Six Sigma is built on data and statistical thinking. This reference covers the key statistical concepts, formulas, and tools every Green Belt practitioner needs โ from basic descriptive statistics through to process capability and control charts.
Descriptive Statistics
These foundational statistical measures describe the central tendency and spread of your process data โ the starting point for any Six Sigma analysis.
The arithmetic average of a data set. The most common measure of central tendency.
Measures the spread or dispersion of data around the mean. Small ฯ = consistent process; large ฯ = high variation.
The square of the standard deviation. Used in many statistical calculations. Standard deviation is more intuitive as it shares the same units as the data.
Measures the potential capability of a process โ how well it could perform if perfectly centred within specification limits.
Accounts for both process spread AND centering. Always โค Cp. The most important capability index for real process performance.
Measures how many standard deviations a data point is from the mean. Used to calculate probabilities and convert to sigma levels.
The Normal Distribution
For normally distributed data, a predictable proportion of values fall within each standard deviation band from the mean.
Many natural and process measurements are approximately normally distributed, making it the most important distribution in Six Sigma statistics.
Sample means tend toward a normal distribution as sample size increases โ even if the underlying population is not normal. This underpins control charts.
Before applying many statistical tests, check whether your data is normally distributed using a histogram, normal probability plot, or Anderson-Darling test.
Not all process data is normal โ consider Weibull, Poisson, or binomial distributions for reliability, count, or attribute data respectively.
Statistical Process Control
Choosing the right control chart depends on whether your data is continuous (variable) or discrete (attribute), and your sample size. Use this guide to select the appropriate chart for your process.
Monitors process mean and range for continuous data with subgroup sizes 2โ10.
Variable dataMonitors process mean and standard deviation. Preferred for larger subgroup sizes (n > 10).
Variable dataIndividuals and Moving Range chart for continuous data with subgroup size of 1 โ common in process industries.
Variable dataMonitors the proportion of defective items in a sample. Used when subgroup sizes vary.
Attribute dataMonitors the number of defective items. Used when subgroup sizes are constant.
Attribute dataMonitors the number of defects per unit when sample size is constant.
Attribute dataMonitors defects per unit when sample sizes vary. Most flexible attribute chart.
Attribute dataAdvanced charts that detect small, sustained process shifts more quickly than traditional Shewhart charts.
Advanced SPCReference Materials
Curated links from the site and trusted external sources to support your statistical learning.
A curated collection of resources for building foundational statistical knowledge.
An introduction to SPC concepts, control charts, and process monitoring.
Full sigma level to DPMO conversion table with explanation of the 1.5 sigma shift.
Online calculators for common statistical computations used in Six Sigma projects.
Step-by-step tutorial on constructing and interpreting X-bar R control charts.
A clear explanation of Z-scores and how to use them in Six Sigma analysis.
Detailed walkthrough of process capability calculations and interpretation.
Practical guide to building histograms for data analysis using Microsoft Excel.