The Median Run Length of the Variable Sample Size Xbar Chart with Unknown Process Parameters

Wei Lin Teoh; Michael Boon Chong Khoo; Wai Chung Yeong; Sin Yin Teh

The Median Run Length of the Variable Sample Size Xbar Chart with Unknown Process Parameters

Wei Lin Teoh, Michael Boon Chong Khoo, Wai Chung Yeong, Sin Yin Teh

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Abstract

The variable sample size (VSS) X chart, effectively in detecting small to moderate shifts, is traditionally investigated based on the average run length (ARL). When the process parameters are estimated, the skewness of the run length distribution for the VSS X chart alters with the process mean shifts, number of Phase-I samples and sample sizes. Therefore, the confusing interpretation based on the ARL alone becomes worse when it is applied for the VSS X chart with estimated process parameters. Since the median is smaller than the mean in a highly skewed run length distribution, the median run length (MRL) offers a more intuitive representation of central tendency than the ARL. In such a case, knowledge of the MRL provides a more comprehensive understanding for the VSS X chart with estimated process parameters. This paper investigates the impact of parameter estimation on the MRL-based VSS X chart. Suggestions on the number of Phase-I samples and sample sizes in designing a satisfactory MRL-based VSS X chart with estimated process parameters are provided to quality engineers.

Original language	English
Title of host publication	Proceedings of the 2nd International Conference on Mathematical Sciences & Computer Engineering 2015
Publisher	SandKRS
Pages	15-20
Number of pages	6
Publication status	Published - 2015
Event	2nd International Conference on Mathematical Sciences & Computer Engineering 2015 - Kuala Lumpur, Malaysia Duration: 5 Feb 2015 → 6 Feb 2015 Conference number: 2 https://www.icmsce.net/2015/WB/www.icmsce.net/2012/wb/index.html

Conference

Conference	2nd International Conference on Mathematical Sciences & Computer Engineering 2015
Abbreviated title	ICMSCE 2015
Country/Territory	Malaysia
City	Kuala Lumpur
Period	5/02/15 → 6/02/15
Internet address	https://www.icmsce.net/2015/WB/www.icmsce.net/2012/wb/index.html

Keywords

Median run length
process parameters estimation
statistical process control
variable sample size X chart

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@inproceedings{d379a44a6a9f41fc9aacf0598e31673c,

title = "The Median Run Length of the Variable Sample Size Xbar Chart with Unknown Process Parameters",

abstract = "The variable sample size (VSS) X chart, effectively in detecting small to moderate shifts, is traditionally investigated based on the average run length (ARL). When the process parameters are estimated, the skewness of the run length distribution for the VSS X chart alters with the process mean shifts, number of Phase-I samples and sample sizes. Therefore, the confusing interpretation based on the ARL alone becomes worse when it is applied for the VSS X chart with estimated process parameters. Since the median is smaller than the mean in a highly skewed run length distribution, the median run length (MRL) offers a more intuitive representation of central tendency than the ARL. In such a case, knowledge of the MRL provides a more comprehensive understanding for the VSS X chart with estimated process parameters. This paper investigates the impact of parameter estimation on the MRL-based VSS X chart. Suggestions on the number of Phase-I samples and sample sizes in designing a satisfactory MRL-based VSS X chart with estimated process parameters are provided to quality engineers.",

keywords = "Median run length, process parameters estimation, statistical process control, variable sample size X chart",

author = "Teoh, {Wei Lin} and Khoo, {Michael Boon Chong} and Yeong, {Wai Chung} and Teh, {Sin Yin}",

year = "2015",

language = "English",

pages = "15--20",

booktitle = "Proceedings of the 2nd International Conference on Mathematical Sciences & Computer Engineering 2015",

publisher = "SandKRS",

note = "2nd International Conference on Mathematical Sciences & Computer Engineering 2015, ICMSCE 2015 ; Conference date: 05-02-2015 Through 06-02-2015",

url = "https://www.icmsce.net/2015/WB/www.icmsce.net/2012/wb/index.html",

}

Teoh, WL, Khoo, MBC, Yeong, WC & Teh, SY 2015, The Median Run Length of the Variable Sample Size Xbar Chart with Unknown Process Parameters. in Proceedings of the 2nd International Conference on Mathematical Sciences & Computer Engineering 2015. SandKRS, pp. 15-20, 2nd International Conference on Mathematical Sciences & Computer Engineering 2015, Kuala Lumpur, Malaysia, 5/02/15.

The Median Run Length of the Variable Sample Size Xbar Chart with Unknown Process Parameters. / Teoh, Wei Lin; Khoo, Michael Boon Chong; Yeong, Wai Chung et al.
Proceedings of the 2nd International Conference on Mathematical Sciences & Computer Engineering 2015. SandKRS, 2015. p. 15-20.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The Median Run Length of the Variable Sample Size Xbar Chart with Unknown Process Parameters

AU - Teoh, Wei Lin

AU - Khoo, Michael Boon Chong

AU - Yeong, Wai Chung

AU - Teh, Sin Yin

N1 - Conference code: 2

PY - 2015

Y1 - 2015

N2 - The variable sample size (VSS) X chart, effectively in detecting small to moderate shifts, is traditionally investigated based on the average run length (ARL). When the process parameters are estimated, the skewness of the run length distribution for the VSS X chart alters with the process mean shifts, number of Phase-I samples and sample sizes. Therefore, the confusing interpretation based on the ARL alone becomes worse when it is applied for the VSS X chart with estimated process parameters. Since the median is smaller than the mean in a highly skewed run length distribution, the median run length (MRL) offers a more intuitive representation of central tendency than the ARL. In such a case, knowledge of the MRL provides a more comprehensive understanding for the VSS X chart with estimated process parameters. This paper investigates the impact of parameter estimation on the MRL-based VSS X chart. Suggestions on the number of Phase-I samples and sample sizes in designing a satisfactory MRL-based VSS X chart with estimated process parameters are provided to quality engineers.

AB - The variable sample size (VSS) X chart, effectively in detecting small to moderate shifts, is traditionally investigated based on the average run length (ARL). When the process parameters are estimated, the skewness of the run length distribution for the VSS X chart alters with the process mean shifts, number of Phase-I samples and sample sizes. Therefore, the confusing interpretation based on the ARL alone becomes worse when it is applied for the VSS X chart with estimated process parameters. Since the median is smaller than the mean in a highly skewed run length distribution, the median run length (MRL) offers a more intuitive representation of central tendency than the ARL. In such a case, knowledge of the MRL provides a more comprehensive understanding for the VSS X chart with estimated process parameters. This paper investigates the impact of parameter estimation on the MRL-based VSS X chart. Suggestions on the number of Phase-I samples and sample sizes in designing a satisfactory MRL-based VSS X chart with estimated process parameters are provided to quality engineers.

KW - Median run length

KW - process parameters estimation

KW - statistical process control

KW - variable sample size X chart

M3 - Conference contribution

SP - 15

EP - 20

BT - Proceedings of the 2nd International Conference on Mathematical Sciences & Computer Engineering 2015

PB - SandKRS

T2 - 2nd International Conference on Mathematical Sciences & Computer Engineering 2015

Y2 - 5 February 2015 through 6 February 2015

ER -

The Median Run Length of the Variable Sample Size Xbar Chart with Unknown Process Parameters

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