The Psychology of Quality and More

Histogram: How to do it

The Quality Toolbook > Histogram > How to do it

How to do it

1. Identify the purpose of using a Histogram. Typically this may be one of:
• Checking the shape against an expected distribution (typically a Normal distribution).
• Understanding the capability of the process, particularly in terms of the spread of measurements.
1. Define what to measure. This will include identification of units, scale and tolerances. For example, 'Time taken to complete customer request, measured in seconds, to the nearest ten seconds'.

2. Identify how many measurements must be made. This should be at least 50, and preferably nearer 100. Only use less if this number of measurements is not available - and then be aware of this when evaluating results.
3. If the data may be stratified (for example, by time, people or material), ensure enough measurements are taken to build a Histogram for each group. For example, if there are three groups, then take at least 150 measurements.

4. Identify the width of each Histogram bar. To do this:
5. (a) Decide how many bars you wish to show on the chart. This should be sufficient to show the shape of the overall frequency distribution. A rule of thumb for this is based on the number of measurements made is shown in the table below.

Table 1. Estimating number of bars

 Number of measurements Number of bars Less than 50 5 to 7 50 to 100 6 to 10 100 to 250 7 to 12 Over 250 10 to 20

(b) Identify the range of values that may be measured. This is given by the difference between the largest and the smallest probable measurement values. An expected average can help with this, as it is usually in the middle.

(c) Determine the value range for each bar. This is given by the range of values from (b), divided by the number of bars from (a). Round this to the nearest sensible unit, arranging for any specification limits fall between bars, not within them.

For example, 100 measurements, ranging between 10 and 50 cm are divided into 8 bars of 5 cm each. (8 bars was selected from the choice of 7 to 12 in the table as it resulted in a neat bar width of 5 cm).

6. Define the measurement process, including the design of an appropriate Check Sheet, where and when measurements are made, and by whom. People taking measures should be trained as necessary.

7. Take the measurements, using the process defined in step 5. If all items are not being measured (i.e. a sample is being taken), ensure that samples are selected at random.

8. Organize the measurements to enable the Histogram bars to be sized. This can be done in a frequency table, which may be incorporated into the Check Sheet. For example as in the table below.

Table 2. Example measurement table

 Bar number Measure from Measure to Total of measures 1 10.0 14.9 1 2 15.0 19.9 6 3 20.0 24.9 15 4 25.0 29.9 32 5 30.0 34.9 35 6 35.0 39.9 12 7 40.0 44.9 7 8 45.0 49.9 2

1. Draw the Histogram. Ensure the bars are clear and the diagram is appropriately labeled, including other information about the measurement, such as date and time, identification of the process being charted, etc.

2. Analyze the completed Histogram and act on your findings, for example by checking assumptions made about distribution and then changing the process accordingly.

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