ON OPTIMAL SETTING OF CONTROL LIMITS FOR GEOMETRIC CHART

M. Xie; T. N. Goh; V. Kuralmani

doi:10.1142/9789819812547_0015

ON OPTIMAL SETTING OF CONTROL LIMITS FOR GEOMETRIC CHART

M. Xie^*
, T. N. Goh
, V. Kuralmani

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › Reprint in book › peer-review

Abstract

Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment. © 2025 World Scientific Publishing Co. Pte. Ltd. All rights reserved.

Original language	English
Title of host publication	Reliability Engineering
Editors	Hoang Pham
Publisher	World Scientific Publishing Co. Pte Ltd
Pages	261-269
ISBN (Electronic)	9789819812547, 9789819812554
ISBN (Print)	9789819812530
DOIs	https://doi.org/10.1142/9789819812547_0015
Publication status	Published - Jul 2025
Externally published	Yes

Bibliographical note

This is a reprint of: Xie, M., Goh, T. N., & Kuralmani, V. (2000). On optimal setting of control limits for geometric chart. International Journal of Reliability, Quality and Safety Engineering, 7(1), 17-25. https://doi.org/10.1142/S0218539300000031

Funding

This research is supported by a research grant from the National University of Singapore for the project “Some practical aspects of SPC for automated manufacturing process” (RP3981625).

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

Research Keywords

Average Run Length
Geometric Distribution
High-quality Process Control
Optimal Control Limits
Sensitivity Analysis
Statistical Process Control

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10.1142/9789819812547_0015

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Cite this

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title = "ON OPTIMAL SETTING OF CONTROL LIMITS FOR GEOMETRIC CHART",

abstract = "Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment. {\textcopyright} 2025 World Scientific Publishing Co. Pte. Ltd. All rights reserved.",

keywords = "Average Run Length, Geometric Distribution, High-quality Process Control, Optimal Control Limits, Sensitivity Analysis, Statistical Process Control",

author = "M. Xie and Goh, \{T. N.\} and V. Kuralmani",

note = "This is a reprint of: Xie, M., Goh, T. N., \& Kuralmani, V. (2000). On optimal setting of control limits for geometric chart. International Journal of Reliability, Quality and Safety Engineering, 7(1), 17-25. https://doi.org/10.1142/S0218539300000031",

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doi = "10.1142/9789819812547\_0015",

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AU - Xie, M.

AU - Goh, T. N.

AU - Kuralmani, V.

N1 - This is a reprint of: Xie, M., Goh, T. N., & Kuralmani, V. (2000). On optimal setting of control limits for geometric chart. International Journal of Reliability, Quality and Safety Engineering, 7(1), 17-25. https://doi.org/10.1142/S0218539300000031

PY - 2025/7

Y1 - 2025/7

N2 - Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment. © 2025 World Scientific Publishing Co. Pte. Ltd. All rights reserved.

AB - Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment. © 2025 World Scientific Publishing Co. Pte. Ltd. All rights reserved.

KW - Average Run Length

KW - Geometric Distribution

KW - High-quality Process Control

KW - Optimal Control Limits

KW - Sensitivity Analysis

KW - Statistical Process Control

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U2 - 10.1142/9789819812547_0015

DO - 10.1142/9789819812547_0015

M3 - Reprint in book

SN - 9789819812530

SP - 261

EP - 269

BT - Reliability Engineering

A2 - Pham, Hoang

PB - World Scientific Publishing Co. Pte Ltd

ER -

ON OPTIMAL SETTING OF CONTROL LIMITS FOR GEOMETRIC CHART

Abstract

Bibliographical note

Funding

UN SDGs

Research Keywords

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On optimal setting of control limits for geometric chart

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