Question

A manufacturing company makes runners for cabinet drawers. To assess the quality of the manufacturing process, the company collected one sample of 300 consecutively manufactured runners each day for 20 days and counted the number of defective items. The resulting sample data are:

Sample:             1      2      3      4      5      6      7      8      9    10
Sample Size:   300 300 300 300 300 300 300 300 300 300
Defectives:        8       6     11    15    12    11     9      6      5      4

Based on your previous answers, sketch the p control chart for your own reference. Now plot all the sample points on the chart. Looking at your chart which of the following statements are true?

	A.	The runners manufacturing process is out of control.
	B.	The runners manufacturing process is in statistical control.
	C.	The last three sample points indicate a process that is beginning to show a likely out of control trend.
	D.	Answers A and C are True.
	E.	Answers B and C are True.

Answer 1

S.no. S.size Defectives Proportion np
1 1 300 8    0.02666667    8
2 2 300 6    0.02000000    6
3 3 300 11    0.03666667    11
4 4 300 15    0.05000000    15
5 5 300 12    0.04000000    12
6 6 300 11    0.03666667    11
7 7 300 9    0.03000000    9
8 8 300 6    0.02000000    6
9 9 300 5    0.01666667    5
10 10 300 4    0.01333333    4

Proportion = No.of Defectives / Sample Size

E.G. = 8 / 300 = 0.02666667 and so on.

# Now calculating central p_bar and n_bar
# p_bar is average fraction defective
# n_bar is average sample size

# p_bar = Add up all the n*p values / Add up all the n values

= 87 / 3000

= 0.029

# n_bar = Add up all the n values / No.of Samples.

= 300*10 / 10

= 300

Now limits are

Control limit =

Upper Control Limit =

Lower Control Limit =

Where p = p_bar and n = n_bar and term =

Now term = (0.029) * (1-0.029) / 300

= 9.386333e-05

UCL
0.05806493
LCL
-6.492732e-05
CL
0.029

All the points in the control lines. Hence B is true that the process is under control.

Also, last three points show a decreasing trend which may result in out of control process in future.

Hence E is the correct response.