Question

The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one-hour intervals. Use three-sigma control limits. Use Exhibit 10.13.

	OBSERVATIONS
SAMPLE NUMBER	1	2	3	4	5
1	0.465	0.494	0.493	0.511	0.472
2	0.471	0.501	0.505	0.484	0.515
3	0.472	0.493	0.516	0.493	0.528
4	0.475	0.501	0.495	0.494	0.492
5	0.481	0.498	0.523	0.457	0.485
6	0.472	0.496	0.502	0.495	0.505
7	0.494	0.502	0.494	0.471	0.504
8	0.505	0.499	0.486	0.472	0.487
9	0.472	0.501	0.507	0.504	0.506
10	0.465	0.502	0.505	0.511	0.485
11	0.495	0.495	0.456	0.494	0.491
12	0.458	0.463	0.525	0.504	0.529
13	0.516	0.502	0.495	0.521	0.504
14	0.491	0.521	0.502	0.495	0.508
15	0.493	0.505	0.487	0.511	0.503
16	0.471	0.501	0.484	0.475	0.525
17	0.481	0.481	0.508	0.473	0.484
18	0.507	0.493	0.495	0.472	0.484
19	0.501	0.539	0.494	0.485	0.493
20	0.513	0.494	0.485	0.504	0.502

a. Calculate the mean and range for the above samples. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

Sample Number	Mean	Range
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

b. Determine X=X= and R−R−. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

X=X=
R−R−

c. Determine the UCL and LCL for a -chart. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

UCL
LCL

d. Determine the UCL and LCL for R-chart. (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to 3 decimal places.)

UCL
LCL

e. What comments can you make about the process?

	The process is in statistical control.
	The process is out of statistical control.

Answer 1

a) X-bar (Mean) is the average of all observation for the sample. Range is the difference between the max and min value of the observations in the sample.

b)

c) X-bar chart

For sample size n=5

From the table of control chart constant

A2 = 0.577, D3=0, D4=2.114

d) R Chart

e) The process is in statistical control.

Mean Value of all samples is within the range of UCL and LCL of X-bar so the process is centred. Range value of all samples is within the range of UCL and LCL of R Chart so there is no out of control variability in the process.