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	0.486	0.499	0.493	0.511	0.481
2	0.499	0.506	0.516	0.494	0.529
3	0.496	0.500	0.515	0.488	0.521
4	0.495	0.506	0.483	0.487	0.489
5	0.472	0.502	0.526	0.469	0.481
6	0.473	0.495	0.507	0.493	0.506
7	0.495	0.512	0.490	0.471	0.504
8	0.525	0.501	0.498	0.474	0.485
9	0.497	0.501	0.517	0.506	0.516
10	0.495	0.505	0.516	0.511	0.497
11	0.495	0.482	0.468	0.492	0.492
12	0.483	0.459	0.526	0.506	0.522
13	0.521	0.512	0.493	0.525	0.510
14	0.487	0.521	0.507	0.501	0.500
15	0.493	0.516	0.499	0.511	0.513
16	0.473	0.506	0.479	0.480	0.523
17	0.477	0.485	0.513	0.484	0.496
18	0.515	0.493	0.493	0.485	0.475
19	0.511	0.536	0.486	0.497	0.491
20	0.509	0.490	0.470	0.504	0.512

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

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

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

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.)

e. What comments can you make about the process?

o The process is in statistical control.

o The process is out of statistical control.

Answer 1

Consider the following measurements for a fuel injector:

Construct the control chart for mean and range for the injector as shown below:

Step 1: Calculate the sample means, sample ranges, mean of means, and mean of ranges as shown below:

Hence, x- double bar is 0.499 and R Bar is 0.037.

Step 2: Calculate the UCL and LCL for mean using the formula as shown below:

The upper and lower control limits of x double bar chart are 0.519 and 0.478 respectively.

Note: The value of A2 is taken from exhibit 13.7

Step 3: Draw the control chart for mean as shown below:

It can be seen from the chart that no measurement is outside the control limits. Thus, the process is in control.

Step 4: Calculate the UCL and LCL for mean using the formula as shown below:

Note: The value of D3 and D4 are taken from exhibit 13.7.

The upper and lower control limits of R bar chart are 0.078 and 0 respectively.

Step 5: Draw the control chart for range as shown below:

It can be seen from the chart that no measurement is outside the control limits. Thus, the process is in control.

Conclusion:

All the points are well within the control limits. It forms a good statically controlled system.