HISTOGRAM ANALYSIS

A histogram is the most commonly used graph to show frequency distributions. It is a graphical representation to study distribution pattern of data. A histogram consists of tabular frequencies arranged adjacent in rectangles erected over discrete intervals with an area equal to the frequency of the observations in the interval. The total area of the histogram is equal to the numbers of data. This helpful data collection and analysis tool is considered one of the 7 basic quality tools. 

WHEN TO USE A HISTOGRAM

Use a histogram when:

·       There are large number of observations on a single measurable quality characteristics.

·       To study distribution pattern of the output process.

·       To analyzing whether a process can meet the customer’s requirements.

·       To analyzing what the output from a supplier’s process looks like.

·       For any deviation in process from one time period to another.

·       Comparing two or more processes for any variations.

·       For effective easy and quick communication by graphical presentation.

HOW TO CREATE A HISTOGRAM

Step  by step process of creating histogram can be explained with this example which is as follows-

1.      Collect 50-100 consecutive data points from a process you intended to control.

In a hospital process control values were identified as a CTQ (Critical to Quality) parameter. 50 readings were collected which covered all shifts over a week. They are as follows-

QC values for parameter-

9.6	9.5	9.8	10.2	10.0	9.4	9.9
9.7	9.6	10.3	9.8	9.5	9.8	9.9
10.3	9.6	9.4	9.7	9.4	9.6	9.4
10.1	9.9	10.2	9.7	9.8	9.8	9.2
9.2	9.4	9.8	9.6	9.7	9.9	9.7
10.0	9.6	9.3	10.6	9.7	9.9	9.8
9.6	10.1	9.9	9.8	10.4	10.9	10.2

2.      Calculate Mean= Select the cell where you want value to appear for you. Then follow

After a click on “OK” I got Mean= 9.786

3.      Calculate Max and Min Value

Select the cell where you want the result to appear. Follow-

The Max Value I got is = 10.9

Similarly follow the steps for Minimum Value.

4.      Calculate Interval - Depending on the data range select classes of equal width.

5.      Calculate Stand. Deviation

Select the cell where you want the value to appear. Then Follow-

So the SD = 0.358

6.      Let’s now work out for class width.

You will note that the following cell is increased by the set interval value. Ensure that your class value includes Max. and Min. Value as calculated.

7.      Now the next step to know is the frequency of value i.e number of times a value has occurred in the process. Follow these steps- first place cursor on the applicable cell. Type “=” select “Formulas” got to “More functions” out of which select “Statistical” from drop down list select “Frequency”.

You will be directed to window as shown below-

Note:

In Data_array- click and select your data (here it is QC Value) enter

and

In   Bins_array- click and select calculated class (here it is QC values- Class) enter

Click “OK”

8.      For other results in frequency column use this short-cut-  select the frequency column (including the formula cell). Go to formula bar, place your cursor at the end of the formula, press “Ctrl+ Shift+ Enter”. You will get the frequency of all QC values like shown below-

9.      We are done with our calculation part. Now we will be heading to convert data in Histogram. For this, Select the Frequency column values, go to “Insert” select “Bar Chart” go to “Stacked Column”.

10.      We need to do some settings for the chart since it is a Bar graph and not a histogram chart. So let’s do it!

a.      Remove grid line-  select on any grid line and press delete

b.      On my X-axis I need range of QC Values. For this select on chart area, right      click then select data. It will direct you to further window where there is option to edit on right side, click on edit button and select QC value Class.

It will look like this-

c.       To remove gaps- Right Click on any bar go to “Format Data Series”

Select boarder line to black. Chart will look like histogram-

  d.       To complete the chart label the chart with title,  X-axis and Y-axis etc.

  CONCLUSION –

The pattern is unimodal and is fairly centered.

If we know the specifications example in this case let suppose is 9.8±0.5, the upper limit is 10.30 and lower limit is 9.30. therefore, though the pattern is fairly centered BUT the process spread is much wider than the tolerance. This indicated the process is not  capable of meeting the specifications within the tolerance limits, 2.0% fall below lower specification limits and 10.0% has gone beyond the Upper Specification limits. It needs improvement efforts to get process within the tolerance limits.

let's discuss histogram shapes!

TYPICAL HISTOGRAM SHAPES AND WHAT THEY MEAN-

Normal Distribution

A common pattern is the bell–shaped curve known as the "normal distribution." In a normal or "typical" distribution, points are as likely to occur on one side of the average as on the other.  

 

Skewed Distribution

The skewed distribution is asymmetrical. The distribution’s peak is off center toward the limit and a tail stretches away from it. These distributions are called right- or left-skewed according to the direction of the tail.

Double-Peaked or Bimodal

The bimodal distribution looks like the back of a two-humped camel. The outcomes of two processes with different distributions are combined in one set of data.  

Plateau or Multimodal Distribution

The plateau might be called a “multimodal distribution.” Several processes with normal distributions are combined. Because there are many peaks close together, the top of the distribution resembles a plateau.

Edge Peak Distribution

The edge peak distribution looks like the normal distribution except that it has a large peak at one tail. Usually this is caused by faulty construction of the histogram, with data lumped together into a group labeled “greater than.”

Comb Distribution
In a comb distribution, the bars are alternately tall and short. This distribution often results from rounded-off data and/or an incorrectly constructed histogram.                                                      

Truncated or Heart-Cut Distribution

The truncated distribution looks like a normal distribution with the tails cut off. The supplier might be producing a normal distribution of material and then relying on inspection to separate what is within specification limits from what is out of spec. The resulting shipments to the customer from inside the specifications are the heart cut.

Dog Food Distribution

The dog food distribution is missing something–results near the average. If a customer receives this kind of distribution, someone else is receiving a heart cut, and the customer is left with the “dog food,” the odds and ends left over after the master’s meal. Even though what the customer receives is within specifications, the product falls into two clusters: one near the upper specification limit and one near the lower specification limit. This variation often causes problems in the customer’s process.

Hope the article was useful for you. Keep sending your suggestions and comments. Enjoy reading!