Part I.A company that produces applesauce has hired you to work in their quality assurance team. You have to help design a sampling plan for the evaluation of incoming raw materials. Apple trucks are received on a daily basis, each truck containing about 30,000 apples (ranging from 25,000 to 35,000) and are evaluated for signs of mechanical, microbial or chemical damage.

1.You need to determine a single sampling plan that according to the MIL-STD 105E would give you 95% confidence that the lot is acceptable under an AQL of 1.

HINT: This example is asking you to use the MIL-STD table.

a)Determine the sample size and the acceptance number for this plan

b)What would you do if you found a sample with 5 defective apples? Why?

c)What would you do if a sample contained 5% defective apples? Why?

2.Your supplier is not comfortable using the MIL-Std table criteria, and wants a plan that would provide assurance that all lots containing 1% defective would be accepted 90% of the time. Your company agrees to design such a sampling plan as long as it also guarantees that lots with 3% defectives will be rejected 90% of the time.

HINT: Here, instead of using the MIL-STD table you need to use probabilities to determine the sampling plan (determine sample size n and acceptance number c).

a)Design a single sampling plan that would satisfy both, the supplier and your company (you can suggest two different plans that best fit both parties).

b)According to this new sampling plan, what should you do if you found a sample with 5 defective apples? Why?

c)According to this new sampling plan, what should you do if you found a sample with 5% defective apples? Why?

3.After deciding on a single sampling plan, the operating characteristics curve is prepared:

a)In the graph, label the axis and briefly explain what data is presented. Use the graph to illustrate what would be the risk for the consumer (if a fraction defective level of 0.03 is considered unacceptable) and the risk of the producer (if a fraction defective level of 0.01 is considered acceptable).

b)Show in the figure above:

-How would the curve change if the sample size were increased?

-How would the curve change if the acceptance number were increased?

c)What should be modified in the sampling plan to decrease the risk of the consumer?