This chapter is from the book
This chapter is from the book
This chapter is from the book
16.3 Measure Phase
The Measure phase has three steps. They are: operationally define each CTQ, perform a gage R&R study on each CTQ, and develop a baseline for each CTQ.
Operationally Define Each CTQ
Team members operationally define durability and functionality by establishing criteria for durability and functionality, developing a test for each set of criteria, and formulating a decision rule for each criteria. The operational definitions for durability and functionality are shown below.
Operational Definition for CTQ1: Durability
Criteria for a selected MSD can be seen in Figure 16.4.
)
Figure 16.4 Criteria for Number of Bends of an MSD
Test for a selected MSD:
-
Select the top front box of MSDs on the shelf in the inventory room.
-
Close your eyes, then open the box of MSDs, then haphazardly select one intact MSD. No switching is allowed.
-
Utilize the criteria for the selected MSD.
-
Count the number of bends until breaking.
Decision for a selected MSD:
-
If the number of bends is ≥ 4, then MSD is conforming.
-
If the number of bends is < 4, then MSD is defective.
Operational Definition for CTQ2: Functionality
Criteria for a box of MSDs: Count the number of "broken" clips. A clip is "broken" if it is in two pieces, regardless of the relative sizes of the pieces. It is a fact that clips can be broken only into two pieces.
Test for a box of MSDs:
-
Select the top front box of MSDs on the shelf in the inventory room.
-
Count the number of "broken" clips.
Decision for a box of MSDs:
-
If the number of MSDs that are broken ≤ 5, then the box of MSDs is conforming.
-
If the number of MSDs that are broken > 5, then the box of MSDs is defective.
The same box of MSDs is used for both operational definitions.
Perform a Gage R&R Study on Each CTQ
Team members conduct an attribute Gage R&R (repeatability and reproducibility) study on the measurement system of each CTQ to determine whether it is adequate for the needs of the project. Gage R&R is only part of a measurement system analysis. Linearity, stability, and calibration are also components of a measurement system analysis that can be conducted. These components were not studied as part of this Six Sigma project. The measurement of durability requires a destructive test.
Therefore, a simple Gage R&R study was not done for durability at this time. In the near future, an operational definition of the testing process for durability will be established, and testing will be audited to assure consistency. The measurement system for functionality is studied using the following sampling plan.
-
A shelf in the storage area contains boxes of MSDs purchased throughout the week. There are different types of MSD boxes in the storage area (different vendors, sizes, etc.).
-
The Gage R&R study required two inspectors to sample the same 10 boxes of MSDs twice.
-
The top 10 boxes on the front of the shelf were selected for the Gage R&R study.
-
The study is repeated as is deemed necessary by PSD management.
Two PSD managers have the responsibility of inspecting the MSDs for functionality; they are called Inspector 1 (Tom) and Inspector 2 (Jerry). Both Tom and Jerry counted the number of defective MSDs, twice, in random order. The functionality data is shown in Table 16.17 but not in random order.
Table 16.17. Gage R&R Data for Functionality
|
Box |
Inspector |
Count |
Fuctionality |
Box |
Inspector |
Count |
Fuctionality |
|---|---|---|---|---|---|---|---|
|
1 |
1 |
1 |
10 |
6 |
1 |
1 |
9 |
|
1 |
1 |
2 |
10 |
6 |
1 |
2 |
9 |
|
1 |
2 |
1 |
10 |
6 |
2 |
1 |
9 |
|
1 |
2 |
2 |
10 |
6 |
2 |
2 |
9 |
|
2 |
1 |
1 |
9 |
7 |
1 |
1 |
6 |
|
2 |
1 |
2 |
9 |
7 |
1 |
2 |
6 |
|
2 |
2 |
1 |
9 |
7 |
2 |
1 |
6 |
|
2 |
2 |
2 |
9 |
7 |
2 |
2 |
6 |
|
3 |
1 |
1 |
5 |
8 |
1 |
1 |
6 |
|
3 |
1 |
2 |
5 |
8 |
1 |
2 |
6 |
|
3 |
2 |
1 |
5 |
8 |
2 |
1 |
6 |
|
3 |
2 |
2 |
5 |
8 |
2 |
2 |
6 |
|
4 |
1 |
1 |
4 |
9 |
1 |
1 |
9 |
|
4 |
1 |
2 |
4 |
9 |
1 |
2 |
9 |
|
4 |
2 |
1 |
4 |
9 |
2 |
1 |
9 |
|
4 |
2 |
2 |
4 |
9 |
2 |
2 |
9 |
|
5 |
1 |
1 |
5 |
10 |
1 |
1 |
11 |
|
5 |
1 |
2 |
5 |
10 |
1 |
2 |
11 |
|
5 |
2 |
1 |
5 |
10 |
2 |
1 |
11 |
|
5 |
2 |
2 |
5 |
10 |
2 |
2 |
11 |
|
|
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A Gage run chart shows that there is no variation within inspectors or between inspectors, as seen in Figure 16.5. All the variation is between the 10 boxes of MSDs. Therefore, the measurement system is acceptable to measure functionality. The same is true for durability.
)
Figure 16.5 Minitab Gage Run Chart for Functionality
Develop a Baseline for Each CTQ
Team members conduct a study (as part of routine business) to determine the baseline capability for each CTQ. At the beginning of each hour, one box of MSDs is selected from the stor age area. The procedure for selecting a box of MSDs is simply to select the top-frontmost box on the shelf. The selection process was not altered during a sampling period of two 8-hour shifts. Baseline capability data is shown in Table 16.18.
Table 16.18. Baseline Capability Data
|
Hour |
Durability |
Functionality |
Hour |
Durability |
Functionality |
|---|---|---|---|---|---|
|
Shift 1—Hour 1 |
5 |
12 |
Shift 2—Hour 1 |
12 |
6 |
|
Shift 1—Hour 2 |
7 |
4 |
Shift 2—Hour 2 |
9 |
6 |
|
Shift 1—Hour 3 |
3 |
8 |
Shift 2—Hour 3 |
3 |
9 |
|
Shift 1—Hour 4 |
2 |
6 |
Shift 2—Hour 4 |
1 |
5 |
|
Shift 1—Hour 5 |
9 |
1 |
Shift 2—Hour 5 |
1 |
4 |
|
Shift 1—Hour 6 |
2 |
5 |
Shift 2—Hour 6 |
1 |
5 |
|
Shift 1—Hour 7 |
1 |
11 |
Shift 2—Hour 7 |
1 |
9 |
|
Shift 1—Hour 8 |
1 |
9 |
Shift 2—Hour 8 |
4 |
10 |
|
Yield |
6/16 = 0.375 |
6/16 = 0.375 |
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|
|
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The yields for durability and functionality are both 0.375, as determined by the number of tests out of 16 trials shown in Table 16.18 that met their respective CTQ's (i.e., at least four bends for durability, no more than five broken MSDs per box for functionality). This indicates very poor levels of durability and functionality for the MSDs received into the PSD and supports the initial yield estimates of 40.0%, or 60% defective MSDs (see Table 16.4).
An individuals and moving range (I-MR) chart for the durability baseline data indicates that the variability of durability is not stable over time (see the bottom panel of Figure 16.6). An investigation of the range between the eight and ninth MSDs did not reveal any obvious special cause of variation that could be used to improve the durability of MSDs.
)
Figure 16.6 Minitab Individual and Moving Range Chart for Baseline Durability Data
The I-MR chart assumes approximate normality of the CTQ (durability). The durability data is not normally distributed, as shown in Figure 16.7.
)
Figure 16.7 Minitab Dot Plot of Baseline Durability Data
Hence, use of the durability I-MR chart is not advised at this time. However, the distribution of durability may approximate a Poisson distribution. Consequently, team members constructed a c-chart [**] for the "count of bends" before each MSD breaks, which is displayed in Figure 16.8.
)
Figure 16.8 Minitab c-Chart for Durability
Figure 16.8 indicated a possible special cause Shift 2—Hour 1 when 12 bends were observed for the durability test. Further investigation and notes related to the test did not reveal any obvious differences between the MSD tested and the others, although during the first hour, the tester indicated that he may have bent the MSD slower than usual during the test, which may have caused less stress and consequently more bends.
A c-chart for functionality shown in Figure 16.9 indicates that it is stable over time.
)
Figure 16.9 Minitab c-Chart for Functionality Baseline Data
The functionality data (see Figure 16.10) appears to be approximately Poisson distributed.
)
Figure 16.10 Minitab Dot Plot for Functionality Baseline Data
Hence, use of the functionality c-chart is acceptable at this time. Finally, team members estimate the current process performance for each CTQ in Table 16.19.
Table 16.19. Current Process Performance for CTQs
|
CTQs |
Yield |
DPMO |
||
|---|---|---|---|---|
|
Current |
Desired |
Current |
Desired |
|
|
Durability |
37.50% |
99.38% |
625,000 |
6,210 |
|
Functionality |
37.50% |
99.38% |
625,000 |
6,210 |
Notice the desired 100-fold improvement shown in the DPMO columns (Current = 625,000 and Desired = 6,210). This is consistent with the goals stated in the Define phase of the DMAIC model.