Histogram Common Errors

Jay Arthur
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KnowWare International, Inc.
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Over the years, we've gotten a lot of calls about the histogram. Here are a couple of the most common errors users make with their data.

The histogram uses the Rbar/d2 formula to calculate Cp and Cpk. When you have individuals data (a single column), the ranges are calculated as the difference between each individual measurement.

When you sort the data, it eliminates the natural range between each individual measurement and substitutes an artificial one that's very small. When you do this, Cp and Cpk increase dramatically. Below are two histograms using the same data. The first one has data with normal variation; the second one has sorted data.
Notice that Cp and Cpk skyrocket from 1.2 to 50 in sorted data.

General Rule: When Cp and Pp, or Cpk and Ppk differ dramatically, the data might have been sorted or the process may be too out of control for analysis.

Using Individuals Data Instead of Subgroups

Many machines produce single columns of data, but the data is actually in subgroups with a sample size of five. When using subgroups of five, the range or standard deviation is calculated across the five samples. (5 samples uses Sbar/c4 instead of Rbar/d2).

In 2008 and earlier versions of the QI Macros, you will need to use the Data Transformation tools to convert the single column of data into five columns:

 ----> 

The resulting histogram will have slightly different results than the individuals data:

In 2009, we added a prompt when the Histogram detects individuals data. If you see this prompt, enter the number of samples per subgroup (default is 1):

Using the Wrong Formulas - Cp, Cpk vs Pp, Ppk

Some people still try to calculate Cp and Cpk using standard deviation (stdev) , not Sigma estimator (Rbar/d2). Stdev is used to calculate Pp and Ppk.
See our formulas at http://www.qimacros.com/formulas.html

We recently created a whitepaper on histograms and capability analysis. It's $20.
You can order and download it from http://www.qimacros.com/products.php.

Histogram Resources

• Watch video of how to create a histogram using the QI Macros
• Histogram Examples
• How to Determine Histogram Bin Interval
• Make a Histogram in Excel
• How to Analyze a Histogram
• Comparing Histograms
• Process Capability Analysis with Cp, Cpk, Pp, Ppk
• Frequency Histogram
• Frequency Histogram Examples

Histograms are just one of the tools included in the QI Macros for Excel SPC Software for Excel.

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