Nocaf Drinks, Inc., a producer of decaffeinated coffee, bottles Nocaf. Each bottle should have a net weight of 4 ounces. The machine that fills the bottles with coffee is new, and the operations manager wants to make sure that it is properly adjusted. Bonnie Crutcher, the operations manager, random

Question

Nocaf Drinks, Inc., a producer of decaffeinated coffee, bottles Nocaf. Each bottle should have a net weight of 4 ounces. The machine that fills the bottles with coffee is new, and the operations manager wants to make sure that it is properly adjusted. Bonnie Crutcher, the operations manager, randomly selects and weighs n = 8 bottles and records the average and range in ounces for each sample. The data for several samples is given in the following table. Note that every sample consists of 8 bottles.

SAMPLE	SAMPLE RANGE	SAMPLE AVERAGE	SAMPLE	SAMPLE RANGE	SAMPLE AVERAGE
A	.41	4.00	E	.56	4.17
B	.55	4.16	F	.62	3.93
C	.44	3.99	G	.54	3.98
D	.48	4.00	H	.44	4.01

Is the machine properly adjusted and in control?

SAMPLE	SAMPLE RANGE	SAMPLE AVERAGE	SAMPLE	SAMPLE RANGE	SAMPLE AVERAGE
A	.41	4.00	E	.56	4.17
B	.55	4.16	F	.62	3.93
C	.44	3.99	G	.54	3.98
D	.48	4.00	H	.44	4.01

Is the machine properly adjusted and in control?

Accepted Answer

We first find that [latex]\bar{\bar{x}} = 4.03 and \bar{R} = .505[/latex]. Then, using Table S6.1, we find:

SAMPLE	SAMPLE RANGE	SAMPLE AVERAGE	SAMPLE	SAMPLE RANGE	SAMPLE AVERAGE
A	.41	4.00	E	.56	4.17
B	.55	4.16	F	.62	3.93
C	.44	3.99	G	.54	3.98
D	.48	4.00	H	.44	4.01

[latex]UCL_{\bar{x}} = \bar{\bar{x}} + A_2\bar{R}[/latex] = 4.03 + (.373)(.505) = 4.22

[latex]LCL_{\bar{x}} = \bar{\bar{x}} - A_2\bar{R}[/latex] = 4.03 - (.373)(.505) = 3.84

[latex]UCL_R = D_4 \bar{R}[/latex] = (1.864)(.505) = .94

[latex]LCL_R = D_3 \bar{R}[/latex] = (.136)(.505) = .07

It appears that the process average and range are both in statistical control.
The operations manager needs to determine if a process with a mean (4.03) slightly above the desired mean of 4.00 is satisfactory; if it is not, the process will need to be changed.

Question 6.S6.2: Nocaf Drinks, Inc., a producer of decaffeinated coffee, bott...

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