You need to make some decisions regarding the procurement of bolts from three di

Question

You need to make some decisions regarding the procurement of bolts from three different supplies. You have requested that the shank diameter (above the thread) have specifications of 1.500 0.009 inches. The SPC studies done by the suppliers have indicated that their processes are behaving consistently in statistical control with the following process parameters. The individual measurements follow the normal distribution. Supplier I: = 1.500 inches, sigma x = 0.003 inch, Supplier 2: = 1.500 inches. sigma x = 0.0022 inch. Supplier 3: = 1.4950 inches, sigma x = 0.0015 inch. Which supplier would you purchase from? Why? Explain your logic and show calculations and graphical evidence to back it up.

Explanation / Answer

Assuming I understand the problem correctly, I hope this explanation helps:

Your specifications of 1.500 ± 0.009 inches means you want all the bolts to have a diameter between 1.491 and 1.509 inches. You assume that each bolt you procure from the suppliers are independent of each other. Therefore, we assume we can use the Normal distribution.

Apply the 68-95-99.7 rule for the Normal distribution. In context, we know that 99.7% of the bolts we procure from a supplier will be within 3 standard deviations or 3 of the mean. So, we want the supplier who will have the largest percentage of bolts within our acceptable range of diameters.

The next step is to find the acceptable intervals for each supplier and see which one best satisfies our requirements.

For supplier 1, the mean is 1.5 inches and is 0.003 inches. 3 standard deviations from the mean in both directions gives us a range of 1.5 - 3(0.003) or 1.491 inches and 1.5 + 3(0.003) = 1.509. So, according to the Normal distribution, 99.7% of the bolts we procure from Supplier 1 will have diameters between 1.491 and 1.509 inches.

For supplier 2, the mean is 1.5 inches and is 0.0022 inches. We need not calculate the range for this distribution. Why? The reason is because the for supplier 2 is less than for supplier 1. Therefore, we know that the bolts we procure from supplier 2 will have a greater percentage of satisfying our requirements. In other words, because the standard deviation for supplier 2 is less than that for supplier 1, the variation among diameters for supplier 2 is much less, so more of the bolts will be in the same range as that for supplier 1 (this is wordy and maybe a big confusing). If you think of the Normal distribution, the graph will be less wide for supplier 2 than for supplier 1, so we will be more confident that the percentage of bolts we procure from supplier 2 that satisfies our conditions will be even greater than the 99.7% offered by supplier 1. (This is the answer by the way).

For supplier 3, using similar reasoning, 3 standard deviations form the mean in both directions gives us a range of 1.495 - 3(0.0015) = 1.4905 and 1.495 + 3(0.0015) = 1.4995. Because this range covers some diameters outside of our acceptable range (1.4905 < 1.491), we are uncertain about the percentage of bolts that satisfy our requirements from supplier 3. Because of this, what we can conclude, despite the uncertainty, is that less than 99.7% of the bolts from supplier 3 satisfy our conditions.

Therefore, supplier 2 is the best choice.

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