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One Our Favorite QI Tools
Histograms
June 2007 - Vol 4, Issue 3
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Greetings!

It is summertime here in Vermont and that means it could be 60 degrees one day and 85 degrees the next - talk about variation! Personally, I like this kind of variation in the weather, but in business, when you are trying to deliver a consistant product every time, variation is a problem.

One of my favorite data display tools to help understand the variation in a process is a histogram and that is what this month's newsletter is all about. I hope that the newsletter gives you some great ideas of how you can use a histogram to improve your processes at work.

Pink and purple lupines are a sure sign of summer in Vermont.

A histogram is a simple graphical technique used to help understand the variation in the output of a process. Histograms provide us with a view of the location (the mean or arithmetic average) of the process output as well the variation in the process. The pattern of variation formed by the histogram (normal, bi-modal, skewed or contains outliers) can tell us a lot about the process.

With a histogram, the x-axis represents variable data measurements from the process or its output and the y-axis represents how often those measurements occurred. Because the variable measurements are on a scale from low to high, each measurement has a relationship to the one right before it (it is higher than the measurement to the left) and the one right after it (it is lower than the measurement to the right). So, the histogram shows you how each point relates to all of the other points. All of the points together on a histogram form a pattern. That pattern can tell us a lot about our process, both what the process has done in the past as well as what it will most likely do in the future.

Histograms are a great tool because not only do they display data, but they can also be used to collect data. I love dual purpose tools that make it easy to quickly analyze the results of the data that has been collected.

Taking that data collection/data display one step further, one of my favorite things to do with histograms is to color code the data as it is being plotted. The color coding should pertain to a specific characteristic of the process or product that you suspect might be a major wource of variation. For example, if you think that days of the week might make a difference on the output of your process, you could plot the data using a different color for each day of the week. We go into detail about the power of color coding histograms and provide other examples of how color-coding can be used in our SPC Workout course.

One thing the histogram does not show is how the process output has varied over time. A run chart, which is also known as a trend chart, can be used in conjunction with a histogram to capture process performance over time.

With the information from a histogram you can generate "theories" that can be further explored, putting you on the path to finding the root cause(s) to problems in your processes.

Robin McDermott is director of Training for Resource Engineering, Inc. You can contact her at 800-810-8326 or 802- 496-5888 or by e-mail at robinm@reseng.com.
While a histogram is a great tool, it is rarely used alone. Most often histograms are used to help a team get to the root cause of a problem or they are used as the first step in setting up Control Charts. Because histrograms are usually used with other tools, we don't have a training program solely on histograms. However, because histograms are such a valuable tool, they are covered to varying degrees in several of our training programs.

SPC Workout The first unit of SPC Workout is dedicated to Understanding Variation and histograms play a key role in that unit. This course offers the most comprehensive coverage of histograms.

8-D Problem Solving and DMAIC Problem Solving These courses are similar in nature, each focusing on a structured problem-solving process. In both courses we cover how to construct histograms and provide tips on how they can be used in problem solving projects.

Many of our other courses touch on histograms as well.

Carolyn Burke is Sr. Customer Service Representative. She can be reached toll free directly at 866-791-1003 or you can e-mail her at carolynb@reseng.com.

Capture the Data

  • Histograms are constructed from variable data; variable data are data that can be measured on a continuous scale. Examples include measured dimensions, weights and temperature.

  • It is recommended that at least 40 (and preferably 100 or more) data points be used to construct a histogram.

Set Up the Graph

  • On the X (or horizontal) axis are cells that correspond to the measurements we are taking. The cell size of a histogram depends on the range of data and the number of data points available.

  • To set up the X-axis, as a rule of thumb use approximately 10 equal cells between your lowest and highest data point (although this number can be smaller or larger depending on the amount of data you're working with).  To determine the correct cell size for the data, subtract the lowest measurement from the highest measurement. Then, divide that number by 10.  This is the approximate width each cell should represent although it is usually best to round that to a workable number.  For example, if the calculation results in a cell size of 4.76, round the cell size to 5.

  • On the Y, or vertical, axis is the frequency or the number of times that a particular measurement has occurred.

Plot the Data

  • To enter data into the histogram, imagine that each cell is a chute that you are going to drop your data points into. As points fall into the appropriate chutes, they build on top of one another and a pattern begins to emerge.

 Interpret the Pattern of Variation

  • If we draw a line roughly over the data points on our histogram, the pattern shown by this line can tell us a great deal about the process and how it is performing. While we will often get a normal distribution if our process is stable, we might also get a skewed, bimodal, or other shape to the pattern of variation. The shape can tell us something about the process that could help us reduce variation or get to the root cause of a problem.

  • A common pattern of variation is the normal distribution. A normal distribution is characterized by its bell-shape where most of the data points fall near the center of the distribution and the frequency of the data gradually decreases as the values moves farther away from the center. The normal curve is symmetrical; if you drew a line down the middle of the normal distribution histogram, one side of the curve would approximately mirror the other.

  • A bimodal distribution has two or more peaks or modes. Usually this pattern of variation shows a process that is not stable; it has a special cause of variation present. Something in the process is causing the output to change. We need to identify the reason for the change and eliminate it.

  • A skewed pattern looks like a normal distribution pushed over to one side. For example, a distribution is skewed to the right if the tail heads off to the right. While some processes are naturally skewed, a skewed distribution may also be the sign that something unnatural (such as sorting) has taken place in the process.


Ray Mikulak is president of Resource Engineering, Inc. You can contact him at 800-810-8326 or 802- 496-5888 or by e-mail at raym@reseng.com.
There are lots of great reasons to use a histogram including to:
  • Understand the pattern of variation in a process
  • Understand the variable nature of the process
  • Visually estimate the center and range of process output.

While variation in weather and life for that matter, makes things interesting, variation when you are trying to put out a consistent and reliable product, is not a good thing. A histogram is a powerful, yet simple tool to help you start to understand the variation in your processes. Understanding the variation is the first step to monitoring and controlling it.

Enjoy the summer and all the variation it has to offer!
Robin McDermott
Resource Engineering, Inc.

phone: 802-496-5888 or 800-810-8326