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 ayofoto.info) 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.
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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.
Jianbiao John Pan Minitab Tutorials for Design and Analysis of Experiments After we conclude that there is significant different in etch rate between different power levels. Finding significant factors According to the following Normal plot of the standardized effects and Pareto chart of the standard effects. Interpret the effects plots You can also evaluate the normal probability plot and the Pareto chart of the standardized effects to see which effects influence the response, Hours. Any effects that extend beyond the reference line are significant. Jaganathan Krishnan.
DOE design of experiments helps you investigate the effects of input variables factors on an output variable response at the same time. These experiments consist of a series of runs, or tests, in which purposeful changes are made to the input variables. Data are collected at each run. You use DOE to identify the process conditions and product components that affect quality, and then determine the factor settings that optimize results.
Minitab offers five types of designs: The steps you follow in Minitab to create, analyze, and visualize a designed experiment are similar for all types. After you perform the experiment and enter the results, Minitab provides several analytical tools and graph tools to help you understand the results. This chapter demonstrates the typical steps to create and analyze a factorial design.
You can apply these steps to any design that you create in Minitab. In this chapter, you investigate two factors that might decrease the time that is needed to prepare an order for shipment: The Western center has a new order-processing system. You want to determine whether the new system decreases the time that is needed to prepare an order.
The center also has two different packing procedures.
You want to determine which procedure is more efficient. You decide to perform a factorial experiment to test which combination of factors enables the shortest time that is needed to prepare an order for shipment.
Before you can enter or analyze DOE data in Minitab, you must first create a designed experiment in the worksheet. Minitab offers a variety of designs. You choose the appropriate design based on the requirements of your experiment. After you choose the design and its features, Minitab creates the design and stores it in the worksheet. You want to create a factorial design to examine the relationship between two factors, order-processing system and packing procedure, and the time that is needed to prepare an order for shipping.
Minitab uses the factor names as the labels for the factors on the analysis output and graphs. By default, Minitab randomizes the run order of all design types, except Taguchi designs.
Randomization helps ensure that the model meets certain statistical assumptions. Randomization can also help reduce the effects of factors that are not included in the study.
Setting the base for the random data generator ensures that you obtain the same run order each time you create the design. Each time you create a design, Minitab stores design information and factors in worksheet columns. The RunOrder column C2 indicates the order to collect data.
If you do not randomize the design, the StdOrder and RunOrder columns are the same.
In this example, because you did not add center points or put runs into blocks, Minitab sets all the values in C3 and C4 to 1. If you need to change only the factor names, you can enter them directly in the worksheet.
After you perform the experiment and collect the data, you can enter the data into the worksheet. The characteristic that you measure is called a response. In this example, you measure the number of hours that are needed to prepare an order for shipment.
You obtain the following data from the experiment:. Verify that Print Grid Lines is selected. Use the form to record measurements during the experiment. After you create a design and enter the response data, you can fit a model to the data and generate graphs to assess the effects. Use the results from the fitted model and graphs to determine which factors are important to reduce the number of hours that are needed to prepare an order for shipment.
In this example, you fit the model first. You use the Session window output and the two effects plots to determine which effects are important to your process.
First, look at the Session window output. You can also evaluate the normal probability plot and the Pareto chart of the standardized effects to see which effects influence the response, Hours.
Square symbols identify significant terms. Minitab displays the absolute value of the effects on the Pareto chart. Any effects that extend beyond the reference line are significant.
You can use the stored model to perform additional analyses to better understand your results. Next, you create factorial plots to identify the best factor settings, and you use Minitab's Predict analysis to predict the number of hours for those settings. You use the stored model to create a main effects plot and an interaction plot to visualize the effects. The factorial plots include the main effects plot and the interaction plot.
A main effect is the difference in the mean response between two levels of a factor. The main effects plot shows the means for Hours using both order-processing systems and the means for Hours using both packing procedures. The interaction plot shows the impact of both factors, order-processing system and packing procedure, on the response.
Because an interaction means that the effect of one factor depends on the level of the other factor, assessing interactions is important. Each point represents the mean processing time for one level of a factor.
