After a number of complaints about its directory assistance, a telephone company examined sam- ples of calls to determine the frequency of wrong numbers given to callers. Each sample consisted of 100 calls. Determine 95 percent limits. Is the process stable (i. e., in control)? Explain.

Explanation:

SAMPLE

1       2     3     4     5   6   7     8   9     10   11   12  13   14     15     16

Number of Errors         5     3     5     7     4   6     8     4   5     9     3   4     5       8       6     7

Average Defectives calculated by

This generates 87/ 16 (100) = 0.54.   In order to obtain control limits, we apply the formula

Implying that

= 0.54 ± 0.044, this indicates that

The upper control limit = 0.54 + 0.044 = 0.10 (following conversion into fraction forms)

The lower control limit = 0.54 – 0.044 = 0.01 (following conversion into fraction forms)

From the calculation and table above, it is ideal to conclude that the process is out of control. This is because ¾ of the values appear to be above 0.04 despite all values falling within the limits.