# 2.23. WP Product quality assurance (QA) is a particularly tricky business in the dye manufacturing industry. A slight variation in reaction conditions can lead to a measurable changein the color of the product, and since customers usually require extremely high color reproducibility from one shipment to another, even a small color change can lead to rejection of aproduct batch.Suppose the various color frequency and intensity values that comprise a color analysis are combined into a single numerical value, C, for a particular yellow dye. During a test period inwhich the reactor conditions are carefully controlled and the reactor is thoroughly cleaned between successive batches (not the usual procedure), product analyses of 12 batches run onsuccessive days yield the following color readings:Batch1 2 3410111274.3 71.8 72.0 73.1 75.1 72.6 75-3 73.4 74.8 72.6 73.0 73-7The QA specification for routine production is that a batch that falls more than two standard deviations away from the test period mean must be rejected and sent for reworking.Determine the minimum and maximum acceptable values of C.b. A statistician working in quality assurance and a production engineer are having an argument. One of them, Frank, wants to raise the QA specification to three standard deviationsand the other, Joanne, wants to lower it to one. Reworking is time-consuming, expensive, and very unpopular with the engineers who have to do it. Who is more likely to be thestatistician and who the engineer? Explain.c. Suppose that in the first few weeks of operation relatively few unacceptable batches are produced, but then the number begins to climb steadily. Think of up to five possible causes,and state how you might go about determining whether or not each of them might in fact be responsible for the drop in quality.

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The problem that is listed below need to be solved and you may access that problem via viewing them through the attached images in this request. **Question Number #2.23**

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Step 1

(a) The standard deviation is calculated as:

Step 2

The acceptable values are:

Step 3

(b) Frank is more likely to be the engineer as he would not want to rework batches as it is time consuming and...

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