Glossary of Six Sigma Terms
Accuracy
The difference between the observed average value of the measurements and the true value.
Active Opportunities
Parts of the process or product that are specified and measured.
Aliasing
A synonym for confounding, in which one or more effects that cannot unambiguously be attributed to a single factor or interaction.
Alpha Risk
Producer's Risk. The probability of committing a Type I error - generally, the risk of incorrectly concluding that there is a difference.
Alternative Hypothesis
Statement of change or difference, such as a difference between the means of two samples.
Attribute Data
Count data from membership in a category - such as "Good" or "Bad" parts.
Average
A synonym for "mean": the sum of a set of values divided by the number of values.
Balanced Design
An experiment where each level of each factor is repeated the same number of times for the set of runs or combinations of levels that make up the experiment.
Bartlett's Test
Test for equal variances, assuming normal data.
Beta Risk
Consumer's Risk. The probability of committing a Type II error - generally, the risk of incorrectly concluding that there is no difference.
Binomial Distribution
A distribution usually used for determining confidence for proportions. If there are two possible outcomes, such as either "pass" or "fail" for product tests, or either "heads" or "tails" for coin tosses, then the binomial distribution might be used to estimate the probability of 5 passes and 1 fail in 6 product tests or 2 heads and 2 tails in 4 coin tosses.
Black Belt
Experienced, recognized Six Sigma expert and project leader, full-time quality position.
Block
In a designed experiment, blocks can be used to handle uncontrolled factors that are generally considered "noises, having undesired influence as a source of variability. For example, a block can be used to handle humidity as an undesired "noise factor" that can influence the results but cannot be directly controlled by the experimenter.
Box-Behnken
An experimental design used in Response Surface Modeling to obtain polynomial equations with only three levels for each factor.
Business Process Management
The strategic component of Six Sigma methodology.
C- & u-charts
Control charts for defects.
Center Points
Runs in an experimental design at the midpoint of all of the quantitative factor levels.
Central Composite
An experimental design used in Response Surface Modeling design where star points and center points may be added to a factorial experiment, providing three or five levels for each factor.
Central Limit Theorem
A mathematically provable principle about obtaining means of samples that has two major ramifications:
- The standard deviation of averages of samples from the population will be approximately equal to the standard deviation of the population divided by the square root of the sample size.
- Regardless of the shape of the original distribution (even for very non-normal distributions such as exponential distributions), the distributions of averages of samples from the population approach the shape of a normal distribution.
Champion
Executive sponsor of quality initiative projects.
Chi-Square Distribution
A special case of a Gamma Distribution with one parameter that is used for determining confidence for standard deviations and in the Chi-Square test.
Chi-Square Test
A statistical test used to compare the difference between relative frequency of observed events to the frequency expected based on the assumption that is to be tested.
Coefficient of Determination
R^2, the square of the correlation coefficient, which estimates the percent of the total variation in the response can be attributed to the variation of the input variables given a regression equation or model. It also is used to evaluate the adequacy of a regression model.
Common Cause
Variation inherent to the design of the process.
Confidence Interval
A range describing where the true population parameter lies with a certain degree of confidence. For example, a 95% confidence interval for the mean estimates that the true mean lies within the confidence interval with 95% confidence (with 5% alpha risk).
Confounding
One or more effects that cannot unambiguously be attributed to a single factor or interaction.
Continuous Data
Data from a measurement scale that can be divided into finer and finer increments. Examples of continuous data include time, temperature, and weight.
Contour Plot
A two-dimensional graph of three measurement variables: two inputs (x1 and x2) and one response (y), where contour lines connect points on the x1 and x2 plane that have the same value for y.
Control Limits
Natural process limits, determined from historical data of how the process will run if undisturbed. The control limits are at the historical mean or target +/- 3 x the historical standard deviation.
Control Plan
The summary of all the control actions for a process.
Correlation Coefficient
A statistic used for quantifying the strength of a linear association between variable inputs and outputs. It ranges from +1 (perfect positive correlation: higher input goes with higher output) to -1 (perfect negative correlation: higher input goes with lower output).
Cpk
The distance between the mean and the nearest specification limit divided by (3 x standard deviation).
Critical Difference
The practical change that the experimenter wants to have a high probability of detecting.
Critical Mass
The number of people who become committed to Six Sigma that will then influence the organization to share the commitment.
Curvature
When the output of the process does not seem to vary linearly with the input factor; with experimental designs, the output at the center point does not lie along a line between the output values at a low and at a high level of the input.
Cyclical Variation
Piece to piece variation. Often used to describe a repeating pattern, such as a seasonal variation in sales that peaks before Christmas.
Decision Rules
The set of procedures for detecting and handling out of control conditions.
Defect
An output of a process that does not meet specification.
Defectives
Products that have at least one defect.
Definition of a 6s Process
Six standard deviations fit between the mean and the nearest specification limit.
Design Resolution
The worst case confounding scheme associated with a fractional factorial experimental design, conventionally described with Roman numerals. For example, a Design Resolution of IV indicates that main effects are confounded or mathematically indistinguishable from three-way interactions, and two-way interactions are confounded or mathematically indistinguishable from other two-way interactions.
DFSS
Design For Six Sigma. (Also known as DMADV).
DMADV
Define, Measure, Analyze, Design, Verify. (Also known as DFSS).
DMAIC
Define, Measure, Analyze, Improve, Control - Six Sigma process improvement method.
DOE
Design of Experiments, an efficient experimental strategy that allows the investigation of multiple factors at multiple levels.
DOE for Sigma
A designed experiment whose area of interest is reduction of variation.
DPMO
Defects Per Million Opportunities, or 1 million times the Defects Per Unit divided by the opportunities for error per unit.
DPPM
Defective Parts Per Million, or 1 million times the Defective units/total units.
DPU
Total defects observed/total units produced.
Draftsman Plot
Plot for showing the two-variable relationships between a number of variables all at once by showing the projection of the response on three orthogonal surfaces of a cube
Drift
A gradual change in a process characteristic over time.
Effect
The change in the average value of the output caused by a change in an input.
Entitlement
The best potential performance of a process, based on the current design.
Error
Any deviation from the intended process or from the value expected according to a model.
EVOP
Evolutionary Operation, a method developed by George Box to determine the direction for improving a process while production is underway using simple 2^1, 2^2 or 2^3 experiments.
Experimental Error
The variation in data left over after all significant sources of variability have been accounted for. In DOE (design of experiments), experimental error is often a synonym for residuals, the differences between observed values and values expected based on the regression equation obtained from the analysis of the experiment.
Factor
An input variable being studied in an experiment or ANOVA.
Failure Effect
The way a failure impacts the customer.
Failure Mode
The manner in which the process could potentially fail to meet the process or customer requirements.
Fits
The expected values from a model; the predicted values of the output at a specific set of input conditions.
F-Ratio
A statistic for evaluating whether two variances or standard deviations are significantly different, obtained by dividing one variance by another variance.
Full Model
The best-fit predictive equation using all of the factors and interactions in an experiment.
Full-Factorial Experiment
An experiment that examines the effect of all possible combinations of factors and levels.
Goalpost Mentality
Anything outside the specification limits represents quality losses.
Green Belt
Six Sigma trained key contributor and team leader, a part-time quality position.
Hidden Factory
The differences between the documented process and the actual process.
Information Board
Communication tool for tracking EVOP improvements.
Instrument Correlation
A measure of the linear association between two measurement systems.
Interaction
The combined effect of two factors observed over and above the singular effect of each factor against the level the other factor. A significant interaction indicates that the effect of each factor on the response changes depending on the value of the other factor.
Interaction Plots
A graphical display of the interaction in which the means of the responses at each level of a factor are shown for each level of a second factor.
Lean Manufacturing
A manufacturing improvement approach based on the premise that work is accompanied waste or non-value-added effort that should be minimized or eliminated.
Level
The value of an input in an experimental run.
Levene's Test
Test for equal variances that can be used for data that is represented by a non-normal distribution.
Main Effect
The average change of the output observed during a change from one level of an input to another level.
Main Effects Plot
A plot of means at the various levels of each factor compared to the overall mean.
Master Black Belt
Highly experienced, recognized expert; consultant to the Six Sigma project team.
Mean
The arithmetic average of a set of values: the sum of a set of values divided by the number of values.
Median
The middle value found after a set of values has been rank ordered. If there are an even number of values, then it is the average of the middle two numbers.
Mistake-Proofing
Fool-proofing, error-proofing, Poka Yoke: a control method that makes it unlikely or impossible for an error to occur.
Mode
The most frequently occurring value in a data set.
Muda
Waste.
Multiple Regression
A method for determining an optimal equation (least-squared difference between observed and predicted values for the response) for a response as a function of several inputs, y= b0 + b1 X1 + b2 X2 + b3 X3 + error.
Multi-Vari Analysis
A graphical tool, which, through logical subgrouping, analyzes the effects of categorical X's on continuous Y's. The graphical results of Multi-Vari Analysis can be quantified using Nested Analysis of Variance.
Noise Variable
A nuisance or uncontrolled factor that adds variation to a process or product.
Non-Value-Added
An operation that does not transform the product in a way that is meaningful to the customer and is not needed for operational success.
Null Hypothesis
Statement of no change or difference. The default is to assume the Null Hypothesis to be true unless refuted by sufficient evidence. If the Null Hypothesis is refuted, the Alternate Hypothesis is accepted instead, with a certain level of confidence.
Number of Distinct Categories
Ratio of the standard deviation of the parts to standard deviation of the measurement system.
OFAT
An experiment strategy that changes one factor at a time to evaluate its effects on an output. An OFAT experimental strategy can be inefficient in terms of requiring more runs than a DOE approach, and can miss interactions and the optimal settings.
One Way ANOVA
An analysis technique for determining whether any mean is significantly different from other means, and for evaluating single factor experiments.
P- & NP-Charts
Control charts for defectives.
Passive Opportunities
Parts + Connections.
PLEX
A process improvement tool for on-line use in full production.
Poisson Distribution
Probability function that is used for charts for defects.
Poka-Yoke
Fool-proofing, error-proofing, A control method that makes it very unlikely or impossible for an error to occur.
Polynomial Model
A mathematical model or equation in which the response is a described as a function of input factors and input factors raised to integer exponents, such as input factors squared: Y= b0 + b1 X1 + b2 X1^2 + error.
Population Parameter
Fixed, but unknown characteristics describing the distribution for all values of an