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

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,...
Loading next page...
 
/lp/springer_journal/continuity-adjustment-for-control-charts-for-attributes-gPvZ0XrM6f
Publisher
Springer Berlin Heidelberg
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
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

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial