HOW TO USE MINITAB: DESIGN OF Design Space: range of values over which factors are to be varied Factorial designs are good preliminary experiments. ○ A type of . Analysis of Variance for Response (coded units). Minitab is a registered trademark of Minitab, Inc. SAS is a registered Oehlert, Gary W. A first course in design and analysis of experiments / Gary W. Oehlert. DOE Analysis. Response Surface Design. EXPERIMENTS PITFALLS. Having an unknown or unaccounted for input variable be the real reason your Y changed.

Author: | JENNINE BODNER |

Language: | English, Spanish, Hindi |

Country: | Malta |

Genre: | Science & Research |

Pages: | 432 |

Published (Last): | 29.06.2016 |

ISBN: | 548-3-67320-710-7 |

Distribution: | Free* [*Register to download] |

Uploaded by: | MITZIE |

Design and Analysis of Experiments by Douglas Montgomery: A Supplement for Chapter 3 Experiments with a Single Factor: The Analysis of Variance . Homework Problems (This folder contains this file (Homework zmagormisvile.gq) of homework problems MINITAB 14 Macros (This is a collection of design, analysis, and simulation macros. .. (You can create normal paper for manual plotting. Press · Blog · People · Papers · Terms · Privacy · Copyright · We're Hiring! Help Center; less. pdf Design and Analysis of Experiments Eighth Edition DOUGLAS C. . Minitab and JMP are widely available general-purpose statistical software . Student Solutions Manual The purpose of the Student Solutions Manual is to.

Experimental statistics using minitab pdf Additional trademarks of Minitab Inc. Can be found at www. Finally, you perform a designed experiment to determine ways to improve those. Assess the validity of statistical assumptions, are also available with many. Experimental Statistics using Minitab exploits the availability of the statistical computer package Minitab to explain advanced statistical concepts related to the. Here is another example: Stat Tables Tally Individual.

Save the analysis results You can save all the analysis work you have done by choosing File Save Project as. Assume we want to determine sample size in Example 1 before the experiment was conducted. In the dialogue box, input 4 in Number of levels since the number of factor levels in Example 1 is 4. Input the estimated value, 75, in Value of the maximum difference between means provided that we will conclude the factor has statistically significance effect on the response variable if the mean difference in the response variable resulted from two different treatment levels exceeds a specified value, 75 in this example.

Input 0. Input the estimated value, 25, in Standard deviation. The standard deviation is an estimate of the population standard deviation. One can estimate the standard deviation through prior experience or by conducting a pilot study. Click Option and set Significance level to 0. Click OK again to calculate the sample size. Page 8 of 32 Dr. Thus, the total run should be 24 6 x 4 levels. Example 2 Two-factor Factorial Design The purpose of this experiment is to investigate the effect of reflow peak temperature and time above liquidus TAL on lead-free solder joint shear strength.

Step 1. If there are two or more input variables or factors, two-way ANOVA or general linear models should be used. In two-way ANOVA, the data must be balanced all cells must have the same number of observations , and factors must be fixed.

Jianbiao John Pan Minitab Tutorials for Design and Analysis of Experiments general linear models should be used for analyzing two-factor factorial designs. General linear model can be used for analyzing block designs, more than three-factor factorial designs, and others. General linear models can be used for multiple comparisons as well. You will see the above dialogue box. Row factor and Column factor are interchangeable.

In the dialogue box, check Normal plot of residuals, Residuals versus fits and Residuals versus order. Page 10 of 32 Dr. P value None of the P values was below 0. Thus, we cannot reject the null hypothesis, which is the lead-free solder joint shear strength of is same at different reflow profile.

Since none of the p-values was below 0. The analysis can stop here. If at least one of the p-values is below 0. The normality plot of the residuals is used to check the normality of the treatment data. The constant variance assumption is checked by the plot of residuals versus fitted values. If the plot of residual vs. It seems that there is nothing unusual about the residuals in Example 2. Page 11 of 32 Dr. Then select output graphs by click Graph option.

Page 12 of 32 Dr. Page 13 of 32 Minitab Tutorials for Design and Analysis of Experiments Example 3: Randomized Complete Block Design A study is planned to investigate whether the quality of senior projects differs between three student groups.

Eight senior projects were randomly selected from the each of these three groups. Industrial advisory board IAB members were asked to evaluate the quality of senior projects using rubric-based instruments. In this case, general linear model should be used. Double click C1 Reviewer No. Page 14 of 32 Minitab Tutorials for Design and Analysis of Experiments Nuisance factor Review No is a random factor in block design Two charts are selected to validate normality and constant variance assumptions.

Note that no run order was reported in this study. Thus, the independence assumption will not be checked. Step 3. P-value P values for Group was below 0. This indicates that there is statistically difference in average senior project quality between different student groups.

Page 15 of 32 Dr. It seems that there are no unusual residuals here. There is statistically significant difference among groups. Group 2 is the best. Page 16 of 32 Minitab Tutorials for Design and Analysis of Experiments Example 4: Factorial design with Replications Find out the critical process variables that affect the optical output power and develop a regression model.

You may see a popup window with message a copy of the content of this file will be added to the current project. In the pop-up dialogue box, select four input factors by double clicking all four factors for Factors as shown below. Click OK again to finish defining custom factorial design.

Page 17 of 32 Dr.

In the pop-up window, double click C5 Optical output power for Responses. In the pop-up window, click the button Terms and set the maximum order for terms in the model as 2. In the dialogue box for Graph, Check Normal under Effect Plots to display a normal probability plot of the effects; check to plot the Regular Residuals; check to plot Normal plot and Residuals versus fits of the Residual plots.

Page 18 of 32 Minitab Tutorials for Design and Analysis of Experiments Step 4: Validating the assumptions The results show that both normality and constant variance assumptions were met.

Step 5: Finding significant factors and re-analyzing the design According to the following Normal plot of the standardized effects, factors A, B, C, D, AB and BC have significant effect on the response.

The design can be re-analyzed following Step 1 and 2. The only difference is to choose only the significant factors into the Selected Terms in the model. Step 1. If there are two or more input variables or factors, two-way ANOVA or general linear models should be used.

In two-way ANOVA, the data must be balanced all cells must have the same number of observations , and factors must be fixed. General linear model can be used for analyzing block designs, more than three-factor factorial designs, and others.

General linear models can be used for multiple comparisons as well. You will see the above dialogue box. Row factor and Column factor are interchangeable. In the dialogue box, check Normal plot of residuals, Residuals versus fits and Residuals versus order. Page 10 of 32 11 Step 3. P value None of the P values was below Thus, we cannot reject the null hypothesis, which is the lead-free solder joint shear strength of is same at different reflow profile. Since none of the p-values was below 0.

The analysis can stop here.

If at least one of the p-values is below 0. The normality plot of the residuals is used to check the normality of the treatment data. The constant variance assumption is checked by the plot of residuals versus fitted values. If the plot of residual vs.

It seems that there is nothing unusual about the residuals in Example 2. Page 11 of 32 12 Step 5. Then select output graphs by click Graph option.

Page 13 of 32 14 Example 3: Randomized Complete Block Design A study is planned to investigate whether the quality of senior projects differs between three student groups.

Eight senior projects were randomly selected from the each of these three groups. Industrial advisory board IAB members were asked to evaluate the quality of senior projects using rubric-based instruments.

In this case, general linear model should be used. Double click C1 Reviewer No. Page 14 of 32 15 Nuisance factor Review No is a random factor in block design Two charts are selected to validate normality and constant variance assumptions.

Note that no run order was reported in this study. Thus, the independence assumption will not be checked. Step 3. P-value P values for Group was below This indicates that there is statistically difference in average senior project quality between different student groups.

Page 15 of 32 16 Step 4. It seems that there are no unusual residuals here. There is statistically significant difference among groups. Group 2 is the best.

Page 16 of 32 17 Example 4: Factorial design with Replications Find out the critical process variables that affect the optical output power and develop a regression model.

You may see a popup window with message a copy of the content of this file will be added to the current project. In the pop-up dialogue box, select four input factors by double clicking all four factors for Factors as shown below. Click OK again to finish defining custom factorial design. In the pop-up window, double click C5 Optical output power for Responses. In the pop-up window, click the button Terms and set the maximum order for terms in the model as 2. In the dialogue box for Graph, Check Normal under Effect Plots to display a normal probability plot of the effects; check to plot the Regular Residuals; check to plot Normal plot and Residuals versus fits of the Residual plots.

Page 18 of 32 19 Step 4: Validating the assumptions The results show that both normality and constant variance assumptions were met.

Step 5: Finding significant factors and re-analyzing the design According to the following Normal plot of the standardized effects, factors A, B, C, D, AB and BC have significant effect on the response. The design can be re-analyzed following Step 1 and 2.

The only difference is to choose only the significant factors into the Selected Terms in the model. Page 19 of 32 20 Step 6: Validating the assumptions again The results for the re-analysis show that the normality and constant variance assumptions were met.

Page 20 of 32 21 Step 8. Plots for the main effects and interaction effects The ANOVA table shows that all four factors are significant and there are significant interactions between Lens placement and Laser placement, and between Laser placement and Laser facet power.

As stated before, if the interaction is significant, ignore the main effect of these factors and only present the interaction plot. Since the factor Fiber alignment has no interaction with other factors, the main effect plot of Fiber alignment is meaningful. Thus, the interaction plot of Lens placement and Laser placement, interaction plot of Laser placement and Laser facet power, and main effect plot of Fiber alignment should be displayed.

In the dialogue box appears, select Optical output power for Responses and Fiber alignment for Selected factor.

Then Click OK. Note that multiple main factors effect plot can be setup in the dialogue box although in this example only one factor is displayed. In the dialogue box appears, select Laser facet power and Laser placement for Selected factors. Laser placement can be obtained.

You may click Setup button and change the setup in the pop-up window. Then click OK button. The contour plot and surface plot of Example 4 are shown below. Find out the critical process variables that affect the delta insertion loss and setting levels to meet design objective of delta insertion loss less than 1 db. In the pop-up window, double click C5 Delta insertion loss db for Responses. Page 24 of 32 25 In the Analyze Factorial Design Graphs pop-up window, Check Normal and Pareto under Effect Plots to display a normal probability plot and Pareto chart of the effects; check to plot the Regular Residuals; check to plot Normal plot and Residuals versus fits of the Residual plots.

Step 4: Validating the assumptions The results show that both normality and constant variance assumptions were met. Page 25 of 32 26 Step 5: Finding significant factors and re-analyzing the design According to the following Normal plot of the standardized effects, factors A, B and AB have significant effect on the response. Pareto chart shows the same results. Since other terms are insignificant, we can drop these terms in the model. Step 6: Validate the assumptions again The results for the re-analysis show that the normality and constant variance assumptions were met.

Since an interaction exists between Weld energy and Weld pattern, only an interaction plot is needed and no main factor plots are necessary. In the dialogue box, choose Interaction Plot and click Setup. In the Setup dialogue box, select factor A and B to include into the plots. Page 27 of 32 28 The interaction plot is displayed below. Thus, example 6A has only 8 runs. In the pop-up dialogue box, select all four factors by double clicking these four factors for Factors as shown below.

Then click OK back to previous dialogue box.