# 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

, Volume 19 (3) – Mar 3, 2017

## Continuity Adjustment for Control Charts for Attributes

Acta Mathematicae Applicatae Sinica, English Series Vol. 19, No. 3 (2003) 397–404 1 2 3 L.K. Chan ,T.K. Mak ,B. Tao Department of Management Sciences, City University of Hong Kong 83 Tat Chee Avenue, Kowloon, Hong Kong (E-mail: fblkchan@cityu.edu.hk) Department of Decision Sciences & M.I.S., Concordia University 1445 De Maisonneuve Blvd. West, Montreal, H3G 1M8 Canada Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100081, China 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., np  and c ). The adjusted sample statistic then has a continuous distribution. Conse- i i quently, 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. Keywords Control charts for attributes, continuity adjustments, np, p,and c control charts, statistical process control 2000 MR Subject Classiﬁcation ? 1 Introduction Let X be the number of occurrences in a sample (i.e., subgroup) in a control chart for attributes, e.g., number of nonconforming items in an np-chart, or number of nonconformities in a c-chart. A conventional control chart for attributes, to be called a Shewhart chart, is Center Line = µ , Shewhart (SH) chart Upper Control Limit (UCL) = µ +3σ , x x Lower Control Limit (LCL) = µ − 3σ , x x where µ and σ are the mean and standard deviation of X.As X is a discrete random variable x x taking on values, 0,...

Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
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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