You are working for a company that makes cannabis oil products for medical users. One of the products is a gelatin capsule (or “gel cap”, a type of pill) containing cannabis oil. The design specification states that the oil in each capsule should contain 20.00 mg of CDB, but any amount between 18.00 and 22.00 mg is acceptable. Capsules with CBD levels outside of those limits are discarded at a cost of $0.50 each.

Your company makes this product on 2 processing lines: one is in the north end of your building and one is in the south end. Both processes run 2 shifts per day, 5 days per week. The company

has not yet developed standard operating procedures for these processes; each worker has their own preferred way of running the machines.

Your supervisor is concerned about the growing number of customer complaints about this product and is also looking for ways to boost productivity. For both reasons, you have been assigned to help the workers improve this product and process.

1. What are the sample mean and sample standard deviation of the amount of CBD per capsule for the north processing line? How many capsules had CBD levels outside of the specification limits? What are the corresponding 3 numbers for the south processing line? (You do not need to show calculations for this question, as they are easy to do in Excel; just report your answers.)

2. With respect to CBD levels, what was the yield of the north process and the yield of the south process? Which one was better?

3. What is the Taguchi quadratic loss function for this product? For each process, what is the expected loss per capsule? Which process was better?

4. Calculate the Cp, Cpk, and Cpm capability scores for each process. Which processes were capable on their best days? Which ones were capable on typical days? Which process was better?

5. Calculate the Sigmap, Sigmapk, Sigmapm scores for each process. (Hint: simply convert the capability scores you calculated above.) Which processes met the Six-Sigma standard on their best days? Which ones met it on their typical days? Which process was better?

 

1 2 3 4 5 6 North line 7 Capsule CBD 8 9 10 11 12 13 14 15 16 17 For assignments 1 and 2 CBD in 2 samples of finished products Each sample includes 40 capsules CBD measured in mg per capsule 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 -40 41 42 43 44 45 46 47 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 17.28 19.44 19.78 19.89 21.99 19.90 21.46 19.80 19.80 19.78 19.67 18.56 20.63 18.12 19.74 19.38 18.30 20.61 18.95 20.44 17.70 19.46 19.45 21.73 19.78 20.69 18.83 19.89 18.89 21.88 20.54 20.04 19.45 19.12 19.80 20.09 17.14 18.68 18.991 17.23 South line Capsule CBD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 116 18 19 20 21 22 23 24 25 26 27 28 29 UWNHOS 30 31 32 33 34 35 36 37 38 39 40 19.2 20.5 21.7 19.0 22.8 18.5 17.9 19.8 19.3 19.3 20.6 21.2 23.1 20.5 20.2 21.8 23.3 21.8 20.9 22.2 18.6 19.8 18.4 19.9 19.7 16.9 23.2 22.3 18.8 20.5 22.16 20.58 20.54 23.44 18.27 19.96 16.76 20.79 18.46 17.84