Question

Problem 10-7 The postmaster of a small western town receives a certain number of complaints each day about mail delivery. 1 4 2 10 3 15 4 8 5 9 6 6 7 5 DAY 8 13 9 15 10 7 11 6 Number of complaints a.Determine two-sigma control limits using the above data. (Round your intermediate calculations to 4 decimal places and final answers to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Round up any negative controllimit value to zero.) UCL LCL b. Is the process in control? No Yes

Answer 1

The postmaster of a small western town receives a certain number of complaints each day about mail delivery.

Days	Number of complaints
1	4
2	10
3	15
4	8
5	9
6	6
7	5
8	13
9	15
10	7
11	6
Total	98

For the above data, we can use c-chart because it is without a specific sample size

C-bar = Total Number of defects / Total number of samples

= 98/ 11 = 8.9091

1. Upper control limits (UCL) can be calculated by using 2-sigma control limits, where z = 2

UCL = c-bar + z *√(c-bar)

= 8.9091 + 2 * √ (8.9091)

= 14.879

Lower control limits (LCL) can be calculated by using 2-sigma control limits, where z = 2

LCL = c-bar - z *√(c-bar)

= 8.9091 - 2 * √ (8.9091)

= 2.939

1. The process is not under control because complaints for each day does not fall between Upper control limits (UCL = 14.879) and Lower control limits (LCL =2.939). For day 3 and day 9; it is 15 which are more than 14.879.