Question

2. The following data gives the number of defectives in 10 independent samples of varying sizes from a production process: 

Draw the control chart for fraction defectives and comment on it. 

3.Draw a suitable control chart for the following data pertaining to the number of coloured threads(considered as defects) in 15 pieces of cloth in a certain make of synthetic fibres and state your conclusions: 7,12,3,20,21,5,4,3,10,8,0,9,6,7,20

Answer 1

2. P-chart: From the given data

S. No.	Sample Size (n)	Defective Units (di)	pi=di/ni
1	2000	425	0.2125
2	1500	430	0.2867
3	1400	216	0.1543
4	1350	314	0.2326
5	1250	225	0.1800
6	1760	322	0.1830
7	1875	280	0.1493
8	1955	306	0.1565
9	3125	337	0.1078
10	1575	305	0.1937
Total:	17790	3160

Now we calculate LCL and UCL values from the above formula with different sample sizes(ni)

				UCL	LCL
S. No.	Sample Size (n)	Defective Units (di)	pi=di/ni	p-bar+3*sqrt((p-bar * q-bar)/ni)	p-bar-3*sqrt((p-bar * q-bar)/ni)
1	2000	425	0.2125	0.2033	0.1520
2	1500	430	0.2867	0.2072	0.1480
3	1400	216	0.1543	0.2083	0.1470
4	1350	314	0.2326	0.2088	0.1464
5	1250	225	0.1800	0.2101	0.1452
6	1760	322	0.1830	0.2050	0.1503
7	1875	280	0.1493	0.2041	0.1511
8	1955	306	0.1565	0.2036	0.1517
9	3125	337	0.1078	0.1981	0.1571
10	1575	305	0.1937	0.2065	0.1487
Total:	17790	3160

P-chart:

The process is out of control since 5 subgroups are out of control.
i.e. the low proportion of defective items 7 and 9
and the high proportion of defective items 1,2 and 4

3) C-Chart: From the given data

Sample	defects
1	7
2	12
3	3
4	20
5	21
6	5
7	4
8	3
9	10
10	8
11	0
12	9
13	6
14	7
15	20

.Total : 135

The process is out of control since 3 subgroups are out of control.
i.e.the high number of defects per unit are 4,5 and 15