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Continuity Adjustment for Control Charts for Attributes

Continuity Adjustment for Control Charts for Attributes A unified approach is proposed for making a continuity adjustment on some control charts for attributes, e.g., np-chart and c-chart, through adding a uniform (0, 1) random observation to the conventional sample statistic (e.g., $$ n\hat{p}_{i} $$ and c i ). The adjusted sample statistic then has a continuous distribution. Consequently, given any Type I risk α (the probability that the sample statistic is on or beyond the control limits), control charts achieving the exact value of α can be readily constructed. Guidelines are given for when to use the continuity adjustment control chart, the conventional Shewhart control chart (with ±3 standard deviations control limits), and the control chart based on the exact distribution of the sample statistic before adjustment. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Continuity Adjustment for Control Charts for Attributes

Acta Mathematicae Applicatae Sinica , Volume 19 (3) – Mar 3, 2017

Continuity Adjustment for Control Charts for Attributes

Acta Mathematicae Applicatae Sinica , Volume 19 (3) – Mar 3, 2017

Abstract

A unified approach is proposed for making a continuity adjustment on some control charts for
attributes, e.g., np-chart and c-chart, through adding a uniform (0, 1) random observation to the conventional
sample statistic (e.g.,

$$
n\hat{p}_{i}
$$
and c

i
). The adjusted sample statistic then has a continuous distribution. Consequently,
given any Type I risk α (the probability that the sample statistic is on or beyond the control limits),
control charts achieving the exact value of α can be readily constructed. Guidelines are given for when to use
the continuity adjustment control chart, the conventional Shewhart control chart (with ±3 standard deviations
control limits), and the control chart based on the exact distribution of the sample statistic before adjustment.

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-003-0114-2
Publisher site
See Article on Publisher Site

Abstract

A unified approach is proposed for making a continuity adjustment on some control charts for attributes, e.g., np-chart and c-chart, through adding a uniform (0, 1) random observation to the conventional sample statistic (e.g., $$ n\hat{p}_{i} $$ and c i ). The adjusted sample statistic then has a continuous distribution. Consequently, given any Type I risk α (the probability that the sample statistic is on or beyond the control limits), control charts achieving the exact value of α can be readily constructed. Guidelines are given for when to use the continuity adjustment control chart, the conventional Shewhart control chart (with ±3 standard deviations control limits), and the control chart based on the exact distribution of the sample statistic before adjustment.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 3, 2017

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