Question: A plant manager is interested in developing a quality-control program for an assembly line that produces light bulbs. To do so, the manager considers the quality of the products that come from the line. The light bulbs are packed in boxes of 12, and the line produces several thousand boxes of bulbs per day. To develop baseline data, workers test all the bulbs in 100 boxes. They obtain the following results:
Run @RISK's distribution fitting procedure on the preceding data choosing Discrete Sample Data (Counted Format) for the type of data.
a. The Fit Results window shows that the Poisson is the best fitting theoretical distribution. Is the Poisson a good choice? Why or why not? What is the interpretation of the parameter for the Poisson in this setting?
b. Noticing that there are only two boxes with three defective bulbs, you combine the last two categories in the preceding data. Rerunning @RISK's fitting procedure, we see that the binomial now fits best according to the Chi-Square measure, with the Poisson coming in a close second. How much has the parameter (m) for the Poisson changed from the case with four categories? Is there a reasonable interpretation of the parameters n and p for the binomial in this setting?
c. Which distribution would you use if you were the plant manager? Why?