is sufficiently large.

“…. , x k )) 2 , by averaging these squares over the 10 000 training samples, and by substituting the appropriate averages into the above formula for the SDRL.…”

Section: Simulationsmentioning

confidence: 99%

A Comparison of Shewhart Individuals Control Charts Based on Normal, Non‐parametric, and Extreme‐value Theory

Vermaat

Ion²,

Quality & Reliability Eng

et al. 2003

“…Moreover, these control structures help implementing each rule independently and hence avoiding simultaneous application (cf. [9]) of many rules, which results in a simpler design structure.…”

Section: Proposed Control Charting Schemesmentioning

confidence: 99%

Control charts for location based on different sampling schemes

Mehmood

Riaz

Journal of Applied Statistics

2013

Control charts for location based on different sampling schemesMehmood, R.; Riaz, M.; 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. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Statistics, 2013 Vol. 40, No. 3, 483-494, http Control charts are the most important statistical process control tool for monitoring variations in a process. A number of articles are available in the literature for theX control chart based on simple random sampling, ranked set sampling, median-ranked set sampling (MRSS), extreme-ranked set sampling, double-ranked set sampling, double median-ranked set sampling and median double-ranked set sampling. In this study, we highlight some limitations of the existing ranked set charting structures. Besides, we propose different runs rules-based control charting structures under a variety of sampling strategies. We evaluate the performance of the control charting structures using power curves as a performance criterion. We observe that the proposed merger of varying runs rules schemes with different sampling strategies improve significantly the detection ability of location control charting structures. More specifically, the MRSS performs the best under both single-and double-ranked set strategies with varying runs rules schemes. We also include a real-life example to explain the proposal and highlight its significance for practical data sets. Journal of Applied

“…Therefore, another solution is to apply corrections to the control chart limits to take parameter estimation into account. For example, Hillier (1969), Does and Schriever (1992) and Schoonhoven, Riaz, and Does (2009) provide corrections leading to a desired value of the FAR in expectation. Next to that, more recent works (e.g.…”

Section: Introductionmentioning

confidence: 99%

Correction factors for Shewhart and control charts to achieve desired unconditional ARL

Goedhart

Schoonhoven

International Journal of Production Research

2016

In this paper we derive correction factors for Shewhart control charts that monitor individual observations as well as subgroup averages. In practice, the distribution parameters of the process characteristic of interest are unknown and, therefore, have to be estimated. A well-known performance measure within Statistical Process Monitoring is the expectation of the average run length (ARL), defined as the unconditional ARL. A practitioner may want to design a control chart such that, in the in-control situation, it has a certain expected ARL. However, accurate correction factors that lead to such an unconditional ARL are not yet available. We derive correction factors that guarantee a certain unconditional in-control ARL. We use approximations to derive the factors and show their accuracy and the performance of the control charts -based on the new factors -in out-of-control situations. We also evaluate the variation between the ARLs of the individually estimated control charts.