Question

1. Jon Snow is preparing his army to face the white walkers. He wants his archers to be equipped with the best quality arrowheads. His blacksmith will work around the clock with a team of experienced crafters to meet his orders. Jon has asked that each hour, 20 randomly selected arrowheads to be delivered to him so that he can personally check on the quality. The results for 20 hours of sampling are provided below.

Sample Defectives	1 3	2 3	3 2	4 4	5 1	6 2	7 3	8 3	9 2	10 3
Sample Defectives	11 4	12 2	13 1	14 1	15 0	16 1	17 1	18 1	19 2	20 2

Construct a control chart for the number of defective arrowheads. Does the process appear to be in control?

Answer 1

Since it is a count type data so we will use  the c-chart.

Sample	Defectives (C)
1	3
2	3
3	2
4	4
5	1
6	2
7	3
8	3
9	2
10	3
11	4
12	2
13	1
14	1
15	0
16	1
17	1
18	1
19	2
20	2

Control limits are given by

cbar = 41/20 = 2.05

UCL = 6.345346

CL = 2.050000

LCL = 0.000000

Since all points lies within the control limits hence the process in statistical quality control.