The horizontal center line shows the mean processing time for all runs. How to obtain data? An engineer is interested in investigating the relationship between the RF power setting and the etch rate. He is interested in a particular gas C2F6 and gap 0. The experiment is replicated 5 times. Step 1: Click Open button. Then you will see the data of the experiment in the worksheet. Corresponding values of the response variable We input the levels of the treatment in one column C2 and the corresponding values of the response variable in another column C3.
This type of data input is called the stacked case in Minitab. It is a preferred way because it allows arranging data with the corresponding run order in column C1 so that the independence assumption can be checked in ANOVA analysis.
In unstacked case, the response values of a given treatment are inputted in a separate column. Note that the Run No. Step 2: Performing Data Analysis Example 1 is a one-factor factorial design. In the dialogue box. Page 4 of Then Click OK back to previous dialogue box. The boxplot. Then Click Graphs to select the output graphs of the analysis. Step 4. P-value P-value is a measure of how likely the sample results are. The population normality can be checked with a normal probability plot of residuals.
Page 5 of Normality Normality — ANOVA requires the population in each treatment from which you draw your sample be normally distributed. If the distribution of residuals is normal. P-values range from 0 to 1. Page 6 of This plot should show a random pattern of residuals on both sides of 0. The independence. A common pattern is that the residuals increase as the fitted values increase. The constant variance assumption can be checked with Residuals versus Fits plot. Step 5.
A positive correlation or a negative correlation means the assumption is violated. Independence Independence — ANOVA requires that the observations should be randomly selected from the treatment population. The boxplot shows that the etch rate increases as the power level increases. If the plot does not reveal any pattern. Both plot of residuals versus fitted values and plot of residuals versus run order do not show any pattern.
The Effect of the factor power level can be displayed using a boxplot as shown below. The variance of the observations in each treatment should be equal. The normality plot of the residuals above shows that the residuals follow a normal distribution. Page 7 of In this case. Jianbiao John Pan Minitab Tutorials for Design and Analysis of Experiments After we conclude that there is significant different in etch rate between different power levels.
Step 6. Input the estimated value. One can estimate the standard deviation through prior experience or by conducting a pilot study. The standard deviation is an estimate of the population standard deviation. Click OK again to calculate the sample size. If there are two or more input variables or factors. 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.
Page 9 of Response variable: Shear Force Input factors: The required sample size for each level is 6 if the maximum difference in treatment mean is Page 10 of Row factor and Column factor are interchangeable. 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 models can be used for multiple comparisons as well. Method 1: You will see the above dialogue box. General linear model can be used for analyzing block designs. If the plot of residual vs. The normality plot of the residuals is used to check the normality of the treatment data. It seems that there is nothing unusual about the residuals in Example 2. The constant variance assumption is checked by the plot of residuals versus fitted values. The analysis can stop here. If at least one of the p-values is below 0.
Page 11 of Since none of the p-values was below 0. P value None of the P values was below 0. Page 12 of Then select output graphs by click Graph option. In the General Linear Model dialogue box. In Model. If no interaction term is specified. Page 13 of Eight senior projects were randomly selected from the each of these three groups.
Group Nuisance factor: Reviewer General Linear Model in Minitab can be used for this analysis. Industrial advisory board IAB members were asked to evaluate the quality of senior projects using rubric-based instruments.
Page 14 of Randomized Complete Block Design A study is planned to investigate whether the quality of senior projects differs between three student groups. Blocking is used to remove the effects of Reviewers Step 2: This indicates that there is statistically difference in average senior project quality between different student groups.
Step 3. Page 15 of P-value P values for Group was below 0. Note that no run order was reported in this study. There is statistically significant difference among groups. It seems that there are no unusual residuals here. Page 16 of Group 2 is the best. Page 17 of In the pop-up dialogue box. Input factors Response variable Step 2: Defining the Factorial Design. Click OK again to finish defining custom factorial design. Factorial design with Replications Find out the critical process variables that affect the optical output power and develop a regression model.
In the dialogue box for Graph. In the pop-up window. Analyzing the factorial design After define the factorial design. Check Normal under Effect Plots to display a normal probability plot of the effects. All main effects and 2-way interactions will be displayed in Selected Terms.
Minitab removes all three-way and higher-order interactions from Selected Terms and displays them in Available Terms.