Data Input
Data Upload
Data Selection
📊 Data Quality Check
Data Structure
Missing Values by Column
✏️ Data Editor
🔍 Data Filtering
Filter Your Data
Select which rows to keep based on column values:
Transform Tools - Stack/Unstack/Subsets
🧪 Data Lab: Transform & Clean
🎯 Step 1: What's your goal?
🗂️ Step 2: Select columns
▶️ Step 3: Run & Save
🔍 Preview
🎯 Step 1: Pick a column to filter
🔧 Step 2: Set your condition
▶️ Step 3: Apply & Save
🔍 Preview
🎯 Step 1: What needs cleaning?
🔧 Step 2: Fill or replace NAs
▶️ Step 3: Apply & Save
🧹 Cleaning Report
🎯 Step 1: What do you need?
🔧 Step 2: Configure
▶️ Step 3: Run & Save
📝 Result
📋 Transformation History
Every action you've taken is logged here. You can undo or download any snapshot.💾 Save Current Data
Save your transformed data to use in Visualization or Statistical Analysis modules.Download Current Data
📊 Quick Data Summary
Sample Size Calculator
Sample Size & Power Calculator
Plan your study with confidence - supports t-tests, ANOVA, proportions, correlation & more
Two different questions. The baseline asks how precisely you will know your number; detecting a difference asks how many readings make a real change visible against the noise. A project usually asks the first in Measure and the second at the pilot.
How many readings do I need to know a value to within +/- a margin?
The question for a baseline: not 'can I detect a change' (that is the other question, at the top of this page) but 'how precisely will I know my number'. Choose what you want to know, say how precisely, and the answer is the number of readings.
STEP 1: Analysis Type
What are you comparing?
STEP 2: What to Calculate?
Choose your unknown
STEP 3: Basic Parameters
Standard settings
STEP 4: Effect Size
The difference you want to detect
STEP 5: Get Results
Results update automatically
Results calculate automatically as you change inputs
(2 second delay after last change)
RESULTS
Power Curve
Effect Size Guide: What Numbers Should I Use?
What is Effect Size?
Effect size = How big is the difference you want to detect?
Think of it like this: If you're looking for a needle in a haystack...
- Large effect: Looking for a sword (easy to find, need fewer samples)
- Medium effect: Looking for a key (moderate difficulty)
- Small effect: Looking for a needle (hard to find, need MANY samples)
How to Choose Your Effect Size
- Best approach: Use historical data or pilot study to estimate the real difference
- Six Sigma projects: Start with medium effect size for process improvements
- When unsure: Use small effect size (conservative, ensures adequate power)
- Breakthrough changes: You can expect large effects (e.g., new technology vs old)
Effect Size Reference Tables
Cohen's d — For Comparing Means (t-tests)
What it measures: The difference between two means, expressed in standard deviation units.
Formula: d = (Mean₁ - Mean₂) / Standard Deviation
| Size | d value | Real-World Example |
|---|---|---|
| Small | 0.2 | Height difference between 15 and 16 year old girls (~0.5 inch) |
| Medium | 0.5 | Height difference between 14 and 18 year old girls (~1.5 inch) |
| Large | 0.8 | Height difference between adult men and women (~2.5 inch) |
Cohen's f — For ANOVA (3+ Groups)
What it measures: The spread of group means relative to within-group variation.
When to use: Comparing 3 or more groups (e.g., 3 machines, 4 suppliers, 5 shift teams).
| Size | f value | Real-World Example |
|---|---|---|
| Small | 0.10 | Subtle difference between 4 suppliers (hard to notice visually) |
| Medium | 0.25 | Noticeable difference between machines (visible in box plots) |
| Large | 0.40 | Obvious difference between methods (anyone can see it) |
Cohen's w — For Chi-Square (Categorical Data)
What it measures: How much the observed proportions differ from expected.
When to use: Contingency tables, testing independence (e.g., defect type vs shift, pass/fail vs supplier).
| Size | w value | Real-World Example |
|---|---|---|
| Small | 0.10 | Slight preference in customer survey (51% vs 49%) |
| Medium | 0.30 | Clear pattern in defect distribution (60% vs 40%) |
| Large | 0.50 | Strong relationship (e.g., 75% defects from one machine) |
Correlation (r) — For Relationship Strength
What it measures: How strongly two variables move together (ranges from -1 to +1).
When to use: Testing if X and Y are related (e.g., temperature vs yield, training hours vs performance).
| Size | r value | Real-World Example |
|---|---|---|
| Small | ±0.10 | Weak link: coffee consumption vs productivity |
| Medium | ±0.30 | Moderate link: study time vs exam scores |
| Large | ±0.50 | Strong link: height vs weight, practice vs skill |
Cohen's f² — For Regression (R² Significance)
What it measures: How much variance in Y is explained by your predictors (X variables).
Formula: f² = R² / (1 - R²)
| Size | f² value | Equivalent R² | Meaning |
|---|---|---|---|
| Small | 0.02 | ~2% | Model explains little variance (but may still be useful) |
| Medium | 0.15 | ~13% | Model explains moderate variance (typical for social sciences) |
| Large | 0.35 | ~26% | Model explains substantial variance (strong predictive model) |
Quick Decision Guide: Which Effect Size Should I Use?
| Don't know what to expect? | → Use SMALL (conservative, won't under-power your study) | |
| Typical process improvement? | → Use MEDIUM (most common in Six Sigma) | |
| Major change or new technology? | → Use LARGE (breakthrough improvements) | |
| Have pilot data or historical data? | → CALCULATE your actual expected effect size! |
How Effect Size Impacts Sample Size
Example: Two-sample t-test at α=5%, Power=80%
| Effect Size | Cohen's d | n per group | Total N |
|---|---|---|---|
| Small | 0.2 | 393 | 786 |
| Medium | 0.5 | 64 | 128 |
| Large | 0.8 | 26 | 52 |
Notice: Detecting small effects requires 15x more samples than detecting large effects!
Analysis
Statistical Analysis
Six Sigma Inferential Statistics Tool
Enter your sample data to calculate confidence intervals or test hypotheses.
Perfect for DMAIC projects when you have collected measurements.
Step 1: Choose Your Analysis
Step 2: Enter Your Sample Data
Step 3: Analysis Settings
Results Summary
Visual Results
Detailed Analysis
Six Sigma Interpretation
Statistical Assumptions
Which test? — Hypothesis Test Guide (step by step)
Four steps a belt can follow without a coach: say what you are comparing, point at the columns, let the guide check the assumptions and pick the valid test, run it here, and leave with a decision sentence for the slide. The specialised tabs stay available for the full output.
Step 1 - Describe the question
Only have summary numbers (n, mean, SD; or counts) rather than the readings themselves?
Open Inferential StatisticsStep 2 - Point at the data
Step 3 - Run and read
Analytics © Dr. Mahmood Al Kindi — assumption checks first, then the test.
Nonparametric & Equal-Variance Tests
Distribution-free alternatives for skewed data, small samples, ordinal scores and outliers. Each test shows the hypotheses, the statistic, a confidence interval where one exists, and what it means.
Analytics © Dr. Mahmood Al Kindi — assumption checks first, then the test.
Multiple Comparisons after ANOVA
Which groups actually differ? Tukey for all pairs with equal variances, Fisher LSD when you have a few planned comparisons, Dunnett when every group is compared with one control, Games-Howell when variances are unequal.
Analytics © Dr. Mahmood Al Kindi — assumption checks first, then the test.
Tables & Chi-Square
Analytics © Dr. Mahmood Al Kindi — assumption checks first, then the test.
Graphical Summary
One page per variable, the classic graphical summary layout: histogram with normal curve, box plot, Anderson-Darling normality test, descriptive statistics and confidence intervals for the mean, median and standard deviation - plus Grubbs' test for a single outlier.
Analytics © Dr. Mahmood Al Kindi — assumption checks first, then the test.
Data Visualization
📊 Plot Mode
📋 Variable Selection
X-Axis Variable(s)
Y-Axis Variable(s) (Optional)
📐 Layout Options
✨ Additional Mappings
📇 Comparison Setup
📊 Distribution Overview
Advanced Visualization
📊 Advanced Plot Setup
📋 Data Requirements
🎯 Map Your Data Columns
🎨 Additional Mappings
📁 Data Source
📋 Data Preview
💾 Export Plot
Lean Six Sigma Graphs
The eight graphs a belt uses at the gemba, annotated with the statistics that matter: run chart with runs tests, histogram with normal curve and specs, interval plot, individual value plot, box plot with means and n, time series by stage, multi-vari chart, and scatter with the fitted line. Choose the graph and the columns; the statistics box explains what you see.
📏 Graph and data
Analytics © Dr. Mahmood Al Kindi — Lean Six Sigma graphs, annotated.
Distribution graphs
Probability plot with the Anderson-Darling test and confidence band, empirical CDF, dotplot, stem-and-leaf, symmetry plot, and a probability distribution plot for teaching and critical values - the full distribution-graph set, Analytics style.
📈 Graph and data
Analysis graphs
Main effects and interaction plots for any columns (with the ANOVA p-values most packages leave out), contour and 3D surface for any three columns with a fitted response surface and its stationary point, tolerance intervals with the normal / distribution-free choice made for you, and the gage run chart.
📊 Graph and data
Cause-and-Effect (Fishbone) Diagram
State the effect, pick the bone set, type the causes (one per line; start a line with '-' for a sub-cause), and the diagram draws itself. Mark a cause verified (turns red) or suspected (amber) as the Analyze phase progresses - the diagram becomes the root-cause status board, not a one-off brainstorm picture.
Analytics © Dr. Mahmood Al Kindi — cause-and-effect diagram (Ishikawa).
Model check - check the model before you trust it
A regression is only as good as its assumptions. Choose Y and the predictors; the tab fits the model and draws the model-check panel (posterior predictive check, linearity, homogeneity of variance, influential points, collinearity, normality of residuals) then says in plain words which check failed and what to do about it. Coefficients and fit statistics follow.
Analytics © Dr. Mahmood Al Kindi
The road map: DMAIC, step by step
Five phases, the tools in each, and an arrow where one hands over to the next. The gold numbers are the twelve steps, the same numbers as the sidebar. Click any box to open it. On the project board the same map lights up from your records and marks your next step.
Your first ten minutes
1 Press Start a project and write the charter: one Y, the problem in numbers, a goal with a date.
2 Then follow the gold numbers in the sidebar, 1 to 12, in order. Each step says what it found and what comes next.
3 Open Continue a project at any time: the board shows what is on record, what the tollgate will ask for, and your next step.
For a Green Belt
- Write a charter a sponsor can sign: one Y, the problem in numbers, a goal with a date, and the X's the team suspects.
- Follow the guides step by step - Gage R&R, capability, control chart, which test - each one says what it found and what to do next.
- See on one board what is on record, what the tollgate will ask for, and the one next step.
For a Black Belt
- Non-normal capability, Johnson and Box-Cox transformations, Bonett's test, DOE with lack of fit and prediction - rigorous, with the assumptions checked.
- Y = f(X) carried through the project: every X suspected, tested, verified or rejected, set, controlled - never lost between phases.
- A handover pack and a project file: the evidence, the control plan and the reaction plans in one printable document, and a file to carry on anywhere.
What it holds
- Define, steps 1-2: the charter and the X list, the Pareto of what goes wrong.
- Measure, steps 3-8: sample size, data loading and cleaning, Gage R&R and attribute agreement, graphs, capability for normal, non-normal and pass/fail data, the baseline chart.
- Analyze, step 9: the Which test? guide, fishbone, correlation and regression, ANOVA, life data.
- Improve, step 10: the DOE guide, a quick planner, decision support.
- Control, steps 11-12: the control chart guide, the control plan with reaction plans, the handover pack.
Nothing is locked: every tool opens from the sidebar. The numbered steps are the order a project usually runs in.
Start with your data
Load a CSV or an Excel sheet, then open any tool below. Every guide checks the assumptions before it answers, and says so in words you can read out in a meeting.
No data yet? Work out how many readings you need before you collect them - Sample size calculator
Open any tool
Every tab in the app, in the sidebar's own order - the order a belt works. Blue is a guide - the step-by-step door, with the checks built in. Nothing here is a gate; the sidebar opens the same tabs.
Help & handbook
What is in this app, in what order to use it, and what its words mean. It does not teach the statistics twice: where the app already explains something, this book shows you that same card rather than a second version of it, so the two cannot drift apart.
Contents
Download the handbook
Pages to come: the DOE Guide, Lean Six Sigma graphs, the Data Lab, the Sample Size Calculator, MSA tools, Attribute Agreement, Decision Support.
Control Chart Guide (step by step)
Four steps. Say what you recorded and how, and the guide names the chart - there is no list to choose from. It points at your columns and checks them, draws the pair with the range chart read first, and leaves you with a verdict, one sentence for the slide and a page for the tollgate.
Step 1 - What did you record?
Use a different chart
For a Black Belt who has a reason. Name one of the seven and the page uses it; every sentence then says the chart was chosen by the analyst. Naming an np, p, c or u chart here also means the plain chart, without the Laney correction.
Step 2 - Point at the columns
More rules
Rules 1 and 2 are always on for the chart of the level, and Rule 1 for the range, S or moving-range chart. The other six are off by default: each one you add makes the chart more sensitive and also more likely to cry wolf.
Step 3 - The chart
Step 4 - Decide and report
These three go in the report header with the name of the file you loaded, and the project name goes in the footer of every printed page. Belt and Project carry over between the guides.
Download HTML report Download CSV of every plotted point
Control plan & handover (step by step)
Two steps, and no arithmetic. Every characteristic you put on the plan from one of the guides arrives here with what that guide found already filled in - the chart, the limits as they were printed, the rules, the capability, the verdict. You type the five things no guide can know, and the page tells you whether the row is ready to hand to the line.
Step 1 - What is on the plan
The project name is how the plan finds its records: a characteristic is filed under the project it was added from. Belt and Project are the same two the guides use.
Step 2 - One characteristic at a time
Step 3 - Reaction plan and handover
Pareto Analysis
Pareto Analysis Settings
A Pareto is used three times in a project: in Define to choose the problem (what goes wrong, counted), in Analyze to find the vital few causes, in Improve to show what remains after the change. Each can come from different data - choose where this one's comes from, then file it with its use.
Pareto Chart
Analysis Results
Pareto Summary
80/20 Analysis
File the vital few to the project (Define)
A project is chosen from evidence: the categories that make up most of what goes wrong. Filing them puts "project selection" on record for the Define gate and lights the Pareto box on the road map; the charter's problem statement should name them.
Capability Guide (step by step)
Four steps. Say what is measured and what the procedure requires, let the guide check that the data can carry a capability statement at all, read the numbers, and leave with a verdict and one sentence for the slide. The guide will not produce a capability index from data that is out of control or not normal - it tells you what is wrong and where to go instead.
Step 1 - What is measured, and what does the procedure require?
Step 2 - How was the data collected, and can it be trusted?
With no column the guide takes groups of that many consecutive rows, in file order, and says so on every page.
The pooled standard deviation uses every reading in every group and is the usual default for a capability study. The other two use one summary number per group; they are what a control chart is drawn from. Whichever you pick, the page names it and shows what the others would have given.
The checks are a control chart of the readings in file order (are they one process?) and a normality test (does the normal curve describe the tail?). Both have to pass before a capability index means anything.
Step 3 - The capability numbers
Step 4 - Decide and report
These three go in the report header with the name of the file you loaded, and the project name goes in the footer of every printed page. Leave any of them blank and nothing is printed in its place. Belt and Project carry over between the guides; the date of data does not.
Download HTML report Download CSV of the numbers
Non-Normal Capability (step by step)
Three steps, for data a normal curve does not describe - repair hours, turnaround times, anything bounded at zero with a long tail. Say what is measured, let the guide check whether the readings came from one process and find the distribution that fits them, then read the numbers, the verdict and one sentence for the slide. The guide chooses the distribution and tells you what it chose and what it would have said under the runner-up.
Step 1 - What is measured, and what does the procedure require?
Step 2 - Can the data be trusted, and what shape is it?
Two checks. A control chart of the readings in file order asks whether they all came from one process; then five distributions are fitted and ranked by how well each one describes the readings. The guide picks one and tells you what the others said.
Use a different distribution
For a Black Belt who has a reason. Pick one by name and the page recomputes under it; every sentence then says the distribution was chosen by the analyst.
Step 3 - The numbers, the verdict and the report
These three go in the report header with the name of the file you loaded, and the project name goes in the footer of every printed page. Leave any of them blank and nothing is printed in its place. Belt and Project carry over between the guides.
Download HTML report Download CSV of the numbers
Distribution Fitting
Distribution Fitting & Identification
Identify the best-fitting distribution for your data
STEP 1: Select Data
Choose numeric variable to analyze
STEP 2: Select Distributions
Choose distributions to fit
Symmetric Distributions
Reliability & Life Data
Right-Skewed Distributions
For Min/Max Data
For Data with Outliers
For Bounded Data
Data Transformations
STEP 3: Options (Optional)
Specification limits & settings
Specification Limits (for Capability)
Advanced Settings
DISTRIBUTION FITTING RESULTS
Distribution Rankings
Legend:
Interpretation Guide
Histogram with Fitted Distributions
Probability Plots
Q-Q Plot (Quantile-Quantile)
P-P Plot (Probability-Probability)
All Distributions - Q-Q Grid
Parameter Estimates
All Parameters Summary:
Percentile Estimates
Inverse Lookup: Find Percentile for a Value
Process Capability (Non-Normal)
Random Data Generation
Generated Data Summary:
Download DataHistogram of Generated Data:
Distribution Selection Guide
Continuous Data
- Normal: Symmetric, bell-shaped
- Lognormal: Right-skewed, positive values
- Gamma: Right-skewed, waiting times
Reliability/Lifetime
- Weibull: Failure times - only when every unit failed; units still running need a censored analysis
- Exponential: Constant failure rate
- Loglogistic: Accelerated life testing
Extreme Values
- Gumbel: Maximum values
- SEV: Minimum values
- Pareto: Heavy-tailed phenomena
Special Cases
- Beta: Bounded [0,1] proportions
- Uniform: Equal probability
- Cauchy: Heavy tails, no mean
Data Transformation
Data Transformation Tools
The curve is fitted from four percentiles of your readings and kept only if the transformed readings pass the normality test (p at or above 0.10). The limits you enter below are transformed with the same curve.
Specification Limits (Optional):
Before and After Transformation
Transformation Results
Normality Test Results:
Transformed Specification Limits:
Use these values for normal capability calculations:
One-Way ANOVA Settings
• Select a numeric response variable (continuous outcome)
• Select a categorical factor variable (groups to compare)
• Numeric variables with ≤10 unique values are included as potential factors
• For continuous predictors with >10 values, use regression analysis instead
Two-Way ANOVA Settings
• Select a numeric response variable (continuous outcome)
• Select two different categorical factor variables
• Numeric variables with ≤10 unique values are included as potential factors
• For continuous predictors with >10 values, use regression analysis instead
• Interaction term tests if the effect of one factor depends on the other
📊 Generalized ANOVA Settings
📈 Analysis Results
ℹ️ Generalized ANOVA Information
About Generalized ANOVA
Generalized ANOVA allows you to analyze the relationship between one continuous response variable and multiple factors and/or covariates.
- Factors: Categorical variables (groups)
- Covariates: Continuous variables used as controls
- Interactions: Test whether the effect of one variable depends on another
- Model Types: Choose between ANOVA, Linear Model, or Mixed Effects approaches
Model Interpretation
- Main Effects: Individual contribution of each factor/covariate
- Interaction Effects: Combined effects between variables
- F-statistic: Test of significance for each effect
- p-value < 0.05: Statistically significant effect
Gage R&R Guide (step by step)
Five steps. Answer the questions on Step 1 and the guide names the measurement study that is valid for how your number is produced - there is no list to choose from. Then it plans the study, checks the file you collected, runs it, and leaves you with a verdict word, one sentence for the slide and a page for the tollgate. The one study it does not run is attribute agreement, and it says so.
