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 eachCTQ, perform a gage R&R study on eachCTQ, and develop a baseline for eachCTQ.
Operationally Define EachCTQ
团队成员在耐用性和定义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
Criteriafor a selectedMSDcan be seen inFigure 16.4.
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Figure 16.4Criteria for Number of Bends of an MSD
Testfor a selectedMSD:
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 intactMSD. No switching is allowed.
Utilize the criteria for the selectedMSD.
Count the number of bends until breaking.
Decisionfor a selectedMSD:
If the number of bends is ≥ 4, thenMSDis conforming.
If the number of bends is < 4, thenMSDis defective.
Operational Definition for CTQ2: Functionality
Criteriafor 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.
Testfor a box of MSDs:
Select the top front box of MSDs on the shelf in the inventory room.
Count the number of "broken" clips.
Decisionfor 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 EachCTQ
Team members conduct an attribute Gage R&R (repeatability and reproducibility) study on the measurement system of eachCTQto 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 ofMSDboxes 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 byPSDmanagement.
TwoPSDmanagers have the responsibility of inspecting the MSDs for functionality; they are calledInspector 1(Tom) andInspector 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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计运行图表显示,没有变化within inspectors or between inspectors, as seen inFigure 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.
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Figure 16.5Minitab Gage Run Chart for Functionality
Develop a Baseline for EachCTQ
Team members conduct a study (as part of routine business) to determine the baseline capability for eachCTQ. 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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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 thePSDand 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 ofFigure 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 16.6Minitab Individual and Moving Range Chart for Baseline Durability Data
The I-MR chart assumes approximate normality of theCTQ(durability). The durability data is not normally distributed, as shown inFigure 16.7.
)
Figure 16.7Minitab 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 ac-chart[**]for the "count of bends" before eachMSDbreaks, which is displayed inFigure 16.8.
)
Figure 16.8Minitab c-Chart for Durability
Figure 16.8indicated 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 theMSDtested and the others, although during the first hour, the tester indicated that he may have bent theMSDslower than usual during the test, which may have caused less stress and consequently more bends.
Ac-chart for functionality shown inFigure 16.9indicates that it is stable over time.
)
Figure 16.9Minitab c-Chart for Functionality Baseline Data
The functionality data (seeFigure 16.10) appears to be approximately Poisson distributed.
)
Figure 16.10Minitab Dot Plot for Functionality Baseline Data
Hence, use of the functionalityc-chart is acceptable at this time. Finally, team members estimate the current process performance for eachCTQin 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 theDPMOcolumns (Current = 625,000 and Desired = 6,210). This is consistent with the goals stated in the Define phase of theDMAICmodel.