2. Stability by Variables with Subgroups

In variable measurement systems we need to assess whether the measurement process is stable over time. This evaluation is done using the control chart of the measurements obtained by an experiment over time.

Example:

The technician must carry out a study on the stability and measurement to evaluate the diameter of a steel bar with a micrometer. The technician selected a piece. which was measured on a daily basis and subgroup size 3. by one evaluator.

The values ​​are in the table:

Data	Timetable	Measure 1	Measure 2	Measure 3
6/8/2001	9:15	4.202	4.201	4.202
8/13/2001	16:35	4.201	4.202	4.203
8/20/2001	14:13	4.199	4.198	4.200
8/27/2001	9:40	4.200	4.201	4.201
4/9/2001	15:28	4.200	4.201	4.200
09/11/2001	10:39	4.202	4.201	4.200
09/19/2001	15:10	4.200	4.201	4.200
9/25/2001	9:25	4.200	4.199	4.199
01/10/2001	15:40	4.198	4.199	4.199
08/10/2001	9:25	4.200	4.202	4.200
10/16/2001	16:10	4.202	4.203	4.203
10/24/2001	10:05	4.201	4.202	4.201
01/11/2001	13:40	4.199	4.199	4.198
08/11/2001	14:55	4.200	4.200	4.201
11/14/2001	11:00	4.199	4.198	4.199
11/22/2001	15:50	4.200	4.199	4.200
11/29/2001	9:42	4.201	4.201	4.200
07/12/2001	8:20	4.199	4.200	4.199
12/12/2001	15:30	4.200	4.201	4.199
12/20/2001	11:05	4.199	4.199	4.200
12/28/2001	15:30	4.201	4.200	4.199
4/1/2002	16:00	4.200	4.200	4.202
10/1/2002	15:15	4.203	4.204	4.203
01/15/2002	16:00	4.204	4.203	4.203

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We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis.

• Click “Select Tests” to decide which tests to run. In our case, we’ll select all of them. Then, click OK.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

The results are:

Xbar Chart

	Value
Upper limit	4.202
Center line	4.200
Lower limit	4.199

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Range Chart

	Value
Upper limit	0.0033
Center line	0.0013
Lower limit	0
Standard deviation	0.0008

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Out of Control points - Xbar Graph

Subgroups	Value	Test
13/08/01	4.2020	1 point greater than 3 sigmas from the center line
20/08/01	4.1990	1 point greater than 3 sigmas from the center line
01/10/01	4.1987	1 point greater than 3 sigmas from the center line
16/10/01	4.2027	1 point greater than 3 sigmas from the center line
01/11/01	4.1987	1 point greater than 3 sigmas from the center line
14/11/01	4.1987	1 point greater than 3 sigmas from the center line
15/01/02	4.2033	1 point greater than 3 sigmas from the center line
13/08/01	4.2020	2 of 3 consecutive points greater than 2 sigmas from the center line
01/10/01	4.1987	2 of 3 consecutive points greater than 2 sigmas from the center line
15/01/02	4.2033	2 of 3 consecutive points greater than 2 sigmas from the center line

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Out of control points - Range Chart

Subgroups	Value	Test
07/12/01	0.0010	7 points or more in sequence on the same side of the center line

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