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Li Zongming

Six Sigma

Using Taguchi Designed Experiment to Reduce Tire Leakage Rates

In many cases, this method is the most cost effective way to implement design of experiments.

Published: Tuesday, August 11, 2009 - 04:00

Design of experiments (DOE) is a crucial tool in Six Sigma quality management and its application is widespread in Japan; nevertheless, many manufacturing companies in other countries have not formally adopted it because of its complex concepts and costs. As a matter of fact, the essence of the DOE method lies in optimizing the parameters of engineering design and mass production. This article features a case study of reducing tire leakage rate with DOE method.

Terminology

DOE is a statistically organized method that is implemented by altering (changing the levels) inputs (factors) and then observing the output (the interaction effects among various factors and the response of specific quality characteristics); that is, y=f(x) where x stands for input and y stands for output. The philosophy of the DOE approach originates from British mathematician R.A. Fisher in the early 20th century.

Full factorial design (FFD), also called a fully-crossed design, measures the effect of each factor on a response variable. That is to say, all possible combinations of levels and factors are treated.

One-factor-at-a-time (OFAT) is the traditional method of experiment that studies only one factor at a time while all of other factors are held fixed in an experimental run. OFAT experiments carry the risk that they do not disclose what significant effect other factors would have on response variable (quality characteristic) if other factors were altered simultaneously. Another drawback of the OFAT technique is that the repetition of experimental results cannot be warranted.

The orthogonal array, popularly referred to as Taguchi Method, is a numeric table where each column stands for a given factor with at least two levels, and each row stands for an experimental run. The orthogonal array omits some combinations and aims at efficiently finding the key input variables (factors) with the least trials. An orthogonal array is balanced; no factor is weighed more or less in an experiment, thus allowing factors to be analyzed independently of each other.


Figure.1 wheel    

 

 
Figure 2. Wire ring ID  

 

 
Figure 3. Seal layer

Case Study

Supplier X manufactures a tubeless wheel with rubber tire. The tires are inflated at 28 psi before shipment and their tire pressure must be more than or equal to 24 psi after 45 days of transit. However, a great number of wheels turn out to be completely flat (see figure 1) or below 24 psi, with a defect rate of between 11.0%  percent and 13.4 percent. Such high percentage of poor products has brought about a large economic loss for supplier X as well as many customer complaints. Based on the customer feedback and years of production experience, the supplier initially determined three factors with respect to the tire leakage: wire ring interior diameter (ID), as seen in figure 2; tire weight; and seal layer thickness, as seen in figure 3. The initial parameters of the wheel were as follows—wire ring ID (135.6 mm), tire weight (1,100 g), and seal layer thickness (1.20 mm). In order to verify the appropriateness of product parameters, supplier X decides to perform relating experiments. After all, if wire ring ID was oversize, the tire would probably not tightly contact the bead seat and consequently air inside the tire would run through the gap between tire and bead seat. Second, once the tire is underweight due to low rubber content, the air within tire could permeate tire surface over time. Third, in the event of an overly-thin seal layer, air within the tire could leak out.

Obviously, a full factorial experiment is not feasible due to resource concerns. A full factorial experiment would examine the influence of all factors under different levels and gain a lot of information, but it would take an excessive amount of time and cost. This type of inexpensive wheel must be observed for 45 days before the leakage fallout rate is accurately calculated. In this case, if a full factorial experiment with three factors and three levels per factor were taken, the number of trials would be 27 (33) and the outcome of the experiment would be too late for quality improvement and market demand. Similarly, the traditional strategy of “one-factor-at-a-time” is not suitable either, for the same reasons. Therefor supplier X adopted the three-level fractional factorial design, or to be more exact, the orthogonal array-L9 (33), which needs only nine experimental runs with three factors and three levels. Note that Statistical software Minitab was used to design the experiment and experimental results are presented as figure 4.

Factors Run

Wire Ring ID (mm)

Tire Weight (g)

Seal Layer Thickness (mm)

Fallout Rate for Leakage (%)

1

135.6

1100

1.2

12.2%

2

135.6

1300

1.5

7.5%

3

135.6

1330

1.8

5.1%

4

135.3

1100

1.5

6.5%

5

135.3

1300

1.8

3.9%

6

135.3

1330

1.2

11.5%

7

135.1

1100

1.8

3.3%

8

135.1

1300

1.2

10.1%

9

135.1

1330

1.5

6.3%

Figure 4. L9 (33): experiment data

  
In the above array, there are three different levels for each of the factors (wire ring ID, seal layer thickness, and tire weight). This table enables the three factors to be assessed independently.

To better evaluate the main effect of factors, Minitab was used. The corresponding main effects plot is shown as figure 5.



Figure 5. Main effects plot for fallout rate

 

The above plot shows that both wire ring ID and seal layer thickness are significantly contributing factors, but the latter plays the most important role in decreasing leakage proportion since the slope of line “seal layer thickness” is sharpest. Moreover, the plot illustrates that the influence of tire weight on tire leakage varies little when it ranges from 1,100 g to 1,330 g; which means that adding rubber content is insignificant with respect to reducing tire leakage rate. However, the plot shows that the average fallout rate contributed by tire weight is around 7.6 percent. Does it signify that the tire weight from 1,100 g to 1,330 g is insufficient to prevent air leakage? To verify this presumption by conducting another experiment, supplier X produced 50 wheels whose ring ID and seal layer thickness were 135.1 mm and 1.80 mm respectively. All samples were inflated at 28 psi and stored in a natural environment for 45 days. Experimental results are shown below in figure 6.


