Question

A soft drink bottling company just ran a long line of 12-ounce soft drink cans filled with cola. A sample of 32 cans is selected by inspectors looking for non-conforming items. Among the things the inspectors look for are paint defects on the can, improper seal, incorrect volume, leaking contents, incorrect mixture of carbonation and syrup in the soft drink, and out-of-spec syrup mixture. The results of this inspection are given here. Construct a c chart from the data.

Can Number Number of Non-conformances Can Number Number of Non-conformances

1 2 17 3 2 1 18 1 3 1 19 2 4 0 20 0 5 2 21 0 6 1 22 1 7 2 23 4 8 0 24 0 9 1 25 2 10 3 26 1 11 1 27 1 12 4 28 3 13 2 29 0 14 1 30 1 15 0 31 2 16 1 32 0

Choose the correct c chart.

A
B
C
D

Answer 1

Answer

Let c be the non-conformances in each of the 32 cans

Let c follow a Poisson Variable with parameter

Therefore, Mean of c, E(c) = and Standard Deviation = ^0.5

The following is the table -

Can Number	Number of non-conformances(c)
1	2
2	1
3	1
4	0
5	2
6	1
7	2
8	0
9	1
10	3
11	1
12	4
13	2
14	1
15	0
16	1
17	3
18	1
19	2
20	0
21	0
22	1
23	4
24	0
25	2
26	1
27	1
28	3
29	0
30	1
31	2
32	0
Total	43

Size of the Sample, n = 32

In this case, the parameter is not specified. So, an appropriate estimate of is (mean of non-conformances)

Mean of the non-conformances, = 43/32 = 1.3437

The c - chart is given as -

Lower Control Limit (L.C.L.) = - 3(^0.5) = 1.3437 - 3(1.3437^0.5) = -2.1338

Since, c cannot be negative, L.C.L. is taken to be 0.

Hence,

L.C.L. = 0

Central Line = = 1.3437

Upper Control Limit (U.C.L.) = + 3(^0.5) = 1.3437 + 3(1.3437^0.5) = 4.8212

(Note that: Here, I considered the 3 limits)

A graph of the above data is given below -

(where the vertical axis represents the number of non - conformances in a can and horizontal axis represents the can number)