The Lean Six Sigma Formula Toolkit
Your software gives you the answer. This shows you where it came from. 227 Lean Six Sigma formulas worked step by step in project order, from COPQ and DPMO through Cp, Cpk, Gage R and R, hypothesis testing and regression, to control limits, Weibull and multi year ROI. Every calculation includes the dataset, the notation with a full symbol legend, the substitution line by line, the chart and a plain explanation of what the number means.
RDMAICS, not DMAIC
Two phases most references skip. Recognise sizes the problem in money before anyone commits, and Sustain proves the gain held years later. Every formula sits in the phase that actually uses it.
227 formulas · 45 lenses · 744 pages · one continuous project
The software hides the part that matters
You open Minitab, load the data and click. A Cpk appears. You put it in the report. Then the sponsor asks why Cpk and Ppk disagree, or whether the sample was big enough, or what happens if the process is not normal, and the button cannot answer any of that.
This is the gap that catches Belts out. Running the calculation is the easy part and the software has made it trivial. Understanding what the formula assumed, which numbers went into it, and what the output actually licenses you to claim is the hard part. No calculator will teach you that, and neither will a formula sheet.
This toolkit opens up every formula and shows the working. Not a cheat sheet. Every calculation arrives with the business reason it was needed, the raw dataset, the notation with each symbol defined in plain language, the substitution line by line, the chart, an interpretation, and a short explanation of the thinking behind the method. After reading it you can run the number and defend it.
How every formula is explained
The same four part template runs through all 227 calculations, so once you learn to read one you can read every one.
Scenario background
Why the team needed this calculation at this point in the project, and what decision hangs on the answer.
Dataset
The raw numbers in a clean table with the source stated, so every input can be traced back.
Formula and legend
Stacked mathematical notation with every symbol defined underneath in plain language.
Calculation and meaning
The substitution shown line by line, a result box, a chart, and what the team did next.
Every formula carries a Why It Matters panel
This is the part software cannot give you and other references leave out. Not what the formula is, but why it is built that way, and what goes wrong when people use it without knowing. Three examples taken straight from the decks.
Why you multiply, not add
Multiplying power by interest is deliberate. A stakeholder with total authority and no interest scores low, which is correct. Adding would promote them into daily management they neither want nor need.
Why two response types are dropped
Reverse and Questionable responses are excluded from both denominators. They describe survey noise rather than customer preference, so including them would understate every coefficient.
Why sorting comes first
Sorting descending before accumulating is not cosmetic. The formula only identifies a vital few if the largest categories are counted first, which is why an unsorted Pareto chart is meaningless.
Why the scale jumps 9, 3, 1, 0
The scale is not linear by accident. The wide spacing forces the team to distinguish a strong relationship from a moderate one instead of scoring everything in the middle.
Why the mean can mislead
CES is a simple mean, so it hides the shape of the distribution. Always read the score next to the histogram, because two very different customer experiences can average to the same number.
Why you quote both numbers
The gap in percentage points is what the process must physically deliver. The percent improvement is what leadership hears. Quoting only one of the two is how projects commit to the wrong thing.
Six slides from the decks
Taken straight from the toolkit, unedited. Each formula runs across two slides, the notation with its reasoning, then the calculation with the chart and what the team concluded. Click any slide to view it full size.
Which Lean Six Sigma formulas are covered?
All of them, in the order a project uses them. The financial formulas include cost of poor quality, return on investment, net present value and multi year benefit realisation. The defect and yield formulas include defect rate, DPU, DPO, DPMO, PPM, first pass yield, rolled throughput yield and sigma level conversion.
Process capability is covered in full, with Cp, Cpk, Pp, Ppk and Cpm, alongside Z scores and the normal distribution. Measurement system analysis covers Gage R and R, repeatability, reproducibility, number of distinct categories and attribute agreement with Kappa. Sampling covers sample size, confidence intervals, margin of error and statistical power.
The statistical testing set runs from one and two sample t tests, paired t tests and Welch, through proportion Z tests, one way and two way ANOVA, chi square, F tests, and the non parametric alternatives including Mann-Whitney, Kruskal-Wallis and Mood's median. Relationships are covered with correlation, simple and multiple regression, R squared and residual analysis.
Lean formulas include takt time, cycle time, lead time, Little's Law, process cycle efficiency, OEE, TEEP, line balance efficiency, EOQ, reorder point and kanban sizing. Experimentation covers full and fractional factorial design, main effects, interactions, Taguchi signal to noise, the loss function and response surface methods.
Control covers X bar R, X bar S, individuals and moving range, EWMA, CUSUM, p, np, c and u charts, control limit calculation, Western Electric and Nelson rules, average run length, OC curves, AQL, LTPD and acceptance sampling. Reliability adds MTBF, MTTR, availability and Weibull. Sustain closes with drift detection, learning curves, maturity scoring and diffusion modelling.
All 227 formulas, phase by phase
Formulas appear in the order a real project uses them, not alphabetically. Each phase groups its calculations into lenses, and opens by carrying forward the numbers the previous phase produced.
Recognise
Before a project is chartered, leadership needs a number. This phase converts four warning signals into a dollar figure, ranks the candidate projects against agreed criteria, and establishes the customer baseline from three independent angles.
What Recognise covers
Define
The phase that turns a signal into a contract. It locks the project Y, sizes the gap, sets a target anchored in evidence rather than ambition, ranks what the customer actually wants, and translates that into process inputs the team can adjust.
What Define covers
Measure
Building a baseline leadership can defend. Defect metrics, capability, the distribution theory underneath both, then an audit of the measurement system itself before any of it is trusted. Flow and equipment effectiveness close the phase.
What Measure covers
Analyse
The largest phase in the toolkit. It confirms that observed differences are real rather than sampling noise, quantifies which inputs actually move the output, ranks the causes, then prices every finding so the Improve queue is ordered by money rather than opinion.
What Analyse covers
Improve
Designing the change, testing it and proving the gain landed. Full experimental design through to response surface optimisation, alongside the lean formulas that size pull systems, balance a line and evaluate capital at the bottleneck.
What Improve covers
Control
Holding the gain and proving it holds. Every chart type with its limit calculations, the rules that decide which patterns count as signals, then acceptance sampling, equipment reliability and the money case for keeping the control plan funded.
What Control covers
Sustain
The phase almost nobody teaches. It detects whether the gain is quietly eroding, compounds the benefit across years for capital decisions, scores programme maturity, and measures the people, knowledge and change factors that decide whether any of it lasts.
What Sustain covers
One project runs through all 227 formulas
Every formula is worked on Tony's Pizza Co., a fictitious quick service business in Brunswick, Melbourne. Not because pizza is clever, but because everybody can picture the process, and because the numbers can then carry forward without needing a new context every chapter.
The project, phase by phase
Who uses the toolkit
Belts who use the software
You can run Minitab, JMP or Sigma Magic. You want to know which formula it applied and what it assumed, so the next question from a sponsor does not stop you.
Belts studying for certification
Exams give you numbers and ask for an answer. Working every formula on real data beats memorising a formula sheet you will forget by the exam.
Belts running a live project
You are mid phase and need the right calculation now, with a worked example and the reasoning beside it.
Trainers and coaches
A consistent teaching set across all seven phases, so your examples stop contradicting each other from one session to the next.
Process improvement teams
A shared reference so everyone calculates Cpk, DPMO, sigma level and control limits the same way, with the same assumptions.
Quality and reliability engineers
Control and Sustain cover MTBF, Weibull, acceptance sampling and reliability growth, which most Lean Six Sigma references skip entirely.
The complete toolkit, sold as one
Phases are not sold separately. Each one carries forward the numbers from the phase before it, so the toolkit only works read as a whole.
The Lean Six Sigma Formula Toolkit
- 227 formulas worked across 740 plus pages
- All seven RDMAICS phases, Recognise to Sustain
- Concept, dataset, notation, calculation, chart and interpretation for every formula
- A Why It Matters panel on every formula
- Free updates to future editions
- Instant PDF download of all seven decks
SECURE CHECKOUT · INSTANT PDF DOWNLOAD
What is inside the toolkit
| Volume | Phase | Formulas | Pages | Lenses |
|---|---|---|---|---|
| 1 | Recognise | 7 | 30 | 4 |
| 2 | Define | 8 | 31 | 5 |
| 3 | Measure | 43 | 138 | 7 |
| 4 | Analyse | 49 | 157 | 7 |
| 5 | Improve | 49 | 157 | 7 |
| 6 | Control | 41 | 133 | 8 |
| 7 | Sustain | 30 | 98 | 7 |
| Total | Complete RDMAICS | 227 | 744 | 45 |
All prices in Australian dollars. Delivered as PDF, immediately after purchase.
Training and team licences
The standard price covers one reader. If you want to distribute copies inside your organisation, or teach from these decks in your own training, a team or trainer licence covers it.
Enquire about a team licenceFrequently asked questions
Do I need statistics training to use this?
No. Every formula includes a symbol legend in plain language, a written interpretation of the result and an explanation of the reasoning behind the method. If you can read a table, you can follow the calculations. A Green Belt or Black Belt background makes it faster, but it is not assumed.
Which software do I need?
None. Every calculation is shown by hand so you can reproduce it in a spreadsheet. Nothing depends on Minitab, JMP, Sigma Magic or any paid statistical package. The point of the toolkit is to explain which formula the software applies and what it assumes when you press the button.
Can I buy just one phase?
No. The toolkit is sold complete. Every phase carries forward the numbers calculated in the phase before it, so one phase read in isolation loses the context that makes the worked examples useful. Buying the set also means the answer to any phase question is always in front of you.
How long is the complete toolkit?
More than 740 pages across seven volumes, covering 227 formulas. Analyse and Improve are the largest at 157 pages and 49 formulas each. Recognise is the shortest at 30 pages and 7 formulas.
Is this the same content as your online courses?
No. The courses teach the method through video lessons. This toolkit is the calculation reference you keep beside you while running a project or preparing for an exam. Many learners use both, and the numbers are consistent with the training material.
Does it go beyond standard DMAIC?
Yes. The toolkit follows RDMAICS, which adds a Recognise phase before Define and a Sustain phase after Control. Control includes acceptance sampling, OC curves, Weibull reliability and cost of quality. Sustain covers drift detection, multi year ROI, programme maturity, knowledge retention and diffusion modelling. Most references stop at Control.
Is Tony's Pizza Co. a real business?
No. It is a fictitious business created for this toolkit. Any resemblance to an actual pizza shop or restaurant is coincidental. The data is constructed to behave the way real operational data behaves.
Can I use this to train my team?
Personal licences cover one reader. For internal distribution, or to teach from this toolkit, contact us for a team or trainer licence.
What format is the download?
PDF, formatted for both screen reading and projection. You receive the download link immediately after purchase.
Are the methods aligned to a certification body?
The methods follow Council for Six Sigma Certification standards and standard Lean Six Sigma practice, including the George Group 70 percent rule for goal setting and conventional Kano, QFD, Pareto, Western Electric and Nelson treatments.
Continue your Lean Six Sigma learning
Stop trusting the button. Understand the formula.
227 formulas. Seven phases. One project. Every calculation shown from the dataset through to the decision it drove. One toolkit, one price.
