Question

The percentage of faulty computer chips produced by a factory in the Pacific Rim is of concern to a customer. Rather than wait for the chips to be shipped to the assembly plant in Canada, the customer has sent a group of managers to the supplier’s factory to start statistical process control there. As each batch of chips comes out of the process, the managers collect a sample of 200 for testing. The chart below shows the number of malfunctioning chips found in each of the last twenty-four samples.

a) What is the average percentage of malfunctioning chips?

b) Graph a P-chart. What would be the upper and lower control limits on a p-chart?

c) Is the process under control?

Samples	# of "Bad" Chips
1	8
2	4
3	3
4	5
5	4
6	6
7	5
8	4
9	5
10	6
11	3
12	4
13	6
14	7
15	5
16	11
17	4
18	5
19	4
20	3
21	0
22	0
23	6
24	3

Answer 1

a. The average percentage of malfunctioning chip is given by p_bar = 0.0231 or 2.31%

This is calculated using the formula p_bar = total defect/total observations = 111/(24*200) = 0.0231

b. The upper and lower control limits are calculated using

UCL = p_bar + 3*sqrt(p_bar*(1-p_bar)/n_bar)

LCL = p_bar - 3*sqrt(p_bar*(1-p_bar)/n_bar)

Here n_bar is average sample size.

Using this formula we have

UCl = 0.0231 + 3*sqrt(0.0231*(1-0.0231)/200) = 0.0549

LCL = 0.0231 - 3*sqrt(0.0231*(1-0.0231)/200) = -0.0087

However, since proportion cannot be in negative, we shall consider the LCL as 0.

c. Once we have the value of UCL, LCL and Cl (same as p_bar), we can plot the p chart and check if the process is in control. It is shown below. We can see that sample 16 crosses the UCl value. This shows that the process is not in control.

# of "Bad" Chips Sample si p chart 1 23456 789 10 11 1 13 14 15 16 17 18 19 20 21 2 23 24 27 p bar 0.023125 Sheet856 Sheet857 Sheet858 Sheet859 Sheet860 Sheet861 AVERAGE: 0.025304179 COUNT: 100 SUM: 2.429201169 豳ロ凹ー 100% a0 0 0 0 0 0. 000000000000000000 EL-ASA ASA ASA ASA ASA ASA ASA ASA ASA ASA ASA ASA ASA ASA ASA ASA 000 ais 8 435465456346 751 45430063 123456789 10 1 2 3 4 5 6 7 8 9 20 21 41 2 3 4 5 6 7 8 9 10 11 12 13 4 5 6 7 8 9 20 21 2 2