ME7711A Quality Monitoring Exercise Assignment Sample
Introduction
The Taguchi Method is among the most widely used experimental methods that can help in finding the minimum number of experiments required to be performed under a given number of factors and levels for each of those factors (Meena, et al., 2018).
The aim of this project is to perform a comparative study that analyses the predicted results based on the Taguchi matrix methodology with the experimental results obtained through experimentation with the identified optimal parameters for the helicopter.
Methodology of the Experiment
Setup
The following table lists the control factors for the experimental design using the Taguchi Matrix. This also depicts the levels of change and variation that have been considered for the project.
Table 1 Specifications for the Control Factor
| Factors | Definition | Level Definitions | |
| A | Wing length | Long | Short |
| B | Body Length | Long | Short |
| C | Body Width | Broad | Narrow |
| D | Additional Weight | One on the body | Two on the body |
| E | Holes | 0 | One on each wing |
| F | Taped Body | No | Two on the body |
| G | Taped Wing | No | One on each wing |
Additional control factors definition:
Position of weight clips: 60mm from the base of the wings of the body
Size and location of the holes: Hole diameter: 5mm
Hole position: 12 mm from the base of the wing
Size and location of Tape: Size of the tape: 22mm x 12mm
Position on Body: Middle of the bottom of the body
Position on Wing: Bottom of the outer side of the wing.
L8 Taguchi Matrix
The following section demonstrates the generation of the Taguchi matrix for the project which will be extremely important for the project.
Table 2. L8 Taguchi Matrix
| C1 | C2 | C3 | C4 | C5 | C6 | C7 | |
| A | B | C | D | E | F | G | |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| 3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 |
| 4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 |
| 5 | 2 | 2 | 2 | 1 | 2 | 1 | 2 |
| 6 | 2 | 2 | 2 | 2 | 1 | 2 | 1 |
| 7 | 2 | 1 | 1 | 1 | 2 | 2 | 1 |
| 8 | 2 | 1 | 1 | 2 | 1 | 1 | 2 |
Team roles and responsibilities
Table 3. Roles and responsibilities of Specific group members
| Code Number | Responsibility |
| 1 | Recording trial time |
| 2 | Preparing the models |
| 3 | Recording the data |
| 4 | Dropping the helicopters |
Process of the Experiment
Eight helicopters were designed based on the above mentioned factors along with the Taguchi Matrix for the varied parameters of each of the helicopters.
An indoor testing environment was chosen for the experiment to reduce the effect of external activities.
The helicopters were dropped from the height of 5m.
All fans and ventilation systems that could impact the result of the experiment were closed.
Five trials were conducted for each test case to find the average flight time.
Preparation of the helicopters
Dropping the helicopter
The observed data
The following table depicts the data from the series of experiments conducted for the project. The times have been presented in seconds.
Table 4. Recorded times for each of the flights
| Serial number of helicopter | Serial number of trials and times observed in each trial | ||||
| 1 | 2 | 3 | 4 | 5 | |
| 1 | 3.85 | 4.09 | 4.08 | 3.8 | 3.10 |
| 2 | 3.87 | 3.82 | 3.73 | 3.71 | 3.83 |
| 3 | 4.55 | 4.08 | 4.09 | 3.98 | 4.24 |
| 4 | 5.18 | 5.25 | 5.01 | 5.28 | 5.07 |
| 5 | 2.90 | 2.88 | 2.97 | 2.79 | 2.94 |
| 6 | 2.37 | 2.87 | 2.59 | 2.34 | 2.67 |
| 7 | 3.21 | 3.30 | 3.59 | 3.09 | 3.26 |
| 8 | 2.45 | 2.56 | 2.58 | 2.70 | 2.42 |
To analyze the above data, MS Excel was used. This allowed us to calculate the mean and variation of the data using statistical functions. This will also be used to identify the signal to noise ratio which will be helpful in identifying the optimal design parameters in the later stages of the project.
Results and Analysis
The following table shows the complete experimental data set along with the Taguchi matric for the experiment.
Table 5 Obtained results along with the Taguchi Matrix
| Helicopter | Factors | Trial Times | ||||||||||
| A | B | C | D | E | F | G | 1 | 2 | 3 | 4 | 5 | |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3.85 | 4.09 | 4.08 | 3.8 | 3.1 |
| 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3.87 | 3.82 | 3.73 | 3.71 | 3.83 |
| 3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 4.55 | 4.08 | 4.09 | 3.98 | 4.24 |
| 4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 5.18 | 5.25 | 5.01 | 5.28 | 5.07 |
| 5 | 2 | 2 | 2 | 1 | 2 | 1 | 2 | 2.9 | 2.88 | 2.97 | 2.79 | 2.94 |
| 6 | 2 | 2 | 2 | 2 | 1 | 2 | 1 | 2.37 | 2.87 | 2.59 | 2.34 | 2.67 |
| 7 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 3.21 | 3.3 | 3.59 | 3.09 | 3.26 |
| 8 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 2.45 | 2.56 | 2.58 | 2.7 | 2.42 |
The mean of the trail times was established through the formula:
Mean T =
Table 6 Table depicting the mean values for the observed times
| Number of Trials and their observed Times | Mean for each helicopter | ||||
| 1 | 2 | 3 | 4 | 5 | |
| 3.85 | 4.09 | 4.08 | 3.8 | 3.1 | 3.784 |
| 3.87 | 3.82 | 3.73 | 3.71 | 3.83 | 3.792 |
| 4.55 | 4.08 | 4.09 | 3.98 | 4.24 | 4.188 |
| 5.18 | 5.25 | 5.01 | 5.28 | 5.07 | 5.158 |
| 2.9 | 2.88 | 2.97 | 2.79 | 2.94 | 2.896 |
| 2.37 | 2.87 | 2.59 | 2.34 | 2.67 | 2.568 |
| 3.21 | 3.3 | 3.59 | 3.09 | 3.26 | 3.29 |
| 2.45 | 2.56 | 2.58 | 2.7 | 2.42 | 2.542 |
Table 7 Presenting the calculated mean flight times along with the Taguchi Matrix
| Helicopter | Factors | Mean | ||||||
| A | B | C | D | E | F | G | ||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3.784 |
| 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3.792 |
| 3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 4.188 |
| 4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 5.158 |
| 5 | 2 | 2 | 2 | 1 | 2 | 1 | 2 | 2.896 |
| 6 | 2 | 2 | 2 | 2 | 1 | 2 | 1 | 2.568 |
| 7 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 3.29 |
| 8 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 2.542 |
Now, in order to analyze the means for the helicopters, the method deemed most prudent I the Level Average Method. This means that the mean times for each factors for both the specific levels (1 & 2) will be calculated separately.
For example, the level average mean for factor A at level will be calculated through the formula:
Mean T =
Delta values will be calculated using the formula:
Delta = |Factor1 – Factor2|
Table 8 Level Average Mean with Delta Values
| Level | A | B | C | D | E | F | G |
| 1 | 4.2305 | 3.352 | 3.352 | 3.5395 | 3.2705 | 3.595 | 2.96 |
| 2 | 2.824 | 3.7025 | 3.7025 | 2.812 | 3.784 | 3.4595 | 3.3545 |
| Delta | 1.4065 | 0.3505 | 0.3505 | 0.7275 | 0.5135 | 0.1355 | 0.3945 |
Based on the results of the level average mean we can conclude with the following inference:
- A, D & E have higher delta values and as such, will be considered as the major factor.
- The factors, B, C, F and G with lower value will be considered as having minor impact on the time of flight.
In order to identify the value of average time, first the total sum of all the averages presented above need to be found.
Total Sum = Sum of all averages = 47.939 s.
Given that the number of entries is 14 the time average will be given as,
Total Average = 47.939/14 = 3.4242 s or 3.42s.
Therefore, any of the flight times higher than the value of total average can be considered as a high value and vice versa.
Therefore, concluding from this and the evaluation of the above table, we can see that, A1, B2, C2, D1, E2, F1, and G2 have an above average optimal design.
Now in order to evaluate the optimum flight time, the average values were subtracted from the Average level values while the lower value figures were omitted.
Table 9 Difference between Average and Max reading
| Difference between Average and Max reading | A | B | C | D | E | F | G | Sum |
| 0.806321 | 0.278321 | 0.278321 | 0.115321 | 0.359821 | 0.170821 | 0.069679 | 2.078607 |
Now, adding this value of 2.078607 to the identified average fight time, we have:
Project flight time: 3.42s + 2.08s = 5.50s
Calculating the Signal to Noise Ratio (S/N)
To calculate the signal to noise ratio, the following formula was used:
Table 10 Calculating the S/N ratio for all helicopters
| No of trials and the observed times | S/N ratio | |||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | 3.85 | 4.09 | 4.08 | 3.8 | 3.1 | 4.697698 |
| 2 | 3.87 | 3.82 | 3.73 | 3.71 | 3.83 | 4.750596 |
| 3 | 4.55 | 4.08 | 4.09 | 3.98 | 4.24 | 5.173694 |
| 4 | 5.18 | 5.25 | 5.01 | 5.28 | 5.07 | 6.086115 |
| 5 | 2.9 | 2.88 | 2.97 | 2.79 | 2.94 | 3.579056 |
| 6 | 2.37 | 2.87 | 2.59 | 2.34 | 2.67 | 3.033842 |
| 7 | 3.21 | 3.3 | 3.59 | 3.09 | 3.26 | 4.124386 |
| 8 | 2.45 | 2.56 | 2.58 | 2.7 | 2.42 | 3.008142 |
Table 11 Presenting the S/N ratios with the Taguchi matrix
| A | B | C | D | E | F | G | S/N Ratio | |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3.784 |
| 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3.792 |
| 3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 4.188 |
| 4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 5.158 |
| 5 | 2 | 2 | 2 | 1 | 2 | 1 | 2 | 2.896 |
| 6 | 2 | 2 | 2 | 2 | 1 | 2 | 1 | 2.568 |
| 7 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 3.29 |
| 8 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 2.542 |
Now to calculate the level wise S/N ratio averages, we find the average for each factor at both the levels (1 and 2).
For example, for the S/N ratio for Factor A at level 1 will be given as,
Table 12 S/N ratio averages based on factor levels and the Delta values
| Level | A | B | C | D | E | F | G |
| 1 | 5.177026 | 4.145205 | 4.145205 | 4.393709 | 3.978344 | 4.342753 | 4.48551 |
| 2 | 3.436356 | 4.468177 | 4.468177 | 4.219674 | 4.635038 | 4.270629 | 4.127872 |
| Delta | 1.74067 | 0.32297 | 0.32297 | 0.174035 | 0.65669 | 0.072124 | 0.357638 |
| Delta Rank | 1 | 4 | 5 | 6 | 2 | 7 | 3 |
From this table we can surmise that the values for delta are the highest at A, E and G.
Therefore, these factors will be considered to be the major factors.
The rest of the factors, B, C, D and F are considered to have a minor effect on the time of flight based on S/N ratios.
Validation of design
Based on the obtained optimal designs, helicopter was created based on these values and tested to seek the comparison with observed values.
Table 13 Observed flight times for helicopter with optimal parameters
| Trial Number and Observed Timings | ||||||
| Helicopter | 1 | 2 | 3 | 4 | 5 | Average |
| 9 (Optimum) | 5.66 | 5.32 | 5.69 | 5.89 | 5.78 | 5.668 |
Comparison and Conclusion
The percentage error is established based on the observed values using optimum parameters and the predicted values through the Taguchi matrix. The formula used to find that value is given as:
This presents a variation of 0.0127% which is an acceptable value for the test.
Discussion and Conclusion
Through this experiment we were able to test the various parameters using the Taguchi matrix to an excellent degree of accuracy. The observed time of flight for the optimal helicopter design was only 0.0127% deviated from the projected values through the Taguchi matrix evaluation. Based on the evaluation using Excel we can definitely understand the importance of the experimental system and its ability in providing accurate results.
References
Meena, A., Mali, H.S., Patnaik, A. & Kumar, S.R. (2018). Investigation of wear characteristics of dental composites filled with nanohydroxyapatite and mineral trioxide aggregate. In: Thomas, S., Balakrishnan, P. & Sreekala, M.S. (Eds.), Woodhead Publishing Series in Biomaterials, Wood Head Publishing, pp. 287-305.
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