Step 1 - Describe the measurement
Accuracy and precision are different properties - and a Gage R&R measures only one of them
A measurement system has to be both. It can be beautifully consistent and consistently wrong; it can be unbiased on average and too noisy to use. Every study below exists because it answers a question none of the others can.
Designing the study, whichever one you run:
- 10 parts, 3 appraisers, 2-3 trials is the standard design. More parts and more trials raise the confidence in every number you report; fewer widen it, sometimes badly.
- The parts must span the real process spread. This is the requirement people break most often. Ten parts from one batch make a good gauge look useless; ten hand-picked extremes make a poor one look excellent. Neither is your process.
- Use the appraisers who normally do the job - the people familiar with the equipment and the procedure, not whoever is free that afternoon.
- Number the parts randomly and hide the numbers. An appraiser who remembers reading 12.41 yesterday will read 12.41 today.
- Have a third person record the part, the appraiser, the trial and the reading. The appraiser should never see their previous value.
Every study type, in one table
The answers above pick one of these for you. This is here for the meeting where someone says “just run a Type 1” and you want to know what they have actually asked for.
| Study | The question it answers | How it is run |
|---|---|---|
| Type 1 gage study | Is the INSTRUMENT capable and unbiased at one point, today? | One appraiser, one certified item, 50 repeat readings, re-set each time. |
| Linearity and bias study | Is the bias the SAME across the range, or does it grow with size? | One appraiser, 12 readings on each of 5 traceable standards across the working range. |
| Resolution / discrimination check | Can the gauge SEE the differences you care about at all? | Arithmetic, not a study: the display increment against the tolerance. |
| Stability study | Does it stay true over TIME? Nothing else can answer this. | One reading of a check standard per day for 20-30 days, on an I-MR chart. |
| Crossed Gage R&R (Type 2) | How much of what you see is the measurement system rather than the parts? | Every appraiser measures every part, several times each. |
| Nested Gage R&R | The same question as crossed, when the test destroys the sample. | Each appraiser measures their OWN specimens - no part is shared. |
| Type 3 study (one-way on parts) | What is the repeatability of the system on its own? | No appraiser at all: an automated system re-measures the same items. |
| Paired duplicates (Wheeler) | Repeatability when the item can never be measured twice - a flowing stream, or a consumed sample. | Two readings taken as close together as possible, 8-20 pairs. |
| Attribute Agreement Analysis (kappa) | Do people agree with themselves, with each other, and with the truth? | Appraisers rate the same items twice against a known standard. |
| Expanded Gage R&R | Which of several nuisance factors is actually moving the measurement? | A crossed study with a third factor - site, shift, fixture, method. |
The order matters: resolution, then bias (Type 1), then linearity, then the R&R, then stability. Every one of the first three can invalidate an R&R, and each is quicker and cheaper to run. A Gage R&R cannot see bias at all - three appraisers can agree with each other perfectly and all be wrong by the same amount.
Reading the result - four numbers, and which one governs
| Metric | What it is | Accept / marginal | When it governs |
|---|---|---|---|
| %Study Variation | sigma of the source / sigma total | < 10 % / 10-30 % | Process control and improvement - can the gauge see a real process change? |
| %Tolerance | 6 sigma GRR / (USL - LSL) | < 10 % / 10-30 % | Product acceptance - pass or fail against a specification. |
| %Contribution | variance of the source / total variance | < 1 % / 1-9 % | Same information, squared scale. Its thresholds are NOT 10 / 30. |
| ndc | 1.41 x sigma part / sigma GRR | 5 or more | How many groups of parts the gauge can separate. Below 5 it cannot support SPC or Cpk. |
The commonest reporting error: quoting %Contribution against the 10 / 30 limits. Those belong to %Study Variation, which is a ratio of standard deviations. %Contribution is the square of it, so a system sitting exactly on the 10 % boundary shows 1 % contribution - judging it against 10 makes the criterion ten times too lenient (and at the 30 % line, 9 % against 30 is more than three times too lenient).
And the threshold is not the whole decision. The same 17 % is workable on a product dimension with an action plan, and a failure on a wall-thickness reading that keeps a vessel in service. Decide which metric governs, and what limit you will hold it to, before you see the number.
The words, in plain language
- Repeatability (EV, equipment variation) — One appraiser, one item, measured again. The question it answers is: if I measure this a second time, how close will I get to my own first answer? It is the gauge, the fixture, the method and the environment - not the people.
- Reproducibility (AV, appraiser variation) — Different appraisers, same item. Do different people get the same answer? If this is LARGER than repeatability, the cause is people or procedure - always. It never points at the instrument, so do not buy a new one.
- Appraiser x part interaction — The difference between appraisers depends on which part is measured - one struggles on thin sections, another on thick. Parallel lines on the interaction plot mean a simple offset; crossing lines mean technique differs by part, which is harder to fix.
- Part-to-part variation (PV) — The real differences between the items you chose. A good gauge has a lot of this relative to its own noise - which is why the parts must span the real process range, not come from one batch.
