The Psychology of Quality and More

# Control Chart: Examples

The Quality Toolbook > Control Chart > Examples

## Example

An accounts department started an improvement project to try to reduce the number of internal purchase forms that its users completed incorrectly. As an overall measure of their success, they used a p-type Control Chart to measure the proportion of purchase forms that were not completed correctly. This was chosen, rather than measuring the actual number of defects, because any number of defects on a form required about the same effort to revise.

Each point on the chart represented all purchase forms for one day. This was chosen as it allowed a 25-point chart to be drawn reasonably quickly. This subgroup size was permissible as, even though the number of forms in each group was less than 50, the number of defective forms in each subgroup was more than 4.

A Pareto Chart indicated that the development department made most mistakes, and a survey indicated that they did not understand the form. On the 15th of the month, a half-hour training class was held for the development people. The table and illustration below shows the calculation and Control Chart for the month. It can be seen that after the training, there were nine points in a row below the center line indicating a statistically significant improvement.

In the next month, the proportion defective was further reduced by extending the training to other departments. Before long, there were so few wrongly completed purchase forms that the subgroup period had to be extended to one week.

Table 1. Example

 Day of month Number of purchase forms, n Number of defective forms proportion defective, p LCL UCL 1 24 14 0.583 0.073 0.663 2 35 16 0.457 0.123 0.613 3 27 12 0.444 0.09 0.646 4 23 12 0.522 0.066 0.67 5 19 5 0.263 0.036 0.7 6 22 14 0.636 0.06 0.677 7 31 12 0.387 0.108 0.628 10 25 6 0.24 0.079 0.657 11 22 14 0.636 0.06 0.677 12 17 5 0.294 0.017 0.719 13 26 11 0.423 0.084 0.652 14 30 16 0.533 0.104 0.632 17 21 8 0.381 0.052 0.684 18 35 10 0.286 0.123 0.613 19 24 7 0.292 0.073 0.663 20 31 7 0.226 0.108 0.628 21 31 6 0.194 0.108 0.628 24 32 11 0.344 0.112 0.624 25 27 5 0.185 0.09 0.646 26 15 5 0.333 0 0.742 27 31 7 0.226 0.108 0.628 28 28 9 0.321 0.095 0.641

Fig. 1. Example Control Chart

### Other examples

• A production team in a glass manufacturer uses a c-chart to measure flaws in sheets of float glass. They address problems that the chart highlights until it becomes stable, then use it as an ongoing monitoring measurement. As other improvements are made, the control limits gradually reduce.
• A customer manager uses a p-chart to measure the weekly proportion of customer feedback forms that contain one or more critical complaints about the company's major product. A detected upward trend results in an early correction of a new service routine.
• A lathe operator uses X-bar and R control charts to show the variation of cut shafts. When a shift towards a control limit is detected, he finds that the cutting tool is wearing, and so replaces it, bringing the process back into control.

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