Second stage short run (X̄, vc) and (X̄, s c) control charts

Matthew E. Elam; Kenneth E. Case; Jong Min Kim

doi:10.18637/jss.v009.i07

Second stage short run (X̄, v_c) and (X̄, s _c) control charts

Matthew E. Elam, Kenneth E. Case, Jong Min Kim

Statistics (Morris)

Research output: Contribution to journal › Article › peer-review

Abstract

In their 1970 paper titled "Mean and Variance Control Chart Limits Based on a Small Number of Subgroups" (Journal of Quality Technology, Volume 2, Number 1, pp. 9-16), Yang and Hillier originally derived equations for calculating the factors required to determine second stage short run control limits for (X̄, v_c) and (X̄, v_c) charts. Two issues have restricted the applicability of this particular control chart methodology. These are the limited tabulated values of factors Yang and Hillier present and no example to illustrate the use of the methodology. This paper addresses the first issue by presenting a computer program that accurately calculates the factors regardless of the values of the required inputs. An example shows how to incorporate the methodology into a two stage short run control charting procedure. The computer program is available at http://program.20m.com.

Original language	English (US)
Pages (from-to)	1-31
Number of pages	31
Journal	Journal of Statistical Software
Volume	9
DOIs	https://doi.org/10.18637/jss.v009.i07
State	Published - 2004

Keywords

Control Chart
Distribution of the Studentized Variance
Distribution of the Variance
Short Run Statistical Process Control
Two Stage Control Charting

Publisher link

10.18637/jss.v009.i07

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Cite this

@article{7034354458dd4aba98a9920833a8e24d,

title = "Second stage short run ({\=X}, vc) and ({\=X}, s c) control charts",

abstract = "In their 1970 paper titled {"}Mean and Variance Control Chart Limits Based on a Small Number of Subgroups{"} (Journal of Quality Technology, Volume 2, Number 1, pp. 9-16), Yang and Hillier originally derived equations for calculating the factors required to determine second stage short run control limits for ({\=X}, vc) and ({\=X}, vc) charts. Two issues have restricted the applicability of this particular control chart methodology. These are the limited tabulated values of factors Yang and Hillier present and no example to illustrate the use of the methodology. This paper addresses the first issue by presenting a computer program that accurately calculates the factors regardless of the values of the required inputs. An example shows how to incorporate the methodology into a two stage short run control charting procedure. The computer program is available at http://program.20m.com.",

keywords = "Control Chart, Distribution of the Studentized Variance, Distribution of the Variance, Short Run Statistical Process Control, Two Stage Control Charting",

author = "Elam, {Matthew E.} and Case, {Kenneth E.} and Kim, {Jong Min}",

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language = "English (US)",

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pages = "1--31",

journal = "Journal of Statistical Software",

issn = "1548-7660",

publisher = "University of California at Los Angeles",

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T1 - Second stage short run (X̄, vc) and (X̄, s c) control charts

AU - Elam, Matthew E.

AU - Case, Kenneth E.

AU - Kim, Jong Min

PY - 2004

Y1 - 2004

N2 - In their 1970 paper titled "Mean and Variance Control Chart Limits Based on a Small Number of Subgroups" (Journal of Quality Technology, Volume 2, Number 1, pp. 9-16), Yang and Hillier originally derived equations for calculating the factors required to determine second stage short run control limits for (X̄, vc) and (X̄, vc) charts. Two issues have restricted the applicability of this particular control chart methodology. These are the limited tabulated values of factors Yang and Hillier present and no example to illustrate the use of the methodology. This paper addresses the first issue by presenting a computer program that accurately calculates the factors regardless of the values of the required inputs. An example shows how to incorporate the methodology into a two stage short run control charting procedure. The computer program is available at http://program.20m.com.

AB - In their 1970 paper titled "Mean and Variance Control Chart Limits Based on a Small Number of Subgroups" (Journal of Quality Technology, Volume 2, Number 1, pp. 9-16), Yang and Hillier originally derived equations for calculating the factors required to determine second stage short run control limits for (X̄, vc) and (X̄, vc) charts. Two issues have restricted the applicability of this particular control chart methodology. These are the limited tabulated values of factors Yang and Hillier present and no example to illustrate the use of the methodology. This paper addresses the first issue by presenting a computer program that accurately calculates the factors regardless of the values of the required inputs. An example shows how to incorporate the methodology into a two stage short run control charting procedure. The computer program is available at http://program.20m.com.

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KW - Short Run Statistical Process Control

KW - Two Stage Control Charting

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