- Bias — The average distance between what the gauge reads and the TRUE value. A Gage R&R cannot see it: three appraisers can agree with each other perfectly and all be wrong by the same amount. Only a reference can reveal it.
- Linearity — Whether the bias stays the same across the range. A gauge can be right at 10 mm and wrong at 5 mm, and a single-point calibration will pass it.
- Stability — Whether bias and spread hold over time. Only repeated readings of a check standard across days or weeks can show drift - and that chart is also your evidence for what the calibration interval should be.
- Resolution / discrimination — The smallest step the display shows. If that step is more than 10 % of the tolerance, identical readings are the display hiding the variation, not the gauge being precise.
- ndc, number of distinct categories — How many non-overlapping groups of parts the gauge can tell apart. Below 5 it cannot support a control chart or a capability index.
- Kappa — Agreement on a judgement, corrected for the agreement you would expect by chance alone. Two inspectors passing everything agree 100 % of the time and have a kappa of zero.
- Miss rate — In an attribute study, the share of genuinely bad items that were called good. It is the safety number, and overall agreement can look healthy while it is unacceptable. Report it on its own line.
Step 2 - Plan the study
Step 3 - Point at the data
Step 4 - Run and read
Full output - every table this engine produces, with the design and the alpha under your own control: Gage R&R (Continuous) . It runs the same engine on the same file, so the figures agree; it asks you to load the file again and it has no verdict word.
Step 5 - Verdict and report
These three go in the report header and in the footer of every printed page. Belt and Project are the same two the capability guides use.
Download HTML report
Capability for pass/fail and count data
When the result is pass/fail, or a count of defects, there is no Cpk. The capability is the rate itself - the share of items defective, or the defects per unit - with an honest interval around it, and whether that interval clears your target. The rate is one number only if the process is stable, so read the chart first.
Life data (reliability) - including units still running
How long do units last? This fits a life distribution to the failure times and counts every unit that has not failed yet as surviving at least as long as it has run . Leaving those units out - the commonest error in reliability work - makes the life look shorter than it is, and nothing in the fit would tell you.
MSA Tools - Type 1 gage study, Gage linearity & bias, Resolution check
Instrument-level studies that a crossed Gage R&R cannot see: bias and repeatability of the instrument against a reference (Type 1), how the bias changes across the range (linearity), and whether the display step can resolve the tolerance at all (rule of tens). Not sure which study your measurement needs? Open the Gage R&R Guide (step by step) .
Rule of tens
Study set-up
One instrument, one reference item, one appraiser, 25-50 consecutive readings without re-zeroing. This isolates the instrument: bias and repeatability only.
Study set-up
Several reference parts spanning the operating range (AIAG: >= 5), each measured >= 10 times by one appraiser in random order. Bias = reading - reference; linearity = how the bias changes across the range.
When the operator's job is to read a screen and write a number
The failure modes are gross, not fine: a transposed digit, the wrong tag, the wrong unit, a 1-minute average read as an instantaneous value, a value copied at the wrong time. That is an attribute question - right or wrong - so it is run as an Attribute Agreement Analysis against a standard , not as a variable Gage R&R.
- Capture 20-30 frozen screens (screenshots or logged snapshots) spanning normal, high and low values, including a few awkward ones (many decimals, negative, near an alarm limit). Record the true value for each - that is the standard.
- Give the screens to each appraiser in random order, twice, at least a shift apart. They record the value exactly as they would in the logbook / e-log.
- Score each recorded value as Agree (exact match to the standard, or within the display step) or Disagree.
- Run the Attribute Agreement (Kappa) tab: within-appraiser (consistency), each-vs-standard (correctness), between-appraiser.
- Acceptance: kappa >= 0.75 and % correct vs standard >= 90 % (AIAG). Every disagreement is investigated as a defect - usually the fix is the screen layout, tag naming or the log sheet, not the person.
Pair this with a Type 1 gage study of the transmitter and a resolution check: together they cover the instrument, the display and the human.
Analytics © Dr. Mahmood Al Kindi - MSA Tools follow AIAG MSA 4th Ed. and VDA 5 conventions.
Gage R&R (Continuous)
Gage R&R Analysis (Variable, Crossed / Nested)
Data Input
New to Gage R&R?
Download a template file to see the required data format:
Download Template CSVThe template includes:
- Part column: Unique part identifiers
- Operator column: Operator names/IDs
- Measurement column: Numeric measurements
- Multiple measurements per part-operator combination
Nested: Each operator measures different/unique parts
Study context (required for the tollgate screen)
Pre-study checklist
- Right measurement for the customer requirement; data-integrity issues (transcription, recording point, timing) ruled out first
- Instrument resolution ≤ 1/10 of the smaller of process variation or tolerance
- Measurement process in statistical control; Type 1 study passed if a reference exists
- Parts span the real operating range (documented); parts are individual units, never time periods or averages
- Tolerance entered = USL − LSL
- Measurement order randomised; operators blind to their own and each other's readings
- Every trial is a full REPLICATE (part removed and re-presented, re-zeroed) - not a repeat
- Appraisers are the people who normally do this work; environmental covariates recorded
- Destructive tests: batch homogeneity demonstrated (nested design)
Gage Evaluation
ANOVA Results
Range Chart
Xbar Chart
These 6 plots are the standard Gage R&R diagnostic set. Use them together to diagnose measurement issues.
1. Components of Variation
2. R Chart by Operator
3. Xbar Chart by Operator
4. Measurements by Part
5. Measurements by Operator
6. Operator x Part Interaction
Bootstrap Confidence Intervals on Variance Components
Bootstrap intervals (rows resampled) - indicative of estimation uncertainty only. AIAG-style analytical (modified large-sample) intervals are reported; row resampling breaks the crossed structure, so treat these as a rough guide, not a sign-off figure.
Generate Management Report
Create a comprehensive HTML report for management presentation.
Download HTML Report
Import Previous Study
Upload a previous JSON export to compare trends.
Report Preview
Click 'Generate & Download Report' above to create and download a comprehensive HTML report with all analysis results and charts.
Gage R&R (Expanded) - three or more factors
For studies that do not fit Part x Operator: a fixture or instrument factor, two labs, day/night, a fixed setting. Declare each factor random (its levels are a sample - operators, fixtures drawn from many) or fixed (the levels ARE the population - the only two instruments, high/low setting). Random terms give variance components; fixed terms contribute their variability across levels (the standard GLM convention). The split repeatability / reproducibility / part-to-part follows the standard convention: error, everything else, and the part terms you name.
1. Data
2. Model
3. Yardsticks
Analytics © Dr. Mahmood Al Kindi — Expanded Gage R&R: GLM expected mean squares (balanced) / REML (unbalanced); expanded Gage R&R conventions (random and fixed terms).
Decision Support (MCDM) - choosing among solutions
For the Improve phase: several countermeasures, several criteria, one decision the sponsor has to sign. Enter the criteria, weight them (directly, or by pairwise comparison with a consistency check), score the alternatives, and read the ranking from three methods at once - weighted sum, TOPSIS and a Pugh matrix . When the three agree and the winner survives the weight-sensitivity check, the decision is defensible; when they disagree, the tab tells you which criterion is deciding it.
1. Criteria and alternatives
Criteria (double-click a cell to edit; Direction from the drop-down)
Alternatives Direction matters: cost, time, risk are 'lower is better'. Weights here are used when 'Direct weights' is selected below; they are rescaled to sum to 1.
2. Weights
3. Scores of each alternative on each criterion
4. Results
Analytics © Dr. Mahmood Al Kindi — Decision Support: Saaty AHP (1980), Hwang & Yoon TOPSIS (1981), Pugh concept selection (1991), simple additive weighting.
Attribute Agreement Analysis
For pass/fail, go/no-go, accept/reject, and ordinal-rating gages. This is the attribute counterpart to continuous Gage R&R.
Data Input
Fleiss' Kappa by Response Level (between appraisers)
Parts where appraisers/trials did not all agree — the parts to investigate first.
Before Regression Analysis
Check your data quality and assumptions before running regression
Regression Diagnostics
Fit a linear model, check all assumptions, download a complete report
Residuals vs Fitted
Normal Q-Q Plot
Scale-Location
Cook's Distance
Correlation Circle Plot
Correlation Heatmap
Regression and Correlation Analysis
Regression and Correlation Analysis
Correlation Highlighting
Categorical Variables
Ridge Regression Parameters
Drawn from the fitted model at x values you already have. The same columns always give the same picture.
Advanced Analysis
Correlation Matrix
High Correlation Warnings
Correlation Visualization
Regression Plot
Full R output (the same numbers as the table below)
Variance Inflation Factor (VIF) - Multicollinearity Analysis
VIF values indicate the degree of multicollinearity. Generally:
- VIF = 1: No correlation
- VIF < 5: Moderate correlation (acceptable)
- VIF > 5: High correlation (concerning)
- VIF > 10: Severe multicollinearity (problematic)
Full R output (the same numbers as the table below)
Variance Inflation Factor (VIF) - Multicollinearity Analysis
VIF values indicate the degree of multicollinearity. Generally:
- VIF = 1: No correlation
- VIF < 5: Moderate correlation (acceptable)
- VIF > 5: High correlation (concerning)
- VIF > 10: Severe multicollinearity (problematic)
Pareto Chart of Standardized Effects
Bars extending beyond the reference line indicate statistically significant predictors at α = 0.05
Ridge Regression Summary
Diagnostic Plots
Regression Equation and Model Details
Model Performance
ANOVA Table
Unusual observations - the rows to go and look at
Prediction Tool
Enter Values for Prediction
Prediction Results
Logistic Regression Analysis
Binary Logistic Regression Analysis
📐 Model Equation
🎯 Business Insights & Strategic Recommendations
Model Summary
Model Performance Metrics
📊 Model Coefficients & Business Impact Analysis
🎯 Odds Ratios & Strategic Impact
Confusion Matrix
Classification Metrics
Diagnostic Plots
ROC Curve Analysis
ROC Statistics
🔮 Strategic Scenario Planning Tool
Enter Values for Prediction
Prediction Results
Design of Experiments (step by step)
Create design → run it → type the results → analyze → plots → optimize. The standard DOE workflow, end to end.1. Design type
Already have results? Go to step 2 and upload the completed worksheet, or use the dataset loaded in the app.
