1. General Assumptions  [3.2.1.]
    
2. Continuous Linear Model  [3.2.2.]
    
3. Analysis of Variance Models (ANOVA)  [3.2.3.]
    
   1. One-Way ANOVA  [3.2.3.1.]
       
      1. One-Way Value-Splitting  [3.2.3.1.1.]
          
   2. Two-Way Crossed ANOVA  [3.2.3.2.]
       
      1. Two-way Crossed Value-Splitting Example  [3.2.3.2.1.]
          
   3. Two-Way Nested ANOVA  [3.2.3.3.]
       
      1. Two-Way Nested Value Splitting Example  [3.2.3.3.1.]
          
4. Discrete Models  [3.2.4.]
   
    

1. Define Goals  [3.3.1.]
    
2. Process Modeling  [3.3.2.]
    
3. Define Sampling Plan  [3.3.3.]
    
   1. Identifying Parameters, Ranges and Resolution  [3.3.3.1.]
       
   2. Choosing a Sampling Scheme  [3.3.3.2.]
       
   3. Selecting Sample Sizes  [3.3.3.3.]
       
   4. Data Storage and Retrieval  [3.3.3.4.]
       
   5. Assign Roles and Responsibilities  [3.3.3.5.]
      
       

1. First Steps  [3.4.1.]
    
2. Exploring Relationships  [3.4.2.]
    
   1. Response Correlations  [3.4.2.1.]
       
   2. Exploring Main Effects  [3.4.2.2.]
       
   3. Exploring First Order Interactions  [3.4.2.3.]
       
3. Building Models  [3.4.3.]
    
   1. Fitting Polynomial Models  [3.4.3.1.]
       
   2. Fitting Physical Models  [3.4.3.2.]
       
4. Analyzing Variance Structure  [3.4.4.]
    
5. Assessing Process Stability  [3.4.5.]
    
6. Assessing Process Capability  [3.4.6.]
    
7. Checking Assumptions  [3.4.7.]
   
    

1. Furnace Case Study  [3.5.1.]
    
   1. Background and Data  [3.5.1.1.]
       
   2. Initial Analysis of Response Variable  [3.5.1.2.]
       
   3. Identify Sources of Variation  [3.5.1.3.]
       
   4. Analysis of Variance  [3.5.1.4.]
       
   5. Final Conclusions  [3.5.1.5.]
       
   6. Work This Example Yourself  [3.5.1.6.]
       
2. Machine Screw Case Study  [3.5.2.]
    
   1. Background and Data  [3.5.2.1.]
       
   2. Box Plots by Factors  [3.5.2.2.]
       
   3. Analysis of Variance  [3.5.2.3.]
       
   4. Throughput  [3.5.2.4.]
       
   5. Final Conclusions  [3.5.2.5.]
       
   6. Work This Example Yourself  [3.5.2.6.]
      
       

4.   Process Modeling - Detailed Table of Contents

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1. Introduction to Process Modeling  [4.1.]
    
