Question

Happy Oil Processing needs to monitor the amount of oil they put in 1-liter containers on their filling line. They have had problems with underfilled containers.

      Samples of 250 containers were collected 4 times a day for 12 days.   They’ve asked you to create an np-chart for the filling process and interpret the results.

a)   What values will be used for the centerline, upper control limit, and lower control limit? (You only need to make a table of the values to answer this question and others like it in this assignment.)

b)   Create the control chart.

c)   Does the process appear to be in statistical control? Why or why not?

d)   What percentage of containers are underfilled?

	Number of Underfilled
Sample	Cans (n = 250)
1	8
2	7
3	5
4	7
5	7
6	6
7	6
8	7
9	12
10	7
11	7
12	0
13	11
14	6
15	10
16	5
17	6
18	7
19	6
20	1
21	6
22	4
23	9
24	5
25	6
26	10
27	6
28	0
29	6
30	7
31	4
32	6
33	3
34	2
35	7
36	4
37	13
38	8
39	6
40	0
41	9
42	6
43	9
44	10
45	10
46	8
47	7
48	11

Answer 1

a) First we calculate the average proportions p_bar. This is done by

P_bar = total defects/total samples = 0.026083

Now we know that n = 250.

The formula for center line (CL) is n*p_bar = 250*0.026083 = 6.52

The formula for UCL and LCL are

UCL = n*p_bar + 3*sqrt(n*p_bar*(1-p_bar)) = 14.08104

LCL = n*p_bar - 3*sqrt(n*p_bar*(1-p_bar)) = -1.03837, however since the defects cannot be in negative, we will take this as 0.

b) The control chart is shown below

c) The process appears to be in statistical control. There is no anomaly in the data or the pattern. Also all the points are within the control limit.

d) P_bar provides the percentage. It is 0.026 or 2.6% of the containers are under filled.