SETTING CONTROL LIMITS FOR PERCENT DEFECTIVE. Clerks at Mosier Data Systems key in thousands of insurance records each day for a variety of client firms. CEO Donna Mosier wants to set control limits to include 99.73% of the random variation in the data entry process when it is in control.
APPROACH \blacktriangleright Samples of the work of 20 clerks are gathered (and shown in the table). Mosier carefully examines 100 records entered by each clerk and counts the number of errors. She also computes the fraction defective in each sample. Equations (S6-9), (S6-10), and (S6-11) are then used to set the control limits.
UCL_p = \bar{p} + z\sigma_p (S6-9)
LCL_p = \bar{p} - z\sigma_p (S6-10)
\hat{\sigma}_p = \sqrt{\frac{\bar{p}(1 - \bar{p})}{n}} (S6-11)
| SAMPLE NUMBER |
NUMBER OF ERRORS |
FRACTION DEFECTIVE |
SAMPLE NUMBER |
NUMBER OF ERRORS |
FRACTION DEFECTIVE |
| 1 | 6 | .06 | 11 | 6 | .06 |
| 2 | 5 | .05 | 12 | 1 | .01 |
| 3 | 0 | .00 | 13 | 8 | .08 |
| 4 | 1 | .01 | 14 | 7 | .07 |
| 5 | 4 | .04 | 15 | 5 | .05 |
| 6 | 2 | .02 | 16 | 4 | .04 |
| 7 | 5 | .05 | 17 | 11 | .11 |
| 8 | 3 | .03 | 18 | 3 | .03 |
| 9 | 3 | .03 | 19 | 0 | .00 |
| 10 | 2 | .02 | 20 | 4 | .04 |
| 80 |