   1. What is process modeling?  [4.1.1.]
       
   2. What terminology do statisticians use to describe process models?  [4.1.2.]
       
   3. What are process models used for?  [4.1.3.]
       
      1. Prediction  [4.1.3.1.]
          
      2. Calibration  [4.1.3.2.]
          
      3. Optimization  [4.1.3.3.]
          
   4. What are the some of the different statistical methods for model building?  [4.1.4.]
       
      1. Linear Least Sum of Squares Regression  [4.1.4.1.]
          
      2. Nonlinear Least Sum of Squares Regression  [4.1.4.2.]
          
      3. Weighted Least Sum of Squares Regression  [4.1.4.3.]
          
      4. LOESS (aka LOWESS)  [4.1.4.4.]
         
          
2. Underlying Assumptions for Process Modeling  [4.2.]
    
   1. What are the typical underlying assumptions in process modeling?  [4.2.1.]
       
      1. The process is a statistical process.  [4.2.1.1.]
          
      2. The means of the random errors are zero.  [4.2.1.2.]
          
      3. The random errors have constant standard deviation.  [4.2.1.3.]
          
      4. The random errors follow a normal distribution.  [4.2.1.4.]
          
      5. The data are randomly sampled from the process.  [4.2.1.5.]
          
      6. The explanatory variables are observed without error.  [4.2.1.6.]
         
          
3. Data Collection for Process Modeling  [4.3.]
    
   1. What is design of experiments (aka DEX or DOE)?  [4.3.1.]
       
   2. Why is experiment design important for process modeling?  [4.3.2.]
       
   3. What are some general design principles for process modeling?  [4.3.3.]
       
   4. I've heard some people refer to "optimal" designs, shouldn't I use those?  [4.3.4.]
       
   5. How can I tell if a particular experiment design is good for my application?  [4.3.5.]
      
       
4. Data Analysis for Process Modeling  [4.4.]
    
   1. What are the basic steps for developing an effective process model?  [4.4.1.]
       
   2. How do I select a function to describe my process?  [4.4.2.]
       
      1. Incorporating Scientific Knowledge into Function Selection  [4.4.2.1.]
          
      2. Using the Data to Select an Appropriate Function  [4.4.2.2.]
          
      3. Using Methods that Do Not Require Function Specification  [4.4.2.3.]
          
   3. How are estimates of the unknown parameters obtained?  [4.4.3.]
       
      1. Least Sum of Squares  [4.4.3.1.]
          
      2. Weighted Least Sum of Squares  [4.4.3.2.]
          
   4. How can I tell if a model fits my data?  [4.4.4.]
       
      1. How can I assess the sufficiency of the functional part of the model?  [4.4.4.1.]
          
      2. How can I detect non-constant of variation across the data?  [4.4.4.2.]
          
      3. How can I tell if there was drift in the measurement process?  [4.4.4.3.]
          
      4. How can I assess whether the random errors are independent from one to the next?  [4.4.4.4.]
          
      5. How can I test whether or not the random errors are distributed normally?  [4.4.4.5.]
          
      6. How can I test whether any significant terms are missing or misspecified in the functional part of the model?  [4.4.4.6.]
          
      7. How can I test whether all of the terms in the functional part of the model are necessary?  [4.4.4.7.]
          
   5. If my current model does not fit the data well, how can I improve it?  [4.4.5.]
       
      1. Updating the Function Based on Residual Plots  [4.4.5.1.]
          
      2. Accounting for Non-Constant Variation Across the Data  [4.4.5.2.]
          
      3. Accounting for Errors with a Non-Normal Distribution  [4.4.5.3.]
         
          
5. Use and Interpretation of Process Models  [4.5.]
    
   1. What types of predictions can I make using the model?  [4.5.1.]
       
      1. How do I predict the average response value for a particular set of predictor variable values and compute its uncertainty?  [4.5.1.1.]
          
      2. What if I am interested in making a large number of future predictions of average response values?  [4.5.1.2.]
          
      3. How can I compute the value and uncertainty of a single observable response, rather than the average response?  [4.5.1.3.]
          
      4. How do I compute an interval that contains a specified proportion of all future response values for a set of predictor variable values?  [4.5.1.4.]
          