Power and sample size (2-level)
How many replicates to detect an effect of a given size (difference between the means at the high and low level).
2. Factors: names, type and levels (edit the table)
Available factorial designs: runs x factors -> resolution
Resolution III: main effects aliased with 2-way interactions (screening only). IV: main effects clear, 2-way interactions aliased with each other. V or higher: main effects and 2-way interactions all clear. Full = no aliasing.
Responses
Run the experiment in RunOrder and type each result into the worksheet on the right (double-click a cell). Add one column per response (e.g. Yield, Viscosity) - responses are never averaged together.
Worksheet (CSV) Worksheet (Excel)
Or bring completed data
Worksheet (design columns locked, response cells editable)
Model
Model summary
What the analysis says
Coded coefficients
Regression equation
Analysis of variance (adjusted SS)
Pareto chart of effects
Normal plot of effects
Half-normal plot
Alias structure
Residual check & Box-Cox
Residuals versus each factor
Level means
Which factors change the SPREAD, not the average?
Needs true replicates: the same settings run again from scratch, not the same part measured twice. The model is fitted to ln(s²) at each replicated design point. A factor that shrinks the spread without moving the mean is free variation reduction - that is the whole point of robust design.
Spread at each design point
Backward elimination log
Fitted responses
Factorial plots
Contour / surface
Where do ALL the responses meet their limits at once?
Set an acceptable range for each fitted response; the white region is where every one of them is met. This is the operating window to hand to production - the optimizer gives one point, this gives the room around it.
Stationary point (second-order models)
Response optimizer (desirability)
Set a goal for each fitted response. Lower / Target / Upper define the desirability (Derringer-Suich); importance weights the responses against each other. Search region: the coded design box (-1 to +1).
Predict at settings
What is it worth? (capability and payback)
Turns the predicted optimum into a defect rate, a sigma level and a saving. Model predictions, not measured results - confirm with a pilot before booking anything.
Optimal settings
Optimization plot
Prediction
Capability and payback at the optimum
Analytics © Dr. Mahmood Al Kindi — DOE engine: two-level factorial (Box-Hunter-Hunter generators, defining relation and alias structure computed, not looked up), Plackett-Burman (cyclic generators, orthogonality asserted), central composite and Box-Behnken; adjusted-SS ANOVA with curvature, lack-of-fit and pure error; Lenth's PSE (1989) for unreplicated designs; R-sq(pred) from PRESS; Derringer-Suich desirability.
DOE (Simplified)
What would you like to do?
What are you trying to improve?
How do you measure it?
What are you going to change?
How many settings for each?
How many tests can you afford?
Will anything change during the experiment that you can't control?
Is any setting expensive or slow to change?
Your experiment plan
Your run sheet
What this plan can and cannot tell you
Will it find the effect you care about?
Download your run sheet
That's the planning done.
Go and run your experiment. Come back with this file filled in, and choose "I have my results".
Upload your filled-in run sheet
Checking your data before analysing it
What your experiment says
What mattered
What to set the process to
How much you should trust this
Graphs
Try any settings
For specialists: every number and plot
Design of Experiments (DOE) Analysis
Taguchi Design of Experiments
Robust parameter design for process optimization using orthogonal arrays and signal-to-noise ratios
The charter, and the X list
A project is one Y and the X's that drive it. Name the Y here the way the sponsor will sign for it, write the problem as what, how much, when and where - not why - and list the X's the team suspects. Every later phase fills in the X list: Measure defines each X, Analyze tests it, Improve sets it, Control holds it. The checks on the right are what a tollgate reviewer will say; nothing here stops you.
The Y
Operational definition - so two people get the same number from the same event:
The problem
The goal
Scope, team and governance
The X list - what the team suspects drives the Y
One row per suspected cause. Say how it is recorded and where the suspicion came from. Leave the status at "suspected" - the Analyze phase moves it, with evidence.
About Al Kindi Analytics
This Analytics Tool is a personal initiative by Dr Mahmood Al Kindi, built for Green Belts and Black Belts: data preparation, graphical and inferential statistics, measurement system analysis, statistical process control, capability, design of experiments and decision support, in one place, with the assumption checks and the plain-language reading attached to every result rather than left to the user.
There is no sponsor and no department behind it. It was written personally, for the belts who use it.
Working together. Deployments for other organisations, and support for developing this tool further, are arranged through Dr Mahmood Al Kindi — alkindi123@gmail.com.
Licence. Free for individual Green Belts and Black Belts, for their own learning and their own projects, with acknowledgment to the author. Use by an organisation - for its belts, its contractors, or on its own servers - is by written agreement with the author. The code is not open source and may not be copied, modified or redistributed.
Your work. Your data is used only for the analyses you run. The results, reports and project files you produce are yours to download and keep. Save the project file from the project board to carry on later or hand a project over.
Version. 10 October 2026 build. Read the handbook for this build .