Question

Statistical Process Control

T. Crews, Inc. has been contracted to make Foolio. The recipe calls for 100 milligrams of taurine in each 16-ounce bottle. To make sure that they are in compliance, T. Crews has pulled eight bottles of Foolio from its last eleven batches and tested them for taurine content. The data from these tests is below.

Use this data for questions 8 – 14.

Mg taurine per bottle
Batch	Bottle 1	Bottle 2	Bottle 3	Bottle 4	Bottle 5	Bottle 6	Bottle 7	Bottle 8
1	103.37	104.15	105.02	105.90	105.45	107.15	109.02	109.50
2	101.00	99.42	96.72	98.50	95.13	96.15	98.83	93.30
3	103.30	100.11	101.96	102.40	100.37	100.22	106.50	101.20
4	101.00	99.73	108.31	103.75	109.70	100.35	108.00	95.93
5	101.35	104.62	108.12	103.10	99.69	103.83	97.16	104.11
6	98.05	98.58	97.35	100.25	101.39	100.55	101.34	109.07
7	96.65	98.96	92.61	107.28	97.08	99.75	107.35	104.48
8	107.00	103.56	101.39	97.65	103.65	102.62	98.26	100.67
9	100.97	103.42	101.98	99.36	112.08	103.18	100.75	104.36
10	107.15	98.30	98.25	105.33	97.45	99.12	103.95	103.71
11	107.02	104.07	106.00	101.89	102.51	103.06	102.48	97.87

1. What is UCL_R?

a. Less than 18.50

b. Between 18.50 and 18.75

c. Between 18.76 and 19.00

d. Greater than 19.00

2. What is LCL_R?

a. Less than 1.00

b. Between 1.00 and 1.25

c. Between 1.26 and 1.50

d. More than 1.50

3. All points on the R-chart are within the control limits.

	True
	False

4. What is UCL_X-bar?

a. Less than 100.00

b. Between 100.00 and 102.00

c. Between 102.01 and 104.00

d. Between 104.01 and 106.00

e. Greater than 106.00

Answer 1

Below is the screenshot of the formula applied -

Below is the screenshot of the result -

Below is the answer of the questions basis above chart -

1. What is UCL_R  - d. Greater than 19.00
2. What is LCL_R - c. Between 1.26 and 1.50
3. All points on the R-chart are within the control limits - True

4. What is UCL_X-bar - d. Between 104.01 and 106.00