   2. How can I use my process model for calibration?  [4.5.2.]
       
      1. Single Use Calibration Intervals  [4.5.2.1.]
          
      2. Multiple Use Calibration Intervals  [4.5.2.2.]
          
   3. How can I optimize my process using the process model?  [4.5.3.]
      
       
6. Case Studies in Process Modeling  [4.6.]
    
   1. Load Cell Calibration  [4.6.1.]
       
      1. Background & Data  [4.6.1.1.]
          
      2. Selection of Initial Model  [4.6.1.2.]
          
      3. Model Fitting - Initial Model  [4.6.1.3.]
          
      4. Graphical Residual Analysis - Initial Model  [4.6.1.4.]
          
      5. Interpretation of Numerical Output - Initial Model  [4.6.1.5.]
          
      6. Model Refinement  [4.6.1.6.]
          
      7. Model Fitting - Model #2  [4.6.1.7.]
          
      8. Graphical Residual Analysis - Model #2  [4.6.1.8.]
          
      9. Interpretation of Numerical Output - Model #2  [4.6.1.9.]
          
      10. Use of the Model for Calibration  [4.6.1.10.]
           
      11. Work This Example Yourself  [4.6.1.11.]
           
   2. Alaska Pipeline  [4.6.2.]
       
      1. Background and Data  [4.6.2.1.]
          
      2. Check for Batch Effect  [4.6.2.2.]
          
      3. Initial Linear Fit  [4.6.2.3.]
          
      4. Transformations to Improve Fit  [4.6.2.4.]
          
      5. Weighting to Improve Fit  [4.6.2.5.]
          
      6. Compare the Fits  [4.6.2.6.]
          
      7. Work This Example Yourself  [4.6.2.7.]
          
   3. Ultrasonic Reference Block Study  [4.6.3.]
       
      1. Background and Data  [4.6.3.1.]
          
      2. Initial Non-Linear Fit  [4.6.3.2.]
          
      3. Transformations to Improve Fit  [4.6.3.3.]
          
      4. Weighting to Improve Fit  [4.6.3.4.]
          
      5. Compare the Fits  [4.6.3.5.]
          
      6. Work This Example Yourself  [4.6.3.6.]
          
   4. Thermal Expansion of Copper Case Study  [4.6.4.]
       
      1. Background and Data  [4.6.4.1.]
          
      2. Rational Function Models  [4.6.4.2.]
          
      3. Initial Plot of Data  [4.6.4.3.]
          
      4. Quadratic/Quadratic Rational Function Model  [4.6.4.4.]
          
      5. Cubic/Cubic Rational Function Model  [4.6.4.5.]
          
      6. Work This Example Yourself  [4.6.4.6.]
         
          
7. References For Chapter 4: Process Modeling  [4.7.]
   
    
8. Some Useful Functions for Process Modeling  [4.8.]
    
   1. Univariate Functions  [4.8.1.]
       
      1. Polynomial FUnctions  [4.8.1.1.]
          
         1. Straight Line  [4.8.1.1.1.]
             
         2. Quadratic Polynomial  [4.8.1.1.2.]
             
         3. Cubic Polynomial  [4.8.1.1.3.]
             
      2. Rational Functions  [4.8.1.2.]
          
         1. Constant / Linear Rational Function  [4.8.1.2.1.]
             
         2. Linear / Linear Rational Function  [4.8.1.2.2.]
             
         3. Linear / Quadratic Rational Function  [4.8.1.2.3.]
             
         4. Quadratic / Linear Rational Function  [4.8.1.2.4.]
             
         5. Quadratic / Quadratic Rational Function  [4.8.1.2.5.]
             
         6. Cubic / Linear Rational Function  [4.8.1.2.6.]
             
         7. Cubic / Quadratic Rational Function  [4.8.1.2.7.]
             
         8. Linear / Cubic Rational Function  [4.8.1.2.8.]
             
         9. Quadratic / Cubic Rational Function  [4.8.1.2.9.]
             
         10. Cubic / Cubic Rational Function  [4.8.1.2.10.]
              
         11. Determining m and n for Rational Function Models  [4.8.1.2.11.]
              

   
    

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   5.    Process Improvement

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   1. Introduction  [5.1.]
       
      1. What is experimental design?  [5.1.1.]
          
      2. What are the terms used in DOE?  [5.1.2.]
          
      3. What are the uses of DOE?  [5.1.3.]
          
      4. What are the steps of DOE  [5.1.4.]
         
          
   2. Assumptions  [5.2.]
       
      1. Is the measurement system capable?  [5.2.1.]
          
      2. Is the process stable  [5.2.2.]
          
      3. Is there a simple model?  [5.2.3.]
          
      4. Are the model residuals well behaved?  [5.2.4.]
         
          
   3. Choosing and running an experimental design  [5.3.]
       
      1. What are the objectives?  [5.3.1.]
          
      2. How do you select and scale the process variables?  [5.3.2.]
          
      3. How do you select an experimental design?  [5.3.3.]
          
         1. Full factorial designs  [5.3.3.1.]
             
            1. Two-level full factorial designs  [5.3.3.1.1.]
                
            2. Full factorial example  [5.3.3.1.2.]
                
            3. Blocking  [5.3.3.1.3.]
                
         2. Fractional factorial designs  [5.3.3.2.]
             
            1. A 2^3-1 design (half of a 2³)  [5.3.3.2.1.]
                
            2. Constructing the 2^3-1 half-fraction design  [5.3.3.2.2.]
                
            3. Confounding (also called "Aliasing")  [5.3.3.2.3.]
                
            4. Design resolution: A measure of merit  [5.3.3.2.4.]
                
            5. Use of fractional factorial designs  [5.3.3.2.5.]
                
            6. Screening designs  [5.3.3.2.6.]
                
            7. Summary tables of useful fractional factorial designs  [5.3.3.2.7.]
                
         3. Plackett-Burman designs  [5.3.3.3.]
             
         4. Response surface method designs  [5.3.3.4.]
             
            1. Central Composite Designs (CCD)  [5.3.3.4.1.]
                
            2. Box-Behnken designs  [5.3.3.4.2.]
                
            3. Comparisons of response surface designs  [5.3.3.4.3.]
                
            4. Blocking a response surface design  [5.3.3.4.4.]
                
         5. Adding centerpoints  [5.3.3.5.]
             
         6. Improving fractional design resolution  [5.3.3.6.]
             
            1. Full foldover designs  [5.3.3.6.1.]
                
            2. Partial or semi-foldover designs  [5.3.3.6.2.]
                
         7. Three-level designs  [5.3.3.7.]
             
         8. Mixed level designs  [5.3.3.8.]
             
      4. How do you execute the design?  [5.3.4.]
         
          
   4. Analysis of DOE data  [5.4.]
       
      1. DOE analysis steps  [5.4.1.]
          
         1. Full factorial example  [5.4.1.1.]
             
         2. Fractional factorial example  [5.4.1.2.]
             
         3. Response surface model example  [5.4.1.3.]
             
      2. What are the steps of a DOE analysis?  [5.4.2.]
          
      3. How do you check assumptions?  [5.4.3.]
          
      4. How do you interpret the DOE results?  [5.4.4.]
          
      5. What are confirmatory runs?  [5.4.5.]
         
          
   5. Advanced Topics  [5.5.]
       
      1. What if classical designs don't work?  [5.5.1.]
          
      2. What is a computer-aided design?  [5.5.2.]
          
      3. What are D-Optimal designs?  [5.5.3.]
          
      4. How can I repair a design?  [5.5.4.]
          
      5. What is a mixture design?  [5.5.5.]
          
      6. How can I account for nested variation (restricted randomization)?  [5.5.6.]
          
      7. What are Taguchi designs?  [5.5.7.]
          
      8. What are John's 3/4 fractional factorial designs?  [5.5.8.]
          
      9. Small composite designs  [5.5.9.]
         
          
   6. Case Studies  [5.6.]
      
       
   7. References  [5.7.]
       

   
    

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   6.    Process or Product Monitoring and Control

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   1. Introduction  [6.1.]
       
      1. How did Statistical Quality Control Begin?  [6.1.1.]
          
      2. What are Process Control Techniques?  [6.1.2.]
          
      3. What is Process Control?  [6.1.3.]
          
      4. What to do if the process is "Out of Control"?  [6.1.4.]
          
      5. What to do if "In Control" but Unacceptable?  [6.1.5.]
          
      6. What is Process Capability?  [6.1.6.]
         
          
   2. Test Product for Acceptability: Lot Acceptance Sampling  [6.2.]
       
      1. What is Acceptance Sampling?  [6.2.1.]
          
      2. What kinds of Lot Acceptance Sampling Plans (LASPs) are there?  [6.2.2.]
          
      3. How do you Choose a Single Sampling Plan?  [6.2.3.]
          
         1. Choosing a Sampling Plan: MIL Standard 105D  [6.2.3.1.]
             
         2. Choosing a Sampling Plan with a given OC Curve  [6.2.3.2.]
             
      4. What is Double Sampling?  [6.2.4.]
          
      5. What is Multiple Sampling?  [6.2.5.]
          
      6. What is a Sequential Sampling Plan?  [6.2.6.]
          
      7. What is Skip Lot Sampling?  [6.2.7.]
         
          
   3. Univariate and Multivariate Control Charts  [6.3.]
       
      1. What are Control Charts?  [6.3.1.]
          
      2. What are Variables Control Charts?  [6.3.2.]
          
         1. Shewhart X bar and R and S Control Charts  [6.3.2.1.]
             
         2. Individuals Control Charts  [6.3.2.2.]
             
         3. Cusum Control Charts  [6.3.2.3.]
             
            1. Cusum Average Run Length  [6.3.2.3.1.]
                
         4. EWMA Control Charts  [6.3.2.4.]
             
      3. What are Attributes Control Charts?  [6.3.3.]
          
         1. Counts Control Charts  [6.3.3.1.]
             
         2. Proportions Control Charts  [6.3.3.2.]
             
      4. What are Multivariate Control Charts?  [6.3.4.]
          
         1. Hotelling Control Charts  [6.3.4.1.]
             
         2. Principal Components Control Charts  [6.3.4.2.]
             
         3. Multivariate EWMA Charts  [6.3.4.3.]
            
             
   4. Introduction to Time Series Analysis  [6.4.]
       
      1. Definitions, Applications and Techniquess  [6.4.1.]
          
      2. What are Moving Average or Smoothing Techniques?  [6.4.2.]
          
         1. Single Moving Average  [6.4.2.1.]
             
         2. Centered Moving Average  [6.4.2.2.]
             
      3. What is Exponential Smoothing?  [6.4.3.]
          
         1. Single Exponential Smoothing  [6.4.3.1.]
             
         2. Forecasting with Single Exponential Smoothing  [6.4.3.2.]
             
         3. Double Exponential Smoothing  [6.4.3.3.]
             
         4. Forecasting with Double Exponential Smoothing(LASP)  [6.4.3.4.]
             
         5. Triple Exponential Smoothing  [6.4.3.5.]
             
         6. Example of Triple Exponential Smoothing  [6.4.3.6.]
             
         7. Exponential Smoothing Summary  [6.4.3.7.]
             
      4. Univariate Time Series Models  [6.4.4.]
          
         1. Sample Data Sets  [6.4.4.1.]
             
            1. Data Set of Monthly CO2 Concentrations  [6.4.4.1.1.]
                
            2. Data Set of Southern Oscillations  [6.4.4.1.2.]
                
         2. Stationarity  [6.4.4.2.]
             
         3. Seasonality  [6.4.4.3.]
             
            1. Seasonal Subseries Plot  [6.4.4.3.1.]
                
         4. Common Approaches to Univariate Time Series  [6.4.4.4.]
             
         5. Box-Jenkins Models  [6.4.4.5.]
             
         6. Box-Jenkins Model Identification  [6.4.4.6.]
             
            1. Model Identification for Southern Oscillations Data  [6.4.4.6.1.]
                
            2. Model Identification for the CO₂ Concentrations Data  [6.4.4.6.2.]
                
            3. Partial Autocorrelation Plot  [6.4.4.6.3.]
                
         7. Box-Jenkins Model Estimation  [6.4.4.7.]
             
         8. Box-Jenkins Model Validation  [6.4.4.8.]
             
         9. Example of Univariate Box-Jenkins Analysis  [6.4.4.9.]
             
         10. Box-Jenkins Analysis on Seasonal Data  [6.4.4.10.]
              
      5. Multivariate Time Series Models  [6.4.5.]
          
         1. Example of Multivariate Time Series Analysis  [6.4.5.1.]
            
             
   5. Tutorials  [6.5.]
       
      1. What do we mean by "Normal" data?  [6.5.1.]
          
      2. What do we do when data are "Non-normal"?  [6.5.2.]
          
      3. Elements of Matrix Algebra  [6.5.3.]
          
         1. Numerical Examples  [6.5.3.1.]
             
         2. Determinant and Eigenstructure  [6.5.3.2.]
             
      4. Elements of Multivariate Analysis  [6.5.4.]
          
         1. Mean vector and Covariance Matrix  [6.5.4.1.]
             
         2. The Multivariate Normal Distribution  [6.5.4.2.]
             
         3. Hotelling T squared  [6.5.4.3.]
             
            1. Example of Hotelling's T-squared Test  [6.5.4.3.1.]
                
            2. Example 1 (continued)  [6.5.4.3.2.]
                
            3. Example 2 (multiple groups)  [6.5.4.3.3.]
                
         4. Hotelling T² Chart  [6.5.4.4.]
             
      5. Principal Components  [6.5.5.]
          
         1. Properties of Principal Components  [6.5.5.1.]
             
         2. Numerical Example  [6.5.5.2.]
            
             
   6. Case Studies in Process Monitoring  [6.6.]
       
      1. Lithography Process  [6.6.1.]
          
         1. Background and Data  [6.6.1.1.]
             
         2. Graphical Representation of the Data  [6.6.1.2.]
             
         3. Subgroup Analysis  [6.6.1.3.]
             
         4. Shewhart Control Chart  [6.6.1.4.]
             
         5. Work This Example Yourself  [6.6.1.5.]
             
      2. Aerosol Particle Size  [6.6.2.]
          
         1. Background and Data  [6.6.2.1.]
             
         2. Model Identification  [6.6.2.2.]
             
         3. Model Estimation  [6.6.2.3.]
             
         4. Model Validation  [6.6.2.4.]
             
         5. Work This Example Yourself  [6.6.2.5.]
            
             
   7. References  [6.7.]
       

   
    

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   7.    Product and Process Comparisons

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   7.   Product and Process Comparisons - Detailed Table of Contents  [7.]

   
   
    

   1. Introduction  [7.1.]
       
      1. What is the scope?  [7.1.1.]
          
      2. What assumptions are typically made?  [7.1.2.]
          
      3. What are statistical tests?  [7.1.3.]
          
      4. What are confidence intervals?  [7.1.4.]
          
      5. What is the relationship between a test and a confidence interval?  [7.1.5.]
         
          
   2. Comparisons based on data vrom one process  [7.2.]
       
      1. Do the observations come from a particular distribution?  [7.2.1.]
          
         1. Chi-square goodness of fit test  [7.2.1.1.]
             
         2. Kolmogorov- Smirnov test  [7.2.1.2.]
             
         3. Anderson-Darling test  [7.2.1.3.]
             
      2. Are the data consistent with the assumed process mean?  [7.2.2.]
          
         1. Confidence interval approach  [7.2.2.1.]
             
         2. Sample sizes required  [7.2.2.2.]
             
      3. Assuming the observations are normal, is the variance a given value?  [7.2.3.]
          
         1. Confidence interval approach  [7.2.3.1.]
             
         2. Sample sizes required  [7.2.3.2.]
             
      4. Based on sample data, where are the process values likely to be?  [7.2.4.]
          
         1. Confidence intervals for percentiles  [7.2.4.1.]
             
         2. Tolerance intervals  [7.2.4.2.]
             
         3. Methods without distribution assumptions  [7.2.4.3.]
             
      5. How can we screen outliers from out data?  [7.2.5.]
          
      6. How can we detect trends in sequential process or product data?  [7.2.6.]
          
      7. How can we determine whether the proportion of defectives produced by a process has changed from the "nominal" value?  [7.2.7.]
          
         1. Confidence limits  [7.2.7.1.]
             
         2. Sample sizes required  [7.2.7.2.]
            
             
   3. Comparisons based on data from two processes  [7.3.]
       
      1. Assuming the observations are normal, do the two processes have the same variance?  [7.3.1.]
          
      2. Assuming the observations are normal, do the two processes have equal means?  [7.3.2.]
          
      3. How can we determine whether two processes produce the same proportion of defectives?  [7.3.3.]
          
      4. Assuming the observations are failure times, are the failure rates (or Mean Times To Failure) the same?  [7.3.4.]
          
      5. Do two arbitrary processes have the same mean?  [7.3.5.]
         
          
   4. Comparisons based on data from more than two processes  [7.4.]
       
      1. Assuming the observations are normal, do the processes have the same variance?  [7.4.1.]
          
      2. Are the means equal?  [7.4.2.]
          
         1. 1-Way ANOVA overview  [7.4.2.1.]
             
         2. The 1-Way ANOVA model and assumptions  [7.4.2.2.]
             
         3. The ANOVA table and tests of hypotheses about means  [7.4.2.3.]
             
         4. 1-Way ANOVA calculations  [7.4.2.4.]
             
         5. Confidence intervals for the difference of treatment means  [7.4.2.5.]
             
         6. Assessing the response from Any factor combination  [7.4.2.6.]
             
         7. The Two-Way ANOVA  [7.4.2.7.]
             
         8. Models and calculations for the two-way ANOVA  [7.4.2.8.]
             
      3. What are variance components?  [7.4.3.]
          
      4. Do all the processes have the same proportion of defects?  [7.4.4.]
          
      5. How can we compare the results of classifying according to several categories?  [7.4.5.]
          
      6. How can we make multiple comparisons?  [7.4.6.]
          
         1. Tukey's method  [7.4.6.1.]
             
         2. Scheffe's method  [7.4.6.2.]
             
         3. Bonferroni's method  [7.4.6.3.]
             
         4. Comparing multiple proportions: The Marascuillo procedure  [7.4.6.4.]
            
             
   5. References  [7.5.]
       

   
    

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   8.    Assessing Product Reliability

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   1. Introduction  [8.1.]
       
      1. Why is the assessment and control of product reliability important?  [8.1.1.]
          
         1. Quality versus reliability  [8.1.1.1.]
             
         2. Competitive driving factors  [8.1.1.2.]
             
         3. Safety and health considerations  [8.1.1.3.]
             
      2. What are the basic terms and models used for reliability evaluation?  [8.1.2.]
          
         1. Repairable systems and non-repairable populations - lifetime distribution models  [8.1.2.1.]
             
         2. Reliability or survival function  [8.1.2.2.]
             
         3. Failure (or hazard) rate  [8.1.2.3.]
             
         4. "Bathtub" curve  [8.1.2.4.]
             
