SAS/QC(R) 9.2 User's Guide
Acknowledgments- Using This Book
- Overview
- Organization
- Typographical Conventions
- Conventions for Examples
- Accessing the SAS/QC Sample Library
- Online Documentation
- Part 1 General Information
- What's New in SAS/QC
- Components of SAS/QC Software
- Overview
- ADX Interface for Design of Experiments
- SQC Menu System for Statistical Quality Control
- Procedures for Design of Experiments
- Procedures for Control Chart Analysis
- Procedure for Process Capability Analysis
- Procedures for Basic Quality Problem Solving
- Procedure for Reliability Analysis
- Procedure for Analysis of Means
- SAS/QC Graphics
- Part 2 The ANOM Procedure
- PROC ANOM and General Statements
- BOXCHART Statement
- Overview
- Getting Started
- Creating ANOM Boxcharts from Response Values
- Creating ANOM Boxcharts from Group Summary Data
- Saving Summary Statistics for Groups
- Saving Decision Limits
- Syntax
- Details
- Constructing ANOM Boxcharts
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- PCHART Statement
- Overview
- Getting Started
- Creating ANOM Charts for Proportions from Group Counts
- Creating ANOM Charts for Proportions from Group Summary Data
- Saving Group Proportions
- Saving Decision Limits
- Syntax
- Details
- Constructing ANOM Charts for Proportions
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- UCHART Statement
- Overview
- Getting Started
- Syntax
- Details
- Constructing ANOM Charts for Rates
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- XCHART Statement
- Overview
- Getting Started
- Creating ANOM Charts for Means from Response Values
- Creating ANOM Charts for Means from Group Summary Data
- Saving Summary Statistics for Groups
- Saving Decision Limits
- Syntax
- Details
- Constructing ANOM Charts for Means
- Constructing ANOM Charts for Two-Way Layouts
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- INSET Statement
- Overview
- Getting Started
- Displaying Summary Statistics on an ANOM Chart
- Formatting Values and Customizing Labels
- Adding a Header and Positioning the Inset
- Syntax
- Details
- References
- Part 3 The CAPABILITY Procedure
- Introduction
- PROC CAPABILITY and General Statements
- Overview
- Getting Started
- Syntax Overview for the CAPABILITY Procedure
- Syntax for the PROC CAPABILITY Statement
- Syntax for the CLASS Statement
- Syntax for the SPEC Statement
- Details
- Input Data Sets
- Output Data Set
- Descriptive Statistics
- Signed Rank Statistic
- Tests for Normality
- Percentile Computations
- Robust Estimators
- Computing the Mode
- Assumptions and Terminology for Capability Indices
- Standard Capability Indices
- Specialized Capability Indices
- Missing Values
- ODS Tables
- Examples
- CDFPLOT Statement
- COMPHISTOGRAM Statement
- HISTOGRAM Statement
- Overview
- Getting Started
- Creating a Histogram with Specification Limits
- Adding a Normal Curve to the Histogram
- Customizing a Histogram
- Syntax
- Details
- Formulas for Fitted Curves
- Kernel Density Estimates
- Printed Output
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- SYMBOL and PATTERN Statement Options
- Examples
- Example 13.1: Fitting a Beta Curve
- Example 13.2: Fitting Lognormal, Weibull, and Gamma Curves
- Example 13.3: Comparing Goodness-of-Fit Tests
- Example 13.4: Computing Capability Indices for Nonnormal Distributions
- Example 13.5: Computing Kernel Density Estimates
- Example 13.6: Fitting a Three-Parameter Lognormal Curve
- Example 13.7: Annotating a Folded Normal Curve
- INSET Statement
- Overview
- Getting Started
- Displaying Summary Statistics on a Histogram
- Formatting Values and Customizing Labels
- Adding a Header and Positioning the Inset
- Syntax
- Details
- Positioning the Inset Using Compass Points
- Positioning the Inset in the Margins
- Positioning the Inset Using Coordinates
- Examples
- INTERVALS Statement
- OUTPUT Statement
- PPPLOT Statement
- PROBPLOT Statement
- QQPLOT Statement
- Overview
- Getting Started
- Syntax
- Details
- Construction of Quantile-Quantile and Probability Plots
- Interpretation of Quantile-Quantile and Probability Plots
- Summary of Theoretical Distributions
- Graphical Estimation
- SYMBOL Statement Options
- ODS Graphics - Experimental
- Examples
- Dictionary of Common Options
- References
- Part 4 The CUSUM Procedure
- Introduction
- PROC CUSUM Statement
- XCHART Statement
- Overview
- Getting Started
- Creating a V-Mask Cusum Chart from Raw Data
- Creating a V-Mask Cusum Chart from Subgroup Summary Data
- Saving Summary Statistics
- Creating a One-Sided Cusum Chart with a Decision Interval
- Saving Cusum Scheme Parameters
- Reading Cusum Scheme Parameters
- Syntax
- Details
- Basic Notation for Cusum Charts
- Formulas for Cumulative Sums
- Defining the Decision Interval for a One-Sided Cusum Scheme
- Defining the V-Mask for a Two-Sided Cusum Scheme
- Designing a Cusum Scheme
- Cusum Charts Compared with Shewhart Charts
- Methods for Estimating the Standard Deviation
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Missing Values
- Examples
- INSET Statement
- References
- Part 5 The FACTEX Procedure
- Introduction to the FACTEX Procedure
- Details of the FACTEX Procedure
- Syntax
- Statement Descriptions
- PROC FACTEX Statement
- BLOCKS Statement
- UNITEFFECTS Statement
- EXAMINE Statement
- FACTORS Statement
- MODEL Statement
- OUTPUT Statement
- SIZE Statement
- Advanced Examples
- Example 25.1: Completely Randomized Design
- Example 25.2: Resolution IV Augmented Design
- Example 25.3: Factorial Design with Center Points
- Example 25.4: Fold-Over Design
- Example 25.5: Randomized Complete Block Design
- Example 25.6: Two-Level Design with Design Replication and Point Replication
- Example 25.7: Mixed-Level Design Using Design Replication and Point Replication
- Example 25.8: Mixed-Level Design Using Pseudo-factors
- Example 25.9: Mixed-Level Design by Collapsing Factors
- Example 25.10: Hyper-Graeco-Latin Square Design
- Example 25.11: Resolution IV Design with Minimum Aberration
- Example 25.12: Replicated Blocked Design with Partial Confounding
- Example 25.13: Incomplete Block Design
- Example 25.14: Design with Inner Array and Outer Array
- Example 25.15: Fractional Factorial Split-Plot Designs
- Example 25.16: Design and Analysis of a Complete Factorial Experiment
- Computational Details
- Types of Factors
- Specifying Effects in the MODEL Statement
- Factor Variable Characteristics in the Output Data Set
- Statistical Details
- Resolution
- Randomization
- Replication
- Confounding Rules
- Alias Structure
- Minimum Aberration
- Split-Plot Designs
- Output
- ODS Tables
- Theory of Orthogonal Designs
- Overview
- Structure of General Factorial Designs
- Suitable Confounding Rules
- Searching for Confounding Rules
- Speeding Up the Search
- General Recommendations
- References
- Part 6 The ISHIKAWA Procedure
- Introduction to the ISHIKAWA Environment
- Details of the ISHIKAWA Environment
- Summary of Operations
- Operations
- Adding Arrows
- Labeling Arrows
- Moving Arrows
- Deleting Arrows
- Resizing Arrows
- Swapping Arrows
- Balancing Arrows
- Notepads
- Managing Complexity
- Zooming Arrows
- Isolating Arrows
- Merging Diagrams
- Creating Graphics Output Using SAS/GRAPH Software
- Creating Bitmap Graphics Output
- Modifying Fonts
- Modifying Box Colors
- Modifying Arrow Colors and Line Styles
- Modifying Text Colors
- Modifying Arrow Heads
- Modifying Environmental Attributes
- Saving an Ishikawa Diagram for Future Editing
- Reading an Existing Ishikawa Diagram
- Displaying Multiple Ishikawa Diagrams
- Input and Output Data Sets
- Syntax
- Examples
- References
- Part 7 The MACONTROL Procedure
- Introduction
- PROC MACONTROL Statement
- EWMACHART Statement
- Overview
- Getting Started
- Creating EWMA Charts from Raw Data
- Creating EWMA Charts from Subgroup Summary Data
- Saving Summary Statistics
- Saving Control Limit Parameters
- Reading Preestablished Control Limit Parameters
- Syntax
- Details
- Constructing EWMA Charts
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- Example 30.1: Specifying Standard Values for the Process Mean and Process Standard Deviation
- Example 30.2: Displaying Limits Based on Asymptotic Values
- Example 30.3: Working with Unequal Subgroup Sample Sizes
- Example 30.4: Displaying Individual Measurements on an EWMA Chart
- Example 30.5: Computing Average Run Lengths
- MACHART Statement
