This chapter is from the book
This chapter is from the book
This chapter is from the book
16.5 Improve Phase
的Improve phase involves designing experiments to understand the relationship between theYs and the vital fewXs and major noise variables (see Chapter 13); generating the actions needed to implement the levels of the vital fewXs that optimize the shape, spread, and center of the distributions of theYs; developing action plans; and conducting pilot tests of the action plans.
Team members conducted an experimental design to determine the effect ofX1(vendor),X2(size), andX3(ridges), and their interactions, on theYs, withX7= 0 (no shelf-life—MSDs are tested immediately upon arrival toPOIbefore they are placed in inventory). A 23full factorial design with two replications (16 trials) was performed for durability and functionality. The factor conditions for vendor (X1) are Office Optimum (–1) or Ibix (1); the factor conditions for size (X2) are small (–1) or large (1), and the factors conditions for ridges (X3) are without ridges (–1) or with ridges (1). The experiment was set up in two blocks to increase experimental reliability, with the first eight runs conducted in the morning and the second eight runs conducted in the afternoon. The runs were randomized within each block. The purpose of the blocks and randomization is to help prevent lurking (background) variables that are related to time (e.g., time of day and order in which data is collected) from confusing the results. Additional information can be gathered because 16 trials were run, rather than the minimum of 8 trials, especially regarding potential interactions. The data from the 23full factorial design (with two replications in run order, the first eight runs constituting the first replicate) is shown in Table 16.22.
Table 16.22. Durability and Functionality Data
Std order |
Run order |
Vendor |
Size |
Ridges |
Durability |
Functionality |
|---|---|---|---|---|---|---|
2 |
1 |
Ibix |
Small |
Without |
1 |
8 |
4 |
2 |
Ibix |
Large |
Without |
9 |
9 |
3 |
3 |
Office Optimum |
Large |
Without |
1 |
8 |
8 |
4 |
Ibix |
Large |
With |
11 |
8 |
5 |
5 |
Office Optimum |
Small |
With |
10 |
0 |
6 |
6 |
Ibix |
Small |
With |
4 |
2 |
7 |
7 |
Office Optimum |
Large |
With |
4 |
3 |
1 |
8 |
Office Optimum |
Small |
Without |
10 |
2 |
16 |
9 |
Ibix |
Large |
With |
9 |
3 |
10 |
10 |
Ibix |
Small |
Without |
3 |
0 |
12 |
11 |
Ibix |
Large |
Without |
9 |
0 |
14 |
12 |
Ibix |
Small |
With |
3 |
7 |
13 |
13 |
Office Optimum |
Small |
With |
9 |
6 |
11 |
14 |
Office Optimum |
Large |
Without |
2 |
4 |
9 |
15 |
Office Optimum |
Small |
Without |
8 |
1 |
15 |
16 |
Office Optimum |
Large |
With |
2 |
4 |
|
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Pareto charts showing which of the vital fewXs and the interactions between them have a statistically significant effect on durability (Y1) and functionality (Y2) at the 10% level of significance can be seen inFigures 6.24and6.25, respectively.
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Figure 16.24Minitab Pareto Chart of Effects for Durability
)
Figure 16.25Minitab Pareto Chart of Effects for Functionality
的major effects (i.e., those that have significance level less than 0.10—in other words, over 90% confidence level) for durability are the interaction of vendor and size and the main effect due to ridges. There are no significant effects due to vendor, size, or ridges present for functionality. This indicates that because the effect of shelf-life was held constant in this designed experiment, although it was shown to affect functionality in the data mining analysis, the team can restrict its attention to improving functionality by addressing shelf-life first. Because durability is the only outcome influenced by vendor, size, or ridges in this designed experiment, further consideration in this study will be restricted to durability. Another project can address shelf-life and its effect on functionality.
Because interaction effects should be interpreted prior to studying main effects, the team decided to construct an interaction effect plot for vendor and size.Figure 16.26is the interaction effect plot for vendor and size, relative to durability.
)
Figure 16.26Minitab Interaction Effect Plot for Vendor and Size, Relative to Durability
大小和之间的相互作用图vendor shown inFigure 16.26indicates that the best results for durability are obtained using small MSDs supplied by Office Optimum or large MSDs supplied by Ibix. The reasons for this interaction may be due to factors such as materials used for each size ofMSD, differences in supplier processes for each size ofMSD, or other supplier-dependent reasons. Team members can ask each vendor why its sizes show significant differences in average durability, if there is a preference to use only one vendor. Otherwise, the Purchasing Department should buy small MSDs from Office Optimum or large MSDs from Ibix to optimize durability (Y1).
的only significant main effect not involved within a significant interaction effect isX3, ridges. The main effect for ridges on durability is shown inFigure 16.27.
)
Figure 16.27Minitab Main Effect Plot for Ridges, Relative to Durability
This plot indicates that the average durability is about 6.5 – 5.4 = 1.1 more when anMSDwith ridges is used rather than anMSDwithout ridges. Therefore, because ridges is a main effect independent of any interaction effects, the right selection of MSDs is to use Office Optimum for small MSDs with ridges and Ibix for large MSDs with ridges. If the experimental results from Table 16.22 are used, the average durability for Office Optimum's small MSDs with ridges is (10 + 9) / 2 = 9.5, and the average durability for Ibix's large MSDs with ridges is (11 + 9) / 2 = 10.0. Both averages are well above the required corresponding概念不同of at least 4. As long as the variation (spread) of results is small enough so that no individual durability result is far from these averages, the team is successful with respect to durability. The variation in these results can be monitored using control charts after changing the purchasing process for selecting MSDs.
