UnitedCo, a division of North American Industries, was about to launch a new pro

Question

UnitedCo, a division of North American Industries, was about to launch a new product. Production Manager Michelle James asked her assistant, Jim Smith to check the capability of the oven used in the process. Jim obtained 18 random samples of n = 20 pieces each. The results of those samples are shown in the following table. After he analyzed the data, he concluded that the process was not capable based on aspecification width of 1.44 cm. Jim’s organization uses a Cp comparison of 1.33.

Michelle was quite disappointed when she heard this. She had hoped that with the introduction of the new product her operation could run close to full capacity and regain some of its lost luster. The company had a freeze on capital expenditures of more than $10,000, and a replacement oven would cost many times that amount. Jim Smith worked with the oven crew to see if perhaps different settings could produce the desired results, but they were unable to achieve any meaningful improvements.

Still not ready to concede, Michelle contacted one of her former professors and explained the problem. The professor suggested obtaining another set of samples, this time using a smaller same size, or n, but taking more samples. Michelle then conferred with Jim and they agreed that he would take 27 samples of n = 5 observations each. The results are shown below:

D. If small samples can reveal something that large samples might not, why not just take small samples in every situation?

Sample Range 0.85 0.89 0.86 0.91 0.87 0.90 0.86 0.89 0.85 Sample 10 45.01 44.99 45.02 45.00 45.04 44.98 44.91 45.04 45.00 12 13 14 15 16 17 18 44.97 45.11 44.96 45.00 44.92 45.06 44.94 45.00 45.03 Range 0.91 0.84 0.87 0.86 0.89 0.87 0.86 0.85 0.88

Explanation / Answer

Standard deviation is a measure of variability from the mean. It increases with decrease in sample size and decreases with increase in sample size. Thus small sample remain less reliable in predicting the mean and other parameters.

Additionally cost of sampling and inspecting also comes into play when selecting a sample size. For example if the cost to obtain sample is high in comparison to inspect an item people prefer to have large sample.

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