- Overview
- Getting Started
- Creating Moving Average Charts from Raw Data
- Creating Moving Average Charts from Subgroup Summary Data
- Saving Summary Statistics
- Saving Control Limit Parameters
- Reading Preestablished Control Limit Parameters
- Syntax
- Details
- Constructing Uniformly Weighted Moving Average Charts
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- INSET Statement
- References
- Part 8 The OPTEX Procedure
- Introduction to the OPTEX Procedure
- Details of the OPTEX Procedure
- Syntax
- Statement Descriptions
- PROC OPTEX Statement
- BLOCKS Statement
- CLASS Statement
- EXAMINE Statement
- GENERATE Statement
- ID Statement
- MODEL Statement
- OUTPUT Statement
- Advanced Examples
- Example 34.1: Nonstandard Linear Model
- Example 34.2: Comparing Fedorov Algorithm to Sequential Algorithm
- Example 34.3: Using an Initial Design to Search an Optimal Design
- Example 34.4: Optimal Design Using an Augmented Best Design
- Example 34.5: Optimal Design Using a Small Candidate Set
- Example 34.6: Bayesian Optimal Design
- Example 34.7: Balanced Incomplete Block Design
- Example 34.8: Optimal Design with Fixed Covariates
- Example 34.9: Optimal Design in the Presence of Covariance
- Example 34.10: Adding Space-Filling Points to a Design
- Data Details
- Computational Details
- References
- Part 9 The PARETO Procedure
- Introduction
- PROC PARETO Statement
- VBAR Statement
- Overview
- Getting Started
- Creating a Pareto Chart from Raw Data
- Creating a Pareto Chart Using Frequency Data
- Restricting the Number of Pareto Categories
- Syntax
- HBAR Statement
- Overview
- Getting Started
- Creating a Pareto Chart from Raw Data
- Creating a Pareto Chart Using Frequency Data
- Restricting the Number of Pareto Categories
- Syntax
- INSET Statement
- Overview
- Getting Started
- Displaying Summary Statistics on a Pareto Chart
- Customizing Labels and Formatting Values
- Adding a Header and Positioning the Inset
- Syntax
- Details
- Details and Examples
- Details
- Terminology
- Labels for Chart Features
- Scaling the Cumulative Percent Curve
- Output Data Sets
- ODS Graphics - Experimental
- Constructing Effective Pareto Charts
- Missing Values
- Role of Variable Formats
- Large Data Sets
- Examples
- Example 39.1: Creating Before-and-After Pareto Charts
- Example 39.2: Creating Two-Way Comparative Pareto Charts
- Example 39.3: Highlighting the ``Vital Few''
- Example 39.4: Highlighting Combinations of Categories
- Example 39.5: Highlighting Combinations of Cells
- Example 39.6: Ordering Rows and Columns in a Comparative Pareto Chart
- Example 39.7: Merging Columns in a Comparative Pareto Chart
- Example 39.8: Creating Weighted Pareto Charts
- References
- Part 10 The RELIABILITY Procedure
- The RELIABILITY Procedure
- Overview
- Getting Started
- Analysis of Right-Censored Data from a Single Population
- Weibull Analysis Comparing Groups of Data
- Analysis of Accelerated Life Test Data
- Weibull Analysis of Interval Data with Common Inspection Schedule
- Lognormal Analysis with Arbitrary Censoring
- Regression Modeling
- Regression Model with Nonconstant Scale
- Regression Model with Two Independent Variables
- Weibull Probability Plot for Two Combined Failure Modes
- Analysis of Recurrence Data on Repairs
- Comparison of Two Samples of Repair Data
- Analysis of Interval Age Recurrence Data
- Analysis of Binomial Data
- Syntax
- Primary Statements
- Secondary Statements
- Graphical Enhancement Statements
- PROC RELIABILITY Statement
- ANALYZE Statement
- BY Statement
- CLASS Statement
- DISTRIBUTION Statement
- FMODE Statement
- FREQ Statement
- INSET Statement
- LOGSCALE Statement
- MAKE Statement
- MCFPLOT Statement
- MODEL Statement
- NENTER Statement
- PROBPLOT Statement
- RELATIONPLOT Statement
- UNITID Statement
- Details
- Abbreviations and Notation
- Types of Lifetime Data
- Probability Distributions
- Probability Plotting
- Nonparametric Confidence Intervals for Cumulative Failure Probabilities
- Parameter Estimation and Confidence Intervals
- Regression Model Observation-wise Statistics
- Recurrence Data from Repairable Systems
- ODS Table Names
- ODS Graph Names - Experimental
- References