         5. Repair rate or ROCOF  [8.1.2.5.]
             
      3. What are some common difficulties frequently found with reliability data and how are they overcome?  [8.1.3.]
          
         1. Censoring  [8.1.3.1.]
             
         2. Lack of failures  [8.1.3.2.]
             
      4. What is "physical acceleration" and how do we model it?  [8.1.4.]
          
      5. What are some common acceleration models?  [8.1.5.]
          
         1. Arrhenius  [8.1.5.1.]
             
         2. Eyring  [8.1.5.2.]
             
         3. Other models  [8.1.5.3.]
             
      6. What are the basic lifetime distribution models used for non-repairable populations?  [8.1.6.]
          
         1. Exponential  [8.1.6.1.]
             
         2. Weibull  [8.1.6.2.]
             
         3. Extreme value distributions  [8.1.6.3.]
             
         4. Lognormal  [8.1.6.4.]
             
         5. Gamma  [8.1.6.5.]
             
         6. Fatigue life (Birnbaum-Saunders)  [8.1.6.6.]
             
         7. Proportional hazards model  [8.1.6.7.]
             
      7. What are some basic repair rate models used for repairable systems?  [8.1.7.]
          
         1. Homogeneous Poisson Process (HPP)  [8.1.7.1.]
             
         2. Non-Homogeneous Poisson Process (NHPP) - power law  [8.1.7.2.]
             
         3. Exponential law  [8.1.7.3.]
             
      8. How can you evaluate reliability from the "bottom - up" (component failure mode to system failure rates)?  [8.1.8.]
          
         1. Competing risk model  [8.1.8.1.]
             
         2. Series model  [8.1.8.2.]
             
         3. Parallel or redundant model  [8.1.8.3.]
             
         4. R out of N model  [8.1.8.4.]
             
         5. Standby model  [8.1.8.5.]
             
         6. Complex systems  [8.1.8.6.]
             
      9. How can you model reliability growth?  [8.1.9.]
          
         1. NHPP power law  [8.1.9.1.]
             
         2. Duane plots  [8.1.9.2.]
             
         3. NHPP exponential law  [8.1.9.3.]
             
      10. How can Bayesian methodology be used for reliability evaluation?  [8.1.10.]
          
           
   2. Assumptions/Prerequisites  [8.2.]
       
      1. How do you choose an appropriate life distribution model?  [8.2.1.]
          
         1. Based on failure mode  [8.2.1.1.]
             
         2. Extreme value argument  [8.2.1.2.]
             
         3. Multiplicative degradation Argument  [8.2.1.3.]
             
         4. Fatigue life (Birnbaum-Saunders) model  [8.2.1.4.]
             
         5. Empirical model fitting - distribution free (Kaplan-Meier) approach  [8.2.1.5.]
             
      2. How do you plot reliability data?  [8.2.2.]
          
         1. Probability plotting  [8.2.2.1.]
             
         2. Hazard and cum hazard plotting  [8.2.2.2.]
             
         3. Trend and growth plotting (Duane plots)  [8.2.2.3.]
             
      3. How can you test reliability model assumptions?  [8.2.3.]
          
         1. Visual tests  [8.2.3.1.]
             
         2. Goodness of fit tests  [8.2.3.2.]
             
         3. Likelihood ratio tests  [8.2.3.3.]
             
         4. Trend tests  [8.2.3.4.]
             
      4. How do you choose an appropriate physical acceleration model?  [8.2.4.]
          
      5. What models and assumptions are typically made when Bayesian methods are used for reliability evaluation?  [8.2.5.]
         
          
   3. Reliability Data Collection  [8.3.]
       
      1. How do you plan a reliability assessment test?  [8.3.1.]
          
         1. Exponential life distribution (or HPP model) tests  [8.3.1.1.]
             
         2. Lognormal or Weibull tests  [8.3.1.2.]
             
         3. Reliability growth (Duane model)  [8.3.1.3.]
             
         4. Accelerated life test  [8.3.1.4.]
             
         5. Bayesian gamma prior model  [8.3.1.5.]
            
             
   4. Reliability Data Analysis  [8.4.]
       
      1. How do you estimate life distribution parameters from censored Data?  [8.4.1.]
          
         1. Graphical estimation  [8.4.1.1.]
             
         2. Maximum likelihood estimation  [8.4.1.2.]
             
         3. A Weibull maximum likelihood estimation example  [8.4.1.3.]
             
      2. How do you fit an acceleration model?  [8.4.2.]
          
         1. Graphical estimation  [8.4.2.1.]
             
         2. Maximum likelihood  [8.4.2.2.]
             
         3. Fitting models using degradation data instead of failures  [8.4.2.3.]
             
      3. How do you project reliability at use conditions?  [8.4.3.]
          
      4. How do you compare reliability between two or more populations?  [8.4.4.]
          
      5. How do you fit system repair rate models?  [8.4.5.]
          
         1. Constant repair rate (HPP/exponential) model  [8.4.5.1.]
             
         2. Power law (Duane) model  [8.4.5.2.]
             
         3. Exponential law model  [8.4.5.3.]
             
      6. How do you estimate reliability using the Bayesian gamma prior model?  [8.4.6.]
          
      7. References For Chapter 8: Assessing Product Reliability  [8.4.7.]