团队成员决定购买所有MSDsridges. In addition, the choice of vendor and size will be as follows: (vendor = Office Optimum) and (size = small) or (vendor = Ibix) and (size = large) to maximize average durability. In addition, the team decided to take on another project to reduce shelf-life to less than 5 days to address functionality. The revised flowchart for the Purchasing Department incorporating the findings of the Six Sigma project is shown inFigure 16.28.
)
Figure 16.28Revised Flowchart of the Purchasing Department
的team members conducted a pilot test of the revised best practice (see the flowchart inFigure 16.28). Data for durability from the pilot test is shown in Table 16.23.
Table 16.23. Data from the Pilot Test
Hour |
Vendor |
Size |
Ridges |
Durability |
|---|---|---|---|---|
Shift 1 — Hour 1 |
Office Optimum |
Small |
With |
10 |
Ibix |
Large |
With |
11 |
|
Shift 1 — Hour 2 |
Office Optimum |
Small |
With |
7 |
Ibix |
Large |
With |
11 |
|
Shift 1 — Hour 3 |
Office Optimum |
Small |
With |
10 |
Ibix |
Large |
With |
11 |
|
Shift 1—Hour 4 |
Office Optimum |
Small |
With |
8 |
Ibix |
Large |
With |
11 |
|
Shift 1—Hour 5 |
Office Optimum |
Small |
With |
9 |
Ibix |
Large |
With |
10 |
|
Shift 1—Hour 6 |
Office Optimum |
Small |
With |
9 |
Ibix |
Large |
With |
9 |
|
Shift 1—Hour 7 |
Office Optimum |
Small |
With |
8 |
Ibix |
Large |
With |
11 |
|
Shift 1—Hour 8 |
Office Optimum |
Small |
With |
9 |
Ibix |
Large |
With |
10 |
|
Shift 2—Hour 1 |
Office Optimum |
Small |
With |
9 |
Ibix |
Large |
With |
11 |
|
Shift 2—Hour 2 |
Office Optimum |
Small |
With |
8 |
Ibix |
Large |
With |
10 |
|
Shift 2—Hour 3 |
Office Optimum |
Small |
With |
10 |
Ibix |
Large |
With |
9 |
|
Shift 2—Hour 4 |
Office Optimum |
Small |
With |
7 |
Ibix |
Large |
With |
9 |
|
Shift 2—Hour 5 |
Office Optimum |
Small |
With |
7 |
Ibix |
Large |
With |
10 |
|
Shift 2—Hour 6 |
Office Optimum |
Small |
With |
9 |
Ibix |
Large |
With |
11 |
|
Shift 2—Hour 7 |
Office Optimum |
Small |
With |
10 |
Ibix |
Large |
With |
9 |
|
Shift 2—Hour 8 |
Office Optimum |
Small |
With |
8 |
Ibix |
Large |
With |
11 |
|
RTY |
32/32 = 1 |
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|
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Table 16.23 on page 533 indicates that the rolled throughput yield (RTY) for durability is 100%. Functionality was also tested (not shown here), using shelf-life = 0 days; that is, the MSDs were tested immediately upon arrival toPOIbefore they were placed in inventory. This resulted in anRTYof 75%, which is better than the baselineRTY. The effect on functionality of shelf-life and inventory control procedures will be investigated in subsequent projects if management decides these projects should be chartered.
Figure 16.29on page534shows that durability is in control, with a higher mean number of bends for all MSDs in the pilot test. The test pilot data shown in Table 16.23 includes results for both small MSDs from Office Optimum and large MSDs from Ibix. Subsequently, team members realized that, with all things being equal, large MSDs from Ibix should have a higher average durability than small MSDs from Office Optimum. Consequently, team members constructed two control charts, one for small MSDs from Office Optimum and another for large MSDs from Ibix (Figures 16.30on page534and16.31on page535, respectively).
)
Figure 16.29Minitab Individual Value and Moving Range Chart for Durability
)
Figure 16.30Minitab Individual Value and Moving Range Chart for Durability of Small MSDs from Office Optimum
)
Figure 16.31Minitab Individual Value and Moving Range Chart for Durability of Large MSDs from Ibix
Figures 16.29,16.30, and16.31show that durability (Y1) is in control, but it is dangerous to compute any process capability statistics due to the small sample sizes. However, estimates for the mean and standard deviation of small MSDs from Office Optimum are 8.625 and 1.05 (calculated from the data but not shown here), respectively. The mean and standard deviation for large MSDs from Ibix are 10.25 and 0.83, respectively. Because the概念不同for durability requires the number of bends to be four or more, this requirement is 4.4 standard deviations below the mean for small MSDs from Office Optimum and 7.5 standard deviations below the mean for large MSDs from Ibix. Team members all agreed that as long as the process for both small MSDs from Office Optimum with ridges and large MSDs from Ibix with ridges remain in control, it is extremely unlikely that the MSDs will fail the概念不同for durability (Y1).