Figure 6. Plot of tire pressure vs. tire weight

The plot illustrates that all 50 samples hold tire pressure at 24.0 psi and above, and that the tire pressure does not strongly correlate with tire weight when it is more than 1,150 g. When rubber tire weight is not less than 1,230 g, however, 92.3% percent of tires hold pressure at 25.0 psi and higher. When rubber tires weigh between 1,150 g and 1,230 g, 75.0 percent of them keep pressure at 25.0 psi and higher. Additionally, the zero defects corroborate the combined contribution of seal layer thickness and wire ring ID.

Here is the theoretical analysis of the impact of rubber content on tire leakage. The infiltration capacity of air is extremely low when air molecules flee from tiny gaps of densely-packed rubber. Consequently, air takes considerable time to leak out of the tire surface. This indicates that wire ring ID and seal layer thickness should be adjusted further to reduce occurrence of tire leakage. From an assembly perspective, however, the wire ring ID cannot shrink any more because an undersize wire ring would fail to fit the bead seat of rim. So the only known factor that can be changed is the seal layer thickness.  

To better enhance the airtight performance of the tire, the supplier eventually chose the following product parameters: wire ring ID—135.1 mm; tire weight—1,300 g; and seal layer thickness—2.1mm. Afterwards, the tire leakage rate fell to 1.4 percent. This conclusion is built on the data collected from both in-house experiments and customer feedback.

Undeniably, it is proven that the thicker the seal layer is, the lower the disqualification ratio. However; the seal layer thickness cannot be increased beyond 2.1 mm, because of the constraint of wheel size. Were the seal layer thickness increased further, the tire outside diameter would have gone out of the engineering specification; in addition, the product cost would have undoubtedly risen as the thickness of the seal layer increased.

Challenging questions began to surface: Why does the plot in figure 5 reveal the mean of fallout rate influenced by tire weight is roughly 7.6 percent? What else should be done to reduce the fallout rate of 1.4 percent even further? In other words, some hidden factors (noise) that lead to tire leakage have not been detected in the experiment. From customer feedback and observations in the workshop, it was determined that the valve stem could possibly be to blame for tire leakage. Careful observation on the shop floor demonstrated that operators tended to throw the wheels onto the ground after tires were inflated to 28 psi. Those tires then underwent a water-leakage test. When the operator throws wheels, the valve stem collides with ground or other wheels, and the valve core is loosened. In such circumstance, the air will leak so slowly that defective tires do not give off bubbles in the water tank test. The corrective action against loosening the valve cores was to utilize open shelves where inflated wheels are put. This measure protects the valve core from loosening in handling. In this way, the fallout rate for tire leakage dropped to roughly 1.0 percent from 1.4 percent.

Still, in high-volume production, tire leakage is not completely eliminated. Perhaps the quality of raw material of rubber is not strictly controlled; perhaps the contour of the bead seat is not good enough to match well with the wire ring; or perhaps the hand-controlled manipulation in some production procedure does not measure up to the requirement. In short, other forms of root cause should be investigated and design of experiments should be done accordingly so as to further minimize tire leakage rate.

Limitations of Taguchi method

Despite the strength of the Taguchi method (orthogonal array), its weaknesses should noted. In statistics, the Taguchi method is not highly rigorous. There is a chance that the orthogonal array omits the combination of factors and levels that are the most significant contributors for response variables. The success of the Taguchi method normally rests on the proper selection of factors (input variables) and level values. If factors could not be found or levels were not set in an appropriate way, the results of the experiment would possibly provide little guidance to conclusion making. In effect, the selection of factors depends mainly on professional knowledge and past experience. In the case study of tire leakage, a fallout rate of 1.0 percent still exists since hidden factors remain unknown and have not been eradicated.

The advantages of the Taguchi method outweigh its shortcomings. In the past decade, the Taguchi method has been increasingly recognized as an essential tool for finding optimized parameters with the least number of experiments. In modern society where millions of enterprises seek competitive excellence by cutting cost and time for research and development, and quality improvement, application of orthogonal array is worthwhile. However, full factorial experiments are encouraged on three occasions: When the number of factors and levels is small, when experiments are not time-consuming, and when the cost for experiments is relatively low. After all, full factorial design affords the greatest opportunity to locate the best parameters for a manufacturing process or product design.

Conclusion

The wheel discussed in this article is proven sensitive to noise (an unfavorable factor in lowering leakage occurrence), and therefore response variation is still out of control. However, the Taguchi method has helped achieve the goal of reducing tire leakage rate tremendously. More in-depth investigation into input variables and consequent design of experiments is required, so as to produce a wheel that manifests consistent performance regardless of its working conditions.

In the case study of the DOE method that this article discusses, no interactions exist among three factors: tire weight, wire ring ID, and seal layer thickness. Therefore, main effects plot can provide the optimized combination of product parameters.

In practical application, design of experiments is generally completed with such dedicated software as Minitab, JMP and SPSS. They greatly alleviate the heavy load of processing data and help with graphic analysis for experimental outcomes. Last but not least, it is vital for enterprise owners to initiate training programs for DOE techniques so that those responsible for quality improvement or robust product design can obtain sufficient knowledge to carry out experiments.

 

References
1. Minitab Inc. Help File of Statistical Software Minitab Release 14. (2004)
2. Wu Jiasheng and Zheng Daxing, the Applied Six Sigma Handbook for Manufacturing, Beijing: China Renmin University Press. (2004)
3. Kenneth Crow. Robust Product Design through Design of Experiments. DRM Associates, (1998).

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About The Author

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Li Zongming

Li Zongming, majoring in mechanical engineering, has six years of experience in quality control. At present, he works as supplier quality engineer with Global Sourcing Group Inc. in Shanghai, where he responsible for quality control on products of plastic and rubber as well as hydraulic valves.