Question

4. The Apparel Company makes expensive polo-style men's and women's short-sleeve knit shirts at its plant in Jamaica. The production process requires that material be cut into large patterned squares by operators, which are then sewn together at another stage of the process. If the squares are not of a correct length, the final shirt will be either too large or too small. In order to monitor the cutting process, management takes a sample of 4 squares of cloth every other hour and measures the length. The length of a cloth square should be 36 inches, and historically, the company has found the length to vary across an acceptable average of 2 inches.

Construct an R-chart for the cutting process using 3 sigma limits.

RAC has taken 10 additional samples with the following results:

Samples		Measurements (in.)
1	37.3	36.2	38.2	36.3
2	33.4	35.4	37.3	36.2
3	32.1	34.8	38.1	35.7
4	36.1	36.5	36.2	34.2
5	35.1	37.3	35.2	33.1
6	33.1	35.3	35.3	32.3
7	38.4	39.1	35.1	32.2
8	35.1	36.8	36.1	34.5
9	37.4	39.5	37.2	36.2
10	32.1	34.4	35.5	36.3

Plot the new sample data on the control chart constructed above and comment on the process variability. What might you have learned from this graph?

Construct an x-chart and an R-chart. Plot the sample observations provided above.
Use both of the x- and R-charts to comment on the process.

Answer 1

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	1	2	3	4	Mean	Range
1	37.3	36.5	38.2	36.1	37.03	2.10
2	33.4	35.8	37.9	36.2	35.83	4.50
3	32.1	34.8	39.1	35.3	35.33	7.00
4	36.1	37.2	36.7	34.2	36.05	3.00
5	35.1	38.6	37.2	33.6	36.13	5.00
6	33.4	34.5	36.7	32.4	34.25	4.30
7	38.1	39.2	35.3	32.7	36.33	6.50
8	35.4	36.2	36.3	34.3	35.55	2.00
9	37.1	39.4	38.1	36.2	37.70	3.20
10	32.1	34	35.6	36.1	34.45	4.00
				Grand mean	35.86	4.16

UCLx = 35.86 + .73(4.16 ) =	38.8993	UCLR = 2.28 (4.16) =	9.4848
LCLx = 35.86 - .73(4.16) =	32.8257	LCLR = 0 (4.16) =	0

Both the X-bar and R charts are in control, thus the process is in control.

Cp =(38-34)/(38.9 - 32.83) = 0.658

However The process is not capable

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