Answer:
Total number of items = 300 units per sample x 10 samples = 3000 units
Total number of defects = 4 + 6 + 0+1+3+5 + 10 + 3 + 2+ 3 = 37
a) Defect rate for sample 2 = 6/300 x 100= 2%
b) Pbar = Total number of defects / Total number of items = 37/3000 x 100 = 0.0123 x 100 = 1.23%
c) Sigma = Square root ( Pbar in fraction term x ( 1 – Pbar in fraction term)/ n)
= Square root ( 0.0123 x ( 1 – 0.0123)/300)
= Square root ( 0.0123 x 0.9877/300)
= 0.00636
= 0.636 % ( or 0.64% rounded to 2 decimal places)
d) Upper control limit ( in % terms)
= pbar + 3 x sigma
= 1.23 + 3 x 0.64
= 1.23 + 1.92
= 3.15%
e) Lower control limit ( in terms of percentage)
=higher of ( 0, Pbar – 3 x Sigma)
= higher of ( 0, 1.23 – 1.92 )
= Higher of ( 0, - 0.69)
= 0
f) Outliers will be those sample defectives which will be outside control limit range of 0 to 3.15%
Percentage defectives in 10 samples as follows :
Number of defects
Percentage defects in sample of 300
4
1.33
6
2
0
0
1
0.33
3
1
5
1.66
10
3.33
3
1
2
0.66
3
1
The outlier is the sample with 10 defects and there is only 1 outlier
Explanation:
