About

About this course

What it covers, how the numbers are checked, how real and constructed examples are labelled, and the licence.

What this course is

A practitioner's course on process capability, statistical process control, and the DMAIC improvement cycle, written for junior and mid-level mechanical and manufacturing engineers who have to run and read capability studies, set up control charts, interpret a gauge R&R report, and lead or support an improvement project. It covers the ground a Six Sigma Green Belt is expected to know, with capability and SPC treated in the most depth, because those are the two things an engineer in a plant is asked about most often and the two most often got wrong.

It assumes one statistics course, mostly forgotten. Every formula is given, explained in words, and applied to numbers. Nothing is derived that does not need to be.

What it is not

It is not certification preparation, and it does not claim to be. There is no exam, no accreditation, and no affiliation with ASQ, AIAG, VDA, ISO or any certifying body. The Green Belt body of knowledge is used as a scope reference, and where the course goes beyond it or declines to follow it, it says so.

It is also not a software course. The calculators here run in your browser and are enough for everything the course teaches, but the point is to understand the calculation, not to learn a menu.

How the numbers are verified

This is a statistics course, so every number in it can be checked, and readers will check them. The protocol:

• Every dataset is generated by a seeded script, saved as CSV, and printed on the page it belongs to, so you can copy it into a spreadsheet and reproduce the result yourself.
• Every statistic shown is computed by script from that CSV with numpy, scipy and statsmodels. No number is typed in from the author's own arithmetic.
• Every one of those numbers is then recomputed by a second, independent route: closed-form textbook formulas written out in plain Python, without the library functions used the first time. The two routes must agree to the precision shown on the page.
• A third script asserts the relationships that have to hold (Cpk ≤ Cp, Cpk = min(Cpu, Cpl), the PPM implied by an index matching the normal tail area, control chart constants correct for the subgroup size, p-values inside [0, 1]), and scans every page to confirm that every number printed on it traces back to a computed result.
• The browser calculators are run on every dataset in the course and must match the same results, which also serves as their test suite. The numerical functions in stats.js are checked against scipy at hundreds of points per function.
• The statistical tables and control chart constants on the tables page are computed, not copied, and then compared against published tables entry by entry.

The current run of that suite covers 172 examples and datasets: 4,829 quantities cross-checked between the two Python routes, 9,655 values compared between Python and JavaScript, and 1,573 checks on the pages themselves. Any failure blocks the example from appearing.

Real examples and constructed ones

Two kinds of example appear, and they are always labelled. Historical claims, published case studies, standards and statistics are researched, cited, and marked with the reading depth behind them; where a widely repeated story turned out not to be documented, the course says that rather than repeating it. Everything else is a constructed example, generated by script and introduced as constructed, because real production datasets with full context are usually proprietary and usually incomplete. Constructed examples use realistic metric quantities, a resolution matching a plausible gauge, and capability values that are interesting rather than tidy. No constructed example names a real company.

Where two credible sources disagree, or where a claim is contested — the 1.5 sigma shift, the origin of the 3.4 DPMO figure, capability indices on non-normal data, the published critiques of Six Sigma programmes' business results — the course presents the disagreement and its strongest sources on both sides instead of picking the tidier answer.

The author

Erdem Yilmaz is a senior manufacturing engineer with about eight years of new product introduction experience: running capability studies, sitting through supplier PPAP reviews, and explaining to programme managers why a Cpk of 1.1 is not close enough. The course is written in that voice, and deliberately contains no data, part, process or supplier detail from any employer.

Licence and reuse

Course content is published under CC BY-NC-SA 4.0: share and adapt it for non-commercial purposes, with attribution, under the same licence. The code — the calculators, the numerical library and the verification scripts — is MIT licensed, so you may use it commercially. Every figure is drawn as inline SVG for this course; no images, text or datasets are copied from other courses, software documentation or books, and standards are paraphrased rather than quoted at length.

Corrections

If a number here is wrong, it is a bug, and it is worth reporting. The verification suite makes silent arithmetic errors unlikely, but it cannot catch a badly chosen example, a claim whose source does not say quite what the course says it does, or an explanation that misleads while being technically true. Those are the corrections most worth having.

How the site is built

Plain HTML, CSS and vanilla JavaScript. No frameworks, no build step, no content delivery network, no cookies, and no third-party fonts. Progress is stored in your own browser only, and clearing your browser data clears it. The pages work from a local file as well as from a web server, and each one prints as a clean handout. Light and dark themes follow your system setting.