- Part 11 The SHEWHART Procedure
- Introduction
- Uses of Shewhart Charts
- Characteristics of Shewhart Charts
- Classification of Shewhart Charts
- Learning to Use the SHEWHART Procedure
- PROC SHEWHART and General Statements
- Overview
- Syntax Overview for the SHEWHART Procedure
- Syntax for the PROC SHEWHART Statement
- Input and Output Data Sets
- BOXCHART Statement
- Overview
- Getting Started
- Creating Box Charts from Raw Data
- Creating Box Charts from Subgroup Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Box Charts
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Percentile Definitions
- Axis Labels
- Missing Values
- Examples
- Example 42.1: Using Box Charts to Compare Subgroups
- Example 42.2: Creating Various Styles of Box-and-Whisker Plots
- Example 42.3: Creating Notched Box-and-Whisker Plots
- Example 42.4: Creating Box-and-Whisker Plots with Varying Widths
- Example 42.5: Creating Box-and-Whisker Plots with Different Line Styles and Colors
- Example 42.6: Computing the Control Limits for Subgroup Maximums
- Example 42.7: Constructing Multi-Vari Charts
- CCHART Statement
- Overview
- Getting Started
- Creating c Charts from Defect Count Data
- Saving Control Limits
- Reading Preestablished Control Limits
- Creating c Charts from Nonconformities per Unit
- Saving Nonconformities per Unit
- Syntax
- Details
- Constructing Charts for Numbers of Nonconformities (c Charts)
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- IRCHART Statement
- Overview
- Getting Started
- Creating Individual Measurements and Moving Range Charts
- Saving Individual Measurements and Moving Ranges
- Reading Individual Measurements and Moving Ranges
- Saving Control Limits
- Reading Preestablished Control Limits
- Specifying the Computation of the Moving Range
- Syntax
- Details
- Constructing Charts for Individual Measurements and Moving Ranges
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Interpreting Charts for Individual Measurements and Moving Ranges
- Axis Labels
- Missing Values
- Examples
- MCHART Statement
- Overview
- Getting Started
- Creating Charts for Medians from Raw Data
- Creating Charts for Medians from Subgroup Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Median Charts
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- MRCHART Statement
- Overview
- Getting Started
- Creating Charts for Medians and Ranges from Raw Data
- Creating Charts for Medians and Ranges from Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Charts for Medians and Ranges
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- NPCHART Statement
- Overview
- Getting Started
- Creating np Charts from Count Data
- Creating np Charts from Summary Data
- Saving Proportions of Nonconforming Items
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Charts for Number Nonconforming (np Charts)
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- PCHART Statement
- Overview
- Getting Started
- Creating p Charts from Count Data
- Creating p Charts from Summary Data
- Saving Proportions of Nonconforming Items
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Charts for Proportion Nonconforming (p Charts)
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- RCHART Statement
- Overview
- Getting Started
- Creating Range Charts from Raw Data
- Creating Range Charts from Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Range Charts
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- SCHART Statement
- Overview
- Getting Started
- Creating Standard Deviation Charts from Raw Data
- Creating Standard Deviation Charts from Subgroup Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Charts for Standard Deviations
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- UCHART Statement
- Overview
- Getting Started
- Creating u Charts from Defect Count Data
- Saving Control Limits
- Reading Preestablished Control Limits
- Creating u Charts from Nonconformities per Unit
- Saving Nonconformities per Unit
- Syntax
- Details
- Constructing Charts for Nonconformities per Unit (u Charts)
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Axis Labels
- Missing Values
- Examples
- XCHART Statement
- Overview
- Getting Started
- Creating Charts for Means from Raw Data
- Creating Charts for Means from Subgroup Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Charts for Means
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- XRCHART Statement
- Overview
- Getting Started
- Creating Charts for Means and Ranges from Raw Data
- Creating Charts for Means and Ranges from Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Charts for Means and Ranges
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Subgroup Variables
- Methods for Estimating the Standard Deviation
- Capability Indices
- Axis Labels
- Missing Values
- Examples
- XSCHART Statement
- Overview
- Getting Started
- Creating Charts for Means and Standard Deviations from Raw Data
- Creating Charts for Means and Standard Deviations from Summary Data
- Saving Summary Statistics
- Saving Control Limits
- Reading Preestablished Control Limits
- Syntax
- Details
- Constructing Charts for Means and Standard Deviations
- Output Data Sets
- ODS Tables
- ODS Graphics - Experimental
- Input Data Sets
- Methods for Estimating the Standard Deviation
- Axis Labels
- Missing Values
- Examples
- INSET and INSET2 Statements
- Overview
- Getting Started
- Displaying Summary Statistics on a Control Chart
- Formatting Values and Customizing Labels
- Adding a Header and Positioning the Inset
- Syntax
- Details
- Dictionary of Options
- Graphical Enhancements
- Overview
- Displaying Stratified Process Data
- Displaying Stratification in Levels of a Classification Variable
- Displaying Stratification in Blocks of Observations
- Displaying Stratification in Phases
- Displaying Multiple Sets of Control Limits
- Displaying Auxiliary Data with Stars
- Creating a Basic Star Chart
- Adding Reference Circles to Stars
- Specifying the Style of Stars
- Specifying the Method of Standardization
- Displaying Trends in Process Data
- Step 1: Preliminary Mean and Standard Deviation Charts
- Step 2: Modeling the Trend
- Step 3: Displaying the Trend Chart
- Clipping Extreme Points
- Labeling Axes
- Selecting Subgroups for Computation and Display
- Tests for Special Causes
- Standard Tests for Special Causes
- Requesting Standard Tests
- Interpreting Standard Tests for Special Causes
- Modifying Standard Tests for Special Causes
- Applying Tests with Varying Subgroup Sample Sizes
- Labeling Signaled Points with a Variable
- Applying Tests with Multiple Phases
- Applying Tests with Multiple Sets of Control Limits
- Enhancing the Display of Signaled Tests
- Nonstandard Tests for Special Causes
- Specialized Control Charts
- Overview
- Autocorrelation in Process Data
- Multiple Components of Variation
- Short Run Process Control
- Analyzing the Difference from Nominal
- Testing for Constant Variances
- Standardizing Differences from Nominal
- Nonnormal Process Data
- Multivariate Control Charts
- Interactive Control Charts
- References
- Part 12 Appendices
- The GAGE Application
- Introduction
- Getting Started
- Invoking the GAGE Application
- Entering Data
- Performing a Range Chart Analysis
- Performing an Average Chart Analysis
- Selecting a Statistical Method
- Performing an Average and Range Analysis
- Performing a Variance Components Analysis
- Saving the Data
- Entering Another Set of Data
- Reading Data from a Data Set
- Details
- The RELIABILITY Graphical Interface
- Functions
- Introduction
- Function Descriptions
- AOQ2 Function
- ASN2 Function
- ATI2 Function
- BAYESACT Call
- C4 Function
- CUSUMARL Function
- D2 Function
- D3 Function
- EWMAARL Function
- PROBACC2 Function
- PROBBNML Function
- PROBHYPR Function
- PROBMED Function
- STDMED Function
- Details
- Special Fonts in SAS/QC Software
- References
Index here
| Product | Release |
|---|---|
| SAS/QC | 9.2 |
- Type
- Usage and Reference
- Copyright Date
- March 2008
- Last Updated
- 28Feb2009
| What's New in SAS/QC |
References
Butler, N.A. (2004), ``Construction of Two-Level Split-Plot Fractional Factorial Designs for Multistage Processes,'' Technometrics, 46, 445 - 451.
Huang, P., Chen, D., and Voelkel, J.O. (1998), "Minimum-Aberration Two-Level Split-Plot Designs," Technometrics, 40, 314 - 326.
Copyright © 2008 by SAS Institute Inc., Cary, NC, USA. All rights reserved.