Question

Random samples of size n= 400 are taken from a population with p= 0.15.

a.Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p
chart.

b.Suppose six samples of size 400 produced the following sample proportions: 0.06, 0.11, 0.09, 0.08, 0.14, and 0.16. Is the production process under control?

Answer 1

Ans(a)- given that

Input:
No. of samples	6
Sample size	400
Sigma limits(z)	3

using the p- chart formula

and CL =

using above formulas we get

Output:
=	0.15
UCL =	0.20
LCL =	0.10

Ans(b)-

		Calculations
		Proportion
Sample		Defective		UCL	LCL
1		0.060	0.15	0.2036	0.0964
2		0.110	0.15	0.2036	0.0964
3		0.090	0.15	0.2036	0.0964
4		0.080	0.15	0.2036	0.0964
5		0.140	0.15	0.2036	0.0964
6		0.160	0.15	0.2036	0.0964

graph-

p-chart-

we clearly see in this graph sample 1 lies below the LCL line since process is out of control.