CBD in 2 samples of finished products
Each sample includes 30 cartridges
CBD measured in mg per 500 mg cartridge
North processing line			South processing line
Cartridge	CBD		Cartridge	CBD
1	181.7		1	171.3
2	174.1		2	170.6
3	144.6		3	166.0
4	174.3		4	172.5
5	180.9		5	171.2
6	169.9		6	170.2
7	173.5		7	176.2
8	170.9		8	168.8
9	181.8		9	169.7
10	194.1		10	169.6
11	180.8		11	171.4
12	177.3		12	171.9
13	181.8		13	172.6
14	174.8		14	172.8
15	175.0		15	165.0
16	161.3		16	173.6
17	182.9		17	168.3
18	184.7		18	177.7
19	150.4		19	163.8
20	171.7		20	170.2
21	179.5		21	170.3
22	147.3		22	171.2
23	188.8		23	164.7
24	179.4		24	176.9
25	179.1		25	175.9
26	198.0		26	170.0
27	171.8		27	169.7
28	161.2		28	177.8
29	155.6		29	163.0
30	164.4		30	161.7

Story

You are beginning your improvement project by doing some descriptive analysis of the CBD oil cartridges. Among other things, you want to investigate how closely the products match the design specification, and whether there are any notable differences between the north and south processes.

You are working for a company that makes cannabis oil products for medical users. One of the company’s most important products is a small transparent cartridge containing 500 mg of oil. The design specification states that each 500 mg cartridge should contain 175 mg of CDB, but any amount between 150 and 200 mg is acceptable. Cartridges with CBD levels outside of those limits are discarded at a cost of $5 each. Your company makes this product on 2 processing lines: one is in the north end of the 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 way of running their machines. Your supervisor is concerned about the growing number of customer complaints about this product. Your supervisor is also looking for ways to boost productivity, as the company is barely profitable. For both reasons, you have been assigned to help the workers improve this product and their processes.

Questions

1. What are the mean and the sample standard deviation of the amount of CBD per cartridge for the north processing line? How many cartridges had CBD levels outside of the specification limits? What are the corresponding 3 numbers for the south processing line?

2. With respect to the CBD levels and specification, 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 each process? For each process, what is the expected loss per cartridge? Which process was better?