# SigmaXL

**Features Of SigmaXL V9 **

**Powerful and Easy-to-Use Time Series Forecasting and Control Charts for Autocorrelated Data **

- Run Chart
- Autocorrelation Function (ACF)/Partial Autocorrelation (PACF) Plots
- Cross Correlation (CCF) Plots with Pre-Whiten Data option
- Seasonal Trend Decomposition Plots
- Spectral Density Plot with Detection of Seasonal Frequency
- Exponential Smoothing
- Forecast with Prediction Intervals
- Exponential Smoothing models use Rob Hyndman’s taxonomy:
- Additive/Multiplicative Error
- Additive/Additive Damped Trend
- Additive/Multiplicative Seasonal
- This includes all of the classical exponential smoothing models such as Simple/Single/EWMA, Double and Holt-Winters

- Multiple Seasonal Decomposition (MSD) option
- Useful for high frequency and/or multiple frequency data, such as Monthly with frequency = 12, Daily with frequency = 7 and Hourly with frequency = 24

- Exponential Smoothing Residuals Control Chart for autocorrelated data
- Individuals and Moving Limits (with One-Step Ahead Forecast) Charts
- Add Data, Show Last 30 Data Points, Enable Scroll options
- MSD option

- Autoregressive Integrated Moving Average (ARIMA)
- Forecast with Prediction Intervals
- ARIMA Forecast with Predictors (Continuous and/or Categorical)
- MSD option

- ARIMA Residuals Control Chart for autocorrelated data
- Individuals and Moving Limits (with One-Step Ahead Forecast) Charts
- ARIMA Control Chart with Predictors
- Add Data, Show Last 30 Data Points, Enable Scroll options
- MSD option

- Utilities
- Difference Data
- Lag Data
- Interpolate Missing Values (seasonally adjusted linear interpolation)

- Time Series Forecasting Model Features
- ARIMA and Exponential Smoothing models are fully automatic or user specified
- Utilizes modern State Space and Kalman Filter models for accurate parameter estimation
- ARIMA estimates missing values with Kalman Filter; Exponential Smoothing uses seasonally adjusted linear interpolation
- Automatic Box-Cox Transformation
- Automatic seasonal frequency detection

- Model Diagnostics
- ACF/PACF Plots
- Ljung-Box p-values
- Log-Likelihood, AIC, AICc, BIC, Residual StDev.
- Residual plots (histogram, normal probability, residual versus fits, residuals versus order)

- Forecast Accuracy
- In-Sample (Estimation) one-step-ahead forecast errors (RMSE, MAE, MASE, MAPE)
- Out-of-Sample (Withhold) one-step-ahead forecast errors
- Out-of-Sample (Withhold) multi-step-ahead forecast errors
- Evaluated using the benchmark standard M4 forecast competition data, a total of 100,000 data sets with Yearly, Quarterly, Monthly, Weekly, Daily and Hourly data. Using a hybrid average of automatic Exponential Smoothing and ARIMA, SigmaXL (unofficially) ranked 10th out of 60 in the Overall Weighted Average forecast accuracy score, ahead of three well known commercial forecast software packages

**New and Improved Control Charts**

- New Control Chart Templates
- Rare Events G and T (Provost-Murray approximation)
- Rare Events Probability-Based G
- Trend/Tool Wear
- Exponentially Weighted Moving Average (EWMA)
- Tabular Cumulative Sum (CUSUM)
- Average Run Length (ARL) Calculators
- Shewhart with Tests for Special Causes
- Attribute C & P
- EWMA & CUSUM
- Markov Chain Approximation - fast and accurate
- Monte Carlo Simulation: Test robustness to non-normality with specified Skewness & Kurtosis; additional Run Length statistics: Standard Deviation and Percentiles

- Tests for Special Causes now supported for menu-based control charts
- Varying Subgroup Sizes (Moving Limits)
- Historical Groups
- MR/Range/StDev Charts (Tests 1-4)

**Features Of SigmaXL V8.1 **

Following new statistical templates have been added:

- MSA Templates for Gage Bias and Linearity Study
- Taguchi DOE templates include:
- 2 Level: L4, L8, L12, L16
- 3 Level: L9, L27
- Mixed 2/3 Level: L18
- Fill in the blanks template, charts automatically update
- Predicted Response Calculator and Charts for Mean, Standard Deviation (or Ln Standard Deviation) and Signal-to-Noise Ratio
- Pareto of Deltas (Effects) and ANOVA SS (Sum-of-Squares) % Contribution (for Main Effects and Two-Way Interactions)

- Statistical Templates for Mean equivalence, proportion equivalence, and Poisson rate equivalence test
- Updated ANOM charts including Nonparametric Transformed Ranks and Variances and Levene Robust Variances

This release adds compatibility with Windows 8 and Office 2013, as well as increased functionality in the form of 4 new and 6 updated templates.

**Compatibility with Excel 2013: 32 bit and 64 bit and Excel Mac 2011**

**Automatic Assumptions Check for t-Tests and ANOVA **

- Color highlightened Text Report: Green (OK), Yellow (Warning) and Red (Serious Violation)
- Normality test check for each sample. If not possible, minimum sample size for robustness of test is checked
- Monte Carlo regression equations being utilized provided in V6.2 template
- A warning is given and a suitable Nonparametric Test is recommended in case of inadequate sample size

- Check for Outliers from sample to sample:
- Potential: Tukey's Boxplot 1.5*IQR; Likely: Tukey's Boxplot 2*IQR; Extreme: Tukey's Boxplot 3*IQR
- If outliers are present, warning and recommendation to review the data with a Boxplot and Normal Probability Plot
- If the removal of outlier(s) result in an Anderson Darling Normality Test P-Value that is >.01, a notice is given that excluding the outlier(s), the sample data are inherently normal

- Randomness (Nonparametric Runs Test)
- In case of non random sample data, warning and recommendation are suggested to review the data with a Run Chart

- Equal Variance (applicable for two or more samples)
- If all sample data are normal, F-Test or Bartlett's Test is utilized, otherwise use Levene's Test
- If the variances are unequal and the test being used is the equal variance option, then a warning is given and Welch’s test is recommended.

**Automatic Normality Check for Pearson Correlation **

- Utilizes the powerful Doornik-Hansen multivariate normality test
- Significant Pearson or Spearman correlation is highlightened in yellow
- Pearson is highlighted if the data are bivariate normal, otherwise Spearman is highlighted

**Exact Statistics for One-Way Chi-Square, Two-Way (Contingecy) Table and Nonparametric Tests **

- Exact or Monte Carlo P-Values
- Appropriate when sample size is too small for Chi-Square or Normal approximation to be valid - for example, a contingency table where more than 20% of the cells have an expected count less than 5.
- Fisher's Exact for Two-Way (Row*Column Contingency) Tables
- Exact or Monte Carlo P-Values
- Exact One-Way Chi-Square godness of fit template is an added feature now.
- Exact Nonparametric Tests: Sign, Wilcoxon, Mann-Whitney, Kruskal-Wallis, Mood's Median, and Runs Test are available

**Binary Attribute Measurement Systems Analysis (MSA)**

- User Defined "Good Part" for Type I and Type II Error Report is a new feature
- Confidence Intervals for Percent Agreement can be Wilson Score or Exact
- Confidence Interval Graphs for Percent Agreement and Fleiss' Kappa Coefficient
- Interpretation is aided by Kappa color highlightening: Green (>.9), Yellow (.7-.9) and Red (<.7)
- Effectiveness Report (treats each appraisal trial as an opportunity) and Misclassifcation Summary

**Newly added Features in Ordinal Attribute MSA **

- Confidence Interval Graphs for Percent Agreement and Kendall's Coefficients (Concordance and Correlation)
- Kendall color highlight to aid interpretation( Green/ Yellow/ Red)
- Attribute MSA Raw Data with color highlight for deviation from reference
- Effectiveness Report and Misclassification Summary

**Newly added Features in Nominal Attribute MSA **

- Confidence Interval Graphs are available now for Percent Agreement and Fleiss' Kappa Coefficient
- Kappa color highlight to aid interpretation: Green (>.9), Yellow (.7-.9) and Red (<.7)
- Effectiveness Report and Misclassification Summary are also added features

This release adds compatibility with Windows 8 and Office 2013, as well as increased functionality in the form of 4 new and 6 updated templates.

**New Statistical Templates**

- Minimum Sample Size for Robust t-Tests and ANOVA
- 1 Poisson Rate Test and Confidence Interval
- 2 Poisson Rates Test and Confidence Interval
- One-Way Chi-Square Goodness-of-Fit Test

**Updated Statistical Templates**

- 1 Sample t-Test and Confidence Interval for Mean
- 2 Sample t-Test and Confidence Interval (Compare 2 Means) with option for equal and unequal variance
- 1 Sample Chi-Square Test and CI for Standard Deviation
- 2 Sample F-Test and CI (Compare 2 Standard Deviations)
- 1 Proportion Test and Confidence Interval
- 2 Proportions Test and Confidence Interval

