{domain:"www.qualitydigest.com",server:"169.47.211.87"} Skip to main content

User account menu
Main navigation
  • Topics
    • Customer Care
    • FDA Compliance
    • Healthcare
    • Innovation
    • Lean
    • Management
    • Metrology
    • Operations
    • Risk Management
    • Six Sigma
    • Standards
    • Statistics
    • Supply Chain
    • Sustainability
    • Training
  • Videos/Webinars
    • All videos
    • Product Demos
    • Webinars
  • Advertise
    • Advertise
    • Submit B2B Press Release
    • Write for us
  • Metrology Hub
  • Training
  • Subscribe
  • Log in
Mobile Menu
  • Home
  • Topics
    • 3D Metrology-CMSC
    • Customer Care
    • FDA Compliance
    • Healthcare
    • Innovation
    • Lean
    • Management
    • Metrology
    • Operations
    • Risk Management
    • Six Sigma
    • Standards
    • Statistics
    • Supply Chain
    • Sustainability
    • Training
  • Login / Subscribe
  • More...
    • All Features
    • All News
    • All Videos
    • Contact
    • Training

Ranges vs. Standard Deviations: Which Way Should You Go?

A look at the mathematical difference between X-bar R and X-bar S

Rip Stauffer
Tue, 06/02/2015 - 13:04
  • Comment
  • RSS

Social Sharing block

  • Print
  • Add new comment
Body

Recently, in one of the many online discussion groups about quality, Six Sigma, and lean, this question was posed: “Can X-bar R and X-bar S be used interchangeably based on samples size (n) if the subgroup size is greater than one and less than eight?” Answers varied, of course.

ADVERTISEMENT

In some of these discussion groups, you get to see how far rule four of W. Edwards Deming’s funnel experiment has pushed some training programs off in one direction or another, especially when it comes to statistical process control (SPC). One set of answers that surprised me, though, came from a couple of consultants in France, who said, “Clearly not... the question is about a sample of 1 to 8. [The] response is definitely no. You can’t calculate a standard deviation with a sample of one or two. A sample higher than 8 is highly recommended.”

The point they were trying to make was that for subgroups of size eight  or smaller, you could only use X-bar R charts.

 …

Want to continue?
Log in or create a FREE account.
Enter your username or email address
Enter the password that accompanies your username.
By logging in you agree to receive communication from Quality Digest. Privacy Policy.
Create a FREE account
Forgot My Password

Comments

Submitted by Rip Stauffer on Tue, 06/02/2015 - 09:05

It was actually faster

One note: the first time I ran this model, it took a little less than 12 minutes. I added several outputs to that initial model, and it actually got faster. I ran it four times in all, and the last three runs took just over 6 minutes each.

  • Reply

Submitted by William A. Levinson on Tue, 06/02/2015 - 11:15

The s chart is slightly more powerful

It is actually possible to calculate the chance of detecting a given change in process variation for the R chart and the s chart. The latter uses the chi square distribution, and the former is somewhat more complicated.

The powers of both tests are equal for a sample of 2, which is not surprising. The power of the s chart increases relative to that of the R chart for samples of 3 or more because the s statistic uses all the information, but the difference is not really much.

  • Reply

Submitted by kkbari on Thu, 06/04/2015 - 05:37

Efficiency

A great simulation, but this could have been done much faster and with actual theory to support.  Well, maybe not faster since it requires calculus but rigorous.

In graduate statistics you learn about Efficiency as it relates to statistics.  A standard deviation is an "efficient" statistic at any sample size (compared with other estimates).  The range is "efficient" at n=2 and then begins to slowly degrade as n increases.  However, the efficiency doesn't degrade significantly as related to standard deviation until n=9.  Hence the rule about n=8. 

I did this exercise as part of a graduate class 30 years ago so I'm rusty on the mechanics but it has stuck with me all these years.

  • Reply

Submitted by Rip Stauffer on Thu, 06/04/2015 - 05:44

In reply to Efficiency by kkbari

Thanks for the comment

I'd be interested to know what you meant by "this could have been done much faster and with actual theory to support."

Efficiency is not really the prime consideration when using control charts...they are more about sensitivity. William Levinson's comment (along with an email from another friend) have made me think I might have expanded this simulation (which was about limits) to include known signal detection, especially when the underlying distributions are skewed. That wasn't the question I was trying to answer here, but that would provide a more comprehensive treatment of the difference betweent the two approaches.

  • Reply

Add new comment

Image CAPTCHA
Enter the characters shown in the image.
Please login to comment.
      

© 2025 Quality Digest. Copyright on content held by Quality Digest or by individual authors. Contact Quality Digest for reprint information.
“Quality Digest" is a trademark owned by Quality Circle Institute Inc.

footer
  • Home
  • Print QD: 1995-2008
  • Print QD: 2008-2009
  • Videos
  • Privacy Policy
  • Write for us
footer second menu
  • Subscribe to Quality Digest
  • About Us
  • Contact Us