# Histograms (Bar Charts) as Quality Improvement Tools

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I am a trainer and consultant in lean manufacturing, Six Sigma, quality management, and business management.

## Continuous Process Improvement

Histograms or bar charts are quality improvement tools that are instantly recognizable but are often neglected. They can offer a powerful analysis of your problems. Continuous process improvement requires that we collect data through simple quality tools such as tally charts, but then we need to be able to analyze this data. One of the simplest tools to do this with is a histogram or bar chart, a quality tool that many of us will be familiar with from school.

## What Is a Histogram?

A histogram is a graphical representation of data. The data is represented by columns on a graph that vary in height depending on the frequency (how many times) the specific range of data occur.

Why use a histogram as a quality tool?

1. Displays data in an easy-to-interpret graphical manner
2. Shows frequency of occurrence of data values
3. Reveals the centering, variation and shape of the data
4. Illustrates the underlying distribution of the data
5. Enables future prediction of process performance
6. Enables identification in changes in processes parameters
7. Allows you to answer the question: “Is the process capable of meeting the customer requirements?”

Continuous process improvement is core to the survival of any business. Histograms and other quality tools are key to achieving continual process improvement of your business.

“A picture can be worth more than a thousand numbers when the picture is a histogram.”

— A.M. Guerry, 1833

## How to Make a Histogram

The first thing to do is to collect your data. We will talk about variable (measured) data for the purposes of this article. We can collect data using a tally chart, recording occurrences of specific ranges of measurement or we can just create a table of results when we take the measurements.

To use this quality tool we must draw the histogram, for this we need to know the number of “class intervals” (number of columns) and the “interval width” (the width of each column on our bar chart).

## Class Intervals on Your Bar Chart

To define the number of class intervals, the “official” method is to take the square root of the total number of measurements, for example if you have 400 measurements then the class interval will be 20. However, if you are not too comfortable with square roots the following table can be used as a simple guide.

Number of Samples Class Intervals

• Under 50: 5–7
• 50–100: 6 - 10
• 100–250: 7–12
• Over 250: 10–20

This will tell you how many individual columns will form your histogram or bar chart when you use this simple quality tool.

## Histogram Video

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## Width of Each Class Interval on Your BarChart

The width of each class interval is the total range of samples (Biggest–smallest) divided by the number of class intervals, so if the range of measurements was from 100 to 102mm and we had 20 class intervals the width would be 0.1 mm.

In the example above the first column would contain the number of times a measurement between 100 and 100.1 occurred, the second 100.11 and 100.2, and so on.

The next stage would be to plot the number of times that each class occurs in your data, so if the first interval occurred once then the column would be one unit high. If the second occurred three times, then it would be three units high, and so on.

## Histogram Analysis

The position of the histogram relevant to the specification limits and the shape of the histogram can tell us a huge amount about the process being analyzed. Data that follows the “normal distribution” forms what is called a bell-shaped curve, this is the typical shape that is seen when we plot a histogram of variable data.

However we do occasionally see different shapes, a multi-modal distribution is one that has more than one peak. A bimodal distribution is one in which there are two peaks on the graph, this would indicate that there is something that has changed during the data gathering, for instance, a change in settings between two shifts or a change in raw materials being processed.

We can also see skewed distributions, those where the data is bunched up to one side with a long tail. This can occur in situations where for instance you cut material to length, the method will not allow longer cuts but it will allow shorter ones.

A comparison of the shape of the distribution of the histogram to the specification limits can tell us whether the process is capable of meeting the required specification. If the tails are within the upper and lower specification limits then we are within the limits. The peak of the bar chart can also tell us if we are close to the nominal specification and allow us to make any necessary corrections.

For such a simple to use quality tool the histogram or bar chart is a very powerful way to find out a lot of information regarding the capability of our processes and to help us to make continuous improvement.

## CP and CPK

Within business statistics or discussions on statistical process control you may here people talking about the process CP or CPK. This is a comparison of the actual process spread and position against the specification.

The simplest way to think about it is to compare the base of your histogram to the specification, if your histogram has a spread of 5 points and your tolerance is 10 points then you would have a CP of 2. This however can be adjusted according to your process setting and the process nominal giving the CPK. The CPK is more often than not lower than the CP due to the actual process being closer to the specification limits.

This is a simplified view of CP and CPK which would otherwise be calculated using the process standard deviation. Six standard deviations (+/- 3) being divided into the total tolerance to give your CP.

## Histograms in Six Sigma

If you are implementing a six sigma project you will almost certainly start your data analysis by plotting your data as a histogram. This often results in a multi-nodal distribution due to multiple influences on your data. Most six sigma projects started by inexperienced black belts fail to ensure that the process that they wish to study is first standardized.

By this, I mean things as simple as making sure that the best method is defined, documented and then followed the same way by everyone. These differences are often the cause of most of the variation that the six sigma project is seeking to reduce and as such takling them initially can actually remove the need for a full-blown six sigma project.

This is why many now implement lean six sigma and implement tools such as 5S which helps you to standardize your project before you begin intensive and sometimes wasteful data collection and analysis.

## Histogram Software

Software that is readily available in most businesses, such as Excel, can be easily used to make bar charts of all sorts of descriptions. Excel will allow you to create histograms not just as bar charts but in other formats such as pie charts.

## Continuous Process Improvement

Histograms and Bar Charts are a simple and important quality tool to help you to continually improve your processes. Continuous Process Improvement however does not just happen, it must be planned and managed carefully. Tools such as histograms are used as part of larger improvement programs and are used in conjunction with other tools such as tally charts or SPC. You can learn about these other quality tools by reading; Seven Quality Tools.