**Excel 2007 Ribbon **

**Menu Layout: Classical or DMAIC **

**Worksheet Manager** **

**Data Manipulation: **

- Subset by Category, Number, Date or Random
- Stack Subgroups Across Rows
- Stack and Unstack Columns
- Standardize Data
- Normal Random Number Generator
- Normal
- Uniform (Continuous & Integer)**
- Lognormal**
- Weibull**
- Triangular**
- Box-Cox Transformation

**Templates & Calculators: **

- DMAIC & DFSS Templates
- Team/Project Charter
- SIPOC Diagram
- Flowchart Toolbar
- Data Measurement Plan
- Cause & Effect (Fishbone) Diagram and Quick Template
- Cause & Effect (XY) Matrix
- Failure Mode & Effects Analysis (FMEA)
- Quality Function Deployment (QFD)
- Pugh Concept Selection Matrix
- Control Plan

- Lean Templates
- Takt Time Calculator
- Value Analysis/Process Load Balance
- Value Stream Mapping**

- Graphical Templates
- Pareto Chart
- Histogram
- Run Chart

- Statistical Templates
- Sample Size – Discrete and Continuous
- 1 Sample t Confidence Interval for Mean**
- 2 Sample t-Test (Assume Equal and Unequal Variances)**
- 1 Sample Confidence Interval for Standard Deviation
- 2 Sample F-Test (Compare 2 StDevs)**
- 1 Proportion Confidence Interval (Normal and Exact)
- 2 Proportions Test & Fisher’s Exact**

- Probability Distribution Calculators**
- Normal, Lognormal, Exponential, Weibull
- Binomial, Poisson, Hypergeometric

- MSA Templates
- Gage R&R Study – with Multi-Vari Analysis
- Attribute Gage R&R (Attribute Agreement Analysis)

- Process Sigma Level – Discrete and Continuous
- Process Capability & Confidence Intervals
- DOE Templates
- 2 to 5 Factors
- 2-Level Full and Fractional-Factorial designs
- Main Effects & Interaction Plots

- Control Chart Templates
- Individuals
- C-Chart

- Basic and Advanced (Multiple) Pareto Charts
- EZ-Pivot/Pivot Charts: Easily create Pivot Tables and Charts
- Basic Histogram
- Multiple Histograms and Descriptive Statistics (includes Confidence Interval for Mean and StDev., and Anderson-Darling Normality Test)
- Multiple Histograms and Process Capability (Pp, Ppk, Cpm, ppm, %)
- Multiple Boxplots, Dotplots
- Run Charts (with Nonparametric Runs Test allowing you to test for Clustering, Mixtures, Lack of Randomness, Trends and Oscillation)
- Overlay Run Chart
- Multiple Normal Probability Plots (with 95% confidence intervals to ease interpretation of normality/non-normality)
- Multi-Vari Charts
- Scatter Plots (with linear regression and optional 95% confidence intervals and prediction intervals)
- Scatter Plot Matrix
- Create Gage R&R (Crossed) Worksheet:
- Generate worksheet with user specified number of parts, operators

- Analyze Gage R&R (Crossed)
- ANOVA, %Total, %Tolerance (with upper and/or lower specifications), %Process, Variance Components, Number of Distinct Categories
- Gage R&R Multi-Vari and X-bar R Charts
- Confidence Intervals for %Total, %Tolerance, %Process and Standard Deviations
- Handles unbalanced data

- Alirtibute MSA (Binary)
- Any number of samples, appraisers and replicates
- Within Appraiser Agreement, Each Appraiser vs Standard Agreement, Each Appraiser vs Standard Disagreement, Between Appraiser Agreement, All Appraisers vs Standard Agreement; Fleiss' kappa

- Multiple Histograms and Process Capability
- Capability Combination Report for Individuals/Subgroups:
- Histogram, Normal Probability Plot and Normality Test
- Capability Report (Cp, Cpk, Pp, Ppk, Cpm, ppm, %)
- Control Charts

- Capability Combination Report for Nonnormal Data (Individuals)**
- Box-Cox Transformation (includes an automatic threshold option so that data with negative values can be transformed)
- Johnson Transformation
- Distributions supported: Half-Normal, Lognormal (2 & 3 parameter), Exponential (1 & 2), Weibull (2 & 3), Beta (2 & 4), Gamma (2 & 3), Logistic, Loglogistic (2 & 3), Largest Extreme Value, Smallest Extreme Value
- Automatic Best Fit based on AD p-value
- Nonnormal Process Capability Indices: Z-Score (Cp, Cpk, Pp, Ppk) and Percentile (ISO) Method (Pp, Ppk)

- Distribution Fitting Report**
- All valid distributions and transformations reported with histograms, curve fit and probability plots
- Sorted by AD p-value

- P-values turn red when results are significant (p-value < alpha)
- Descriptive Statistics including Anderson-Darling Normality test, Skewness and Kurtosis with p-values
- 1 Sample t-test and confidence intervals
- Paired t-test, 2 Sample t-test
- 2 Sample comparison tests:
- Reports AD Normality, F-test and Levene’s for variance, t-test assuming equal and unequal variance, Mann-Whitney test for medians.
- Recommended tests are highlighted based on sample size, normality, and variance

- One-Way ANOVA and Means Matrix
- Two-Way ANOVA (Balanced and Unbalanced)
- Equal Variance Tests (Bartlett, Levene and Welch’s ANOVA)
- Correlation Matrix (Pearson and Spearman’s Rank Correlation)
- Multiple Linear Regression:
- Accepts continuous and/or categorical (discrete) predictors
- Interactive Predicted Response Calculator with 95% Confidence Interval and 95% Prediction Interval
- Residual Plots: histogram, normal probability plot, residuals vs. time, residuals vs. predicted and residuals vs. X factors
- Residual types include Regular, Standardized, Studentized (Deleted t) and Cook's Distance (Influence), Leverage and DFITS
- Highlight of significant outliers in residuals
- Durbin-Watson Test for Autocorrelation in Residuals with p-value
- ANOVA report for categorical predictors
- Pure Error and Lack-of-Fit report
- Collinearity Variance Inflation Factor (VIF) and Tolerance report
- Fit Intercept is optional

- Binary and Ordinal Logistic Regression
- Powerful and user-friendly logistic regression.
- Report includes a calculator to predict the response event probability for a given set of input X values.
- Categorical (discrete) predictors can be included in the model in addition to continuous predictors.
- Model summary and goodness of fit tests include Likelihood Ratio Chi-Square, Pseudo R-Square, Pearson Residuals Chi-Square, Deviance Residuals Chi-Square, Observed and Predicted Outcomes – Percent Correctly Predicted.
- Stored data includes Event Probabilities, Predicted Outcome, Observed-Predicted, Pearson Residuals, Standardized Pearson Residuals, and Deviance Residuals.

- Chi-Square Test (Stacked Column data and Two-Way Table data)
- Nonparametric Tests:
- 1 Sample Sign and 1 Sample Wilcoxon
- 2 Sample Mann-Whitney
- Kruskal-Wallis and Mood’s Median Test
- Kruskal-Wallis and Mood’s include a graph of Group Medians and 95% Median Confidence Intervals
- Runs Test

- Power and Sample Size Calculators for:
- 1 and 2 Sample t-Test
- One-Way ANOVA
- 1 Proportion Test, 2 Proportions Test
- The Power and Sample Size Calculators allow you to solve for Power (1 – Beta), Sample Size, or Difference (specify two, solve for the third).

- Power and Sample Size Chart. Quickly create a graph showing the relationship between Power, Sample Size and Difference.
- Generate 2-Level Factorial and Plackett-Burman Screening Designs
- User-friendly dialog box
- 2 to 19 Factors; 4,8,12,16,20 Runs
- Unique “view power analysis as you design”
- Randomization, Replication, Blocking and Center Points

- Basic DOE Templates
- 2 to 5 Factors, 2-Level Full and Fractional-Factorial designs
- Automatic update to Pareto of Coefficients
- Easy to use, ideal for training

- Main Effects & Interaction Plots
- Analyze 2-Level Factorial and Plackett-Burman Screening Designs
- Used in conjunction with Recall Last Dialog, it is very easy to iteratively remove terms from the model
- Interactive Predicted Response Calculator with 95% Confidence Interval and 95% Prediction Interval.
- ANOVA report for Blocks, Pure Error, Lack-of-Fit and Curvature
- Collinearity Variance Inflation Factor (VIF) and Tolerance report
- Residual plots: histogram, normal probability plot, residuals vs. time, residuals vs. predicted and residuals vs. X factors
- Highlight of significant outliers in residuals
- Durbin-Watson Test for Autocorrelation

- Contour & 3D Surface Plots**
- Response Surface Designs**
- 2 to 5 Factors
- Central Composite and Box-Behnken Designs
- Easy to use design selection sorted by number of runs

- Weibull Analysis
- Complete and Right Censored data
- Least Squares and Maximum Likelihood
- Output includes percentiles with confidence intervals, survival probabilities, and Weibull probability plot.

**Graphical Tools:**

**Measurement Systems Analysis: **

**Process Capability:**

**Statistical Tools: **

**Design of Experiments: **

**Reliability/Weibull Analysis: **