Histograms are used to represent continuous data in the form of a diagram or chart. In the Analysis stage of DMAIC, Six Sigma histogram tools are used. Typically Histograms are represented as bar charts. Large amounts of data that is difficult to understand if represented in a tabular spreadsheet form.
In the Measure stage of DMAIC, the data is collected. Then this data is reviewed by the team. Typically the data collected is is of two types:
- Discrete data (true/false, fail/pass, success/failure )
- Continuous data (example: frequency, color, time). Histograms are best suited for representing this data.
Histograms can provide a visual display of such data by dividing this large data into a finite number of groups or buckets. Once the buckets are defined, you need to match and find out for every number what bucket it belongs to. Once a number is assigned to a bucket, you need to increment the frequency value of that bucket. Once all numbers are counted, you take the buckets and their frequencies and represent them in a bar chart with buckets on X axis and the the frequencies on the Y axis.
- Histograms are used to understand how the output of a process effects customer expectations
- They will help you find out if the process is capable of meeting customer requirements
- Histograms are graphs of a distribution (frequency of occurrence) of data.
- Histograms show centering, dispersion (spread), and shape (relative frequency) of the data.
Lets take the example of a part (a screw) which is manufactured at a plant. The ideal diameter of the screw is 52.3 mm. Lets measure the diameter of a random sample of 16 screws. The diameters are measured as below:
52.1 52.2 52 52.3 52.2 52.5 52.3 52.3 52.2 52.1 52.6 52.4 52.3 52.4 52.5 52.4
Lets group them into the following buckets:
Now lets count how many screws belong to each bucket and compute the frequency
The above data can be represented as a bar chart as shown below:
In Microsoft Excel, you can create a histogram very easily using the “Analysis Toolpack” Add-In. (Go to File/Options/Add-Ins and make sure the Analysis ToolPak AddIn is installed). All you need to do is input your data (in our case all the diameters) into a sheet. You can use one single column or multiple columns. Also decide what your buckets are. Put them in a separate column. Now go to data menu and choose Data Analysis/Histogram. For the Input range, choose the appropriate Excel range containing the diameter data. For the Bin Range choose the column that contains your buckets. For the output, you can choose a range or a new sheet option. Click OK and Excel will automatically create the histogram table and Chart for you. No need to count and find out manually the frequency. Its done for you by the Analysis Pack histogram tool.