answer the following questions 182

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Better Cheddar Case Study

You are employed by a small artisan cheese company in their quality assurance team. They have been having trouble with the Cheddar cheese line. Some of the cheeses have significant flavor and texture defects and the company is not sure why. They are careful about sanitation and they have confirmed that microbial contamination (e.g. spoilage bacteria, molds, yeast) is not the cause of the defects. The quality assurance team has tested cheese samples over several weeks and identified a potential cause of the flavor and texture defects. They think that the cheddaring and pressing processes may not be expelling enough whey from the curd. The excess whey left in the curd results in a cheese with a moisture content that is higher than expected. In addition, the flavor and texture defects identified by the sensory group are typical of those present in cheese that has undergone insufficient pressing and contains excessive whey. You have gathered moisture content data for 30 batches of cheese. The data are shown below. The company wants their cheese to have an average moisture content of 37% and will allow a maximum deviation of 0.3% above or below this average.

Sample Set
Moisture Content (%)
Standard Deviation (%) 1 36.91 0.07 2 37.00 0.07 3 37.18 0.08 4 36.90 0.10 5 36.96 0.12 6 37.13 0.12 7 37.12 0.11 8 37.10 0.10 9 37.18 0.09 10 36.96 0.09 11 36.98 0.10 12 37.18 0.08 13 36.96 0.10 14 37.18 0.11 15 37.04 0.09 16 37.17 0.11 17 37.12 0.09 18 37.15 0.07 19 36.95 0.11 20 36.93 0.07 21 36.96 0.10 22 37.03 0.11 23 36.97 0.08 24 37.01 0.07 25 36.96 0.08 26 37.17 0.10 27 37.01 0.09 28 37.18 0.08 29 37.19 0.10 30 37.06 0.11

Note that these data are also provided in a separate Excel sheet

Questions to answer: 1. What are the specification limits for the moisture content of the cheese? How do they compare to the Code of Federal Regulations for Cheddar cheese? 2. What is the average moisture content of the cheese? How does it compare to the desired average and the specification limits? 3. Calculate the process capability for moisture content. Use the standard deviation of all the moisture contents from the data given. What does the process capability tell you about the moisture content of the Cheddar cheese? 4. Calculate the capability index (Cp) and the capability index that accounts for the process center (Cpk). What do these values tell you about the process? 5. Does the process need to be adjusted to change the average moisture content based on your results for Cp and Cpk? Explain your answer. 6. Would you recommend evaluating the process to reduce variation based on your results for Cp and Cpk? Explain your answer. 7. It costs $5.75 per pound for the company to produce Cheddar cheese. They sell the inspecification cheese to distributors for $8.50 per pound and the out-of-specification cheese to a company that makes process cheese for $4.00 per pound. What is their current net profit for their Cheddar cheese? What would the company’s profit on each pound of cheese be if all of their product met specifications? You may assume that the mean and standard deviation from the data are indicative of population statistics. 8. Aside from profit loss from not being able to sell the Cheddar cheese to the intended consumers, what other problems can arise from producing out-of-specification product? Explain your answers.

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