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In: Statistics and Probability

Exercise 1: Defective Light Bulbs This is a Statistic subject. The data set lists the number...

Exercise 1: Defective Light Bulbs

This is a Statistic subject.

The data set lists the number of defective 60-watt light bulbs found in samples of 100 bulbs selected over 25 days from a manufacturing process. Assume that during these 25 days, the manufacturing process was not producing an excessively large fraction of defectives.

1.Plot a p chart to monitor the manufacturing process. What do you conclude? Is the process out of control?

2. How large must the fraction of defective items be in a sample selected from the manufacturing process before the process is suspected to be out of control?

3. During a given day, suppose a sample of 100 items is selected from the manufacturing process and 15 defective bulbs are found.

(a) Obtain an upper bound on the probability of observing such a sample? (hint: here you can assume that the real proportion p is indeed less than the UCL and thus UCL (upper control limit) is an upper bound for p).

(b) If a decision is made to shut down the manufacturing process in an attempt to locate the source of the implied controllable variation, what is the probability that this decision is based on erroneous conclusions?

Day Defectives
1 4
2 2
3 5
4 8
5 3
6 4
7 4
8 5
9 6
10 1
11 2
12 4
13 3
14 4
15 0
16 2
17 3
18 1
19 4
20 0
21 2
22 2
23 3
24 5
25 3

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