Index SN 1 2 3 4
Description Step by step approach to assemble the KNC Wooden Catapult Basic Components of Six sigma Catapult Analytical Approach Working with Minitab (How to perform DOE with Six sigma Catapult)
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1.
Step by step approach to assemble the KNC Wooden Catapult
This Manual explains step by step approach to assemble the KNC Wooden Catapult once you receive it at your destination Upon receipt of KNC Wooden Catapult, you shall find following components arranged similarly
Open the Tool Kit Bag; on upper Pocket, you should find Two Rubber Band and Two 3M Impact Rubbers
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Remove all the items from main Pocket of the Tool Kit Bag and arrange it as shown in the picture Items are: Nut Bolts: Two of 1”, Three of 3” Eye Bolts: 2 Eye Bolt Rubber Assembly (2 Eye Bolts + 1 Rubber) Spanner: 1 Balls: 2 Rubber + 1 Plastic Screw Driver: 1
Place the ‘Base Block’ on table as shown. The U clip nearest (3”) shall be at your right hand side. You can use spanner to tighten the nuts of two ‘U’ Metal Clips
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Put the Numbered Wooden ‘Cup Arm Stopper Block’ as shown in two pictures
Use 1” Nut Bolt to tighten the block as shown. << Remove nuts from remaining 4 nut bolts as shown >>
Put Rubber Band Block as shown and Insert Bolts (3 of 3”). << Insert the ‘Cup Arm’ with numbers on your right hand side. >>
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Insert Left Side â&#x20AC;&#x2DC;Arm Stopper Blockâ&#x20AC;&#x2122; as shown. This time you may need to bring nuts backwards and insert properly in the Left block carefully
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Put Nuts and tighten them sufficiently
Hold the nut with one hand and tighten the bolt from right hand using screw Driver
Ghten en
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Open the butterfly nut and washer as shown
Fix the cup assembly at Position ‘1’ as shown
Put Washer as shown. << Fasten the Butterfly Nut as shown >>
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Eye Bolt with Nut to be put on ‘Rubber Band Block’ as shown << >> Eye bolt without nut to be put on ‘Cup Arm Stopper Block’
Eye Bolt Rubber Band assembly:
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Eye bolt without Washer and Butterfly Nut to be fitted at the bottom Edge of ‘Rubber Band
Page skipped Fix another end of Eye Bolt Rubber Band Assembly to ‘Cup Arm’ as shown
Block’ Page 7 of 42
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Now, your catapult is ready for Statistical Experiments!
Page skipped Note: Definition of Nut & Bolt
Nut Bolt
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Features: Supports up to Eight factors at two or more levels for experimental design Supports both continuous and categorical factors Robust designs can be practiced using ball type as a noise factor Can be used to teach Variance reduction through process flow and cause and effect diagrams Can be used for hypothesis testing, multiple regression modelling, and control charting With the double cup launcher, can be used to measure gage capability Extremely powerful for teaching design of experiments
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Basic Components of Six sigma Catapult Cup Assembly Cup Arm Two Eye Bolt & Rubber Band Assembly Rubber Band Block Cup Arm Stopper Block -Left Rubber Band Positioning Eye Bolt Cup Arm Stopper Block - Right Base Block
Cup Arm Stopper Eye Bolt
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Analytical Approach
Output is Function of Input: -Y = f (X1, X2, X3...Xn)
Inputs are following variables 1. Stopper Pin Position 2. Rubber band Pin Position (PEG Level) 3. Ball Type 4. Rubber Band Type 5. Rubber Band Pin Position on Ball Arm (Hook) 6. Ball arm Pull angle 7. Ball cup position on ball arm (Arm Length) 8. Catapult base height from ground
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Output = Ball Distance
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Schubert, et al. published an article on a catapult experiment like this in Quality Engineering in 1992, much of what follows is drawn from their work.
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If we consider the catapult shown in Figure 3, we might reasonably conclude that with a little dynamics we could predict exactly how far a marble would be thrown for any combination of factors Schubert et al. report a the following equation for such an analysis
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where I0 is the moment of inertial of the moment arm/ball combination relative to the pivot point 0. q0 and q1 are the initial and launching angles, M an m are the masses of the moment arm and ball, respectively, and rG is the distance from 0 to the mass center G of the moment arm
The other dimensions are shown in figure, F(q) is the force exerted by the rubber band on the moment arm Now that you have the equation, you can measure all the parts and try to model the nonlinear response of the rubber band. According to the paper, the analysis took about 200 man hours and experimental results showed that predicting the ball landing site was accurate to 15 inches. Accuracy is affected by the measurement precision and idealizations in the analysis. The history dependent nonlinear rubber band is also troublesome
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DOE Approach In their case, a design of experiments approach required 6 man hours and accuracy was within 3 inches. The design of experiments approach effectively defines a response envelope for the system. Once the envelope is defined, any combination of factor settings can be estimated
FACTORS
1
For the example in this class we use only three factors Stop angle Hook attachment point Arm length
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LEVELS
2
These factors are each tested at only two levels, high and low A complete set of tests is run as shown in Table 1 In Table 1, a plus sign indicates a high level and a minus sign indicates a low level Thus, in test #1 the hook, the stop angle, and the arm length are all at the low level In test #8, all the levels are high setting
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Table 1
Test matrix for catapult test
INTERACTIVE EFFECTS
3
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You notice three other columns in Table 1, AB, BC, and AC AB is the products of the level values for A and B (hook and arm length). The other columns are also products These products will be indicators of interactive effects between the factors For each test number, four repetitions were made In other words, the marble was thrown four times at each setting and the travel distance was recorded From these an average value for each test is determined Page 15 of 42
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Table 2
Measured values
DATA REDUCTION
4
The interesting thing is how the data is analyzed If we average all the distances from tests in which the hook is at the high level, then compare that with the average from all the tests for the hook is at the low level we would expect to see some difference. Indeed, this difference between high and low settings is the key to this technique Table 3 shows the results for those calculations
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Table 3 Relative effects of each factor and interactive effects
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SCREENING IMPORTANT VARIABLES
5
If we see a small difference we can say that the factor is not so important Thus, the difference defines the relative importance of each factor This also works for the combined factors so we can see the relative importance of the interactive effects From the Y values we can see that the three factors are of relatively equal importance to the travel distance of the marble The interactive effects are of relatively small importance, however Predicting with the Empirical Model The information in Table 3 can be combined to produce a predictive equation for travel distance
â&#x20AC;Śâ&#x20AC;Ś..Equation (2) Where is the predicted travel distance of the marble, A is the Y value for factor A, A is the scaled value of hook position (scaled between -1 and +1) and the other terms follow from those definitions
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PREDICTING THE PAST
6
Let's see if this equation can predict the past For the case of test #1, the values for hook, arm length, and stop angle were all at the low level or -1 Then equation 2 looks like
52.4 inches is close to the 51 inches that was average for the experimental value For Test #8, equation 2 predicts a distance of 80.1 inches, less than 2 inches away from the 82 inch experimental value Page skipped Thus, we can see that the equation is a reasonable predictor of the past Now we need to see if it can predict intermediate values of the different factors
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PREDICTING THE FUTURE
7
To keep things simple, let's set the hook at the low position (A=-1), the stop angle at high position (C=+1), and the arm length halfway between high and low (B=0) Therefore, AB=0, BC=0 and AC=-1 Equation 2 predicts a value of 32.4 You may note that there is an assumption of linearity for the effect of each of the factors If you expect this to not be true, experiments with more levels need to be run With only two levels, a linear model is the most complex possible
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CONCLUSION
The goal was to introduce you to the field of Design of Experiments and to convince you that it has value for engineers and scientists The helicopter drop experiment shows the value of DOE for screening important variables from the noise The catapult experiment shows how DOE can be used to build predictive models and show interactive effects. Page skipped If you want to learn more about this field, courses are offered in the math department at Rose, short courses are offered by software companies and through professional societies, and software and books that cover the field are readily available.
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WORKING WITH MINITAB
Minitab is a statistics package. It was developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in 1972. Minitab began as a light version of OMNITAB, a statistical analysis program by NIST. Today, Minitab is often used in conjunction with the implementation of Six Sigma, CMMI and other statistics-based process improvement methods.
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Uses of Minitab: Data and File Management- spread sheet for better data analysis. Regression Analysis Power and Sample Size Tables and Graphs Multivariate Analysis- includes factor analysis, cluster analysis, correspondence analysis, etc. Non-Parametric- various tests including sign test, runs test, Friedman test, etc. Time Series and Forecasting- tools that help show trends in data as well as predicting future values. Time series plots, exponential smoothing, trend analysis. Statistical Process Control Measurement System Analysis Analysis of Variance- to determine the difference between data points.
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INSTALL MINITAB
Install Minitab after downloading it from website: http://www.minitab.com/en-IN/products/minitab/free-trial.aspx
Put Six sigma Catapult at appropriate height, use some table or bench to raise the height of sixPage sigma skipped catapult from the ground
Decide on what ball you are going to use for the study (Which is fixed in this study as a part of example) We decide to choose following three variables Stop angle Hook attachment point Arm length
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DESIGN OF EXPERIMENTS
Go to : Stat > DOE > Factorial > Create Factorial Design
First we need to specify the type of design. In this study we are studying the effects of three factors. We want to evaluate Stop angle Hook attachment point Arm length At 2 Levels of setting. High and Low ( 6 – High , 1 Low)
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Next we click, Designs. Following Screen is displayed
Select ½ Fraction Design, Number of Replicates 2
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Next we click, Factors Following Screen will be displayed
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You shall get the sequence of experiment
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Create an additional column as â&#x20AC;&#x153;Distanceâ&#x20AC;? to note the distance travelled by the ball
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Make setting on Six sigma Catapult as in row 1 Catapult with above setting Similarly set for all the settings till you reach row 8 and note down the distance travelled
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ANALYSING EXPERIMENT RESULTS
In this section we want to understand how three factors affect the distance travelled by the ball
First, we need to specify the observed measurements in response column. Select “Distance” and click on Select
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Now go to “Terms”
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Now go to “Graphs” Tick check box “Pareto” and “four in one”
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Pareto chart of the Standardised Effects. Hook is the most significant factor (Which really affects the distance) Only one factor (Hook) significantly impact the distance travelled by the ball
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In case of more than 3 factors, say 5 factors, you can reduce the terms which are not significant In this case Stop angle is removed which is not so significant as compared to both terms
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Following are the results
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In case you used 5 or more factors in catapult experiment, it is necessary to check the number of significant factors. In the picture shown, Stop Angle and PEG Level are only two most significant factors
We will remove the non-significant main effects and this will be our final model. Before we use the model to determine the optimal factor settings, it is good practice to check the model assumptions using residual plots.
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The normal probability plot indicates that the data do not deviate substantially from a normal distribution. The error variance is fairly constant across all factor levels. The errors are randomly distributed and independent
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RESPONSE OPTIMISATION
The goal of many designed experiments is to determine the optimal factor settings that produce the best value for a response of interest. In this section, we wanted to identify the settings for two most significant input variables that maximize the distance travelled by the ball. For this we use MINITABs response optimiser, which uses a desirability function, to determine the optimal settings for the factors.
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Select Distance. And go to Setup We need to specify the goal of the optimisation, and the acceptable bounds and target value for distance. To specify the goal, we choose Maximize. Because we are trying to maximize distance. We only need to set a lower bound and a target. For distance we would like to achieve a target value of 111 but not less than 90. So, we type 90 in Lower and 111 in Target and then click OK
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With this output , you can see that with the above settings the maximum distance which can be achieved is 99.62 inches The red letters are showing Current Hook and Arm Length Position
For getting exact 76.3 inch distance you can vary hook position and arm length by selecting red line and shifting it to left. Which tell you that at 4 and 5 position of both the parameters (Hook and Arm Length) respectively
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Thank You! If you like this book, please provide feedback on info@knowledgenetindia.com Your feedback will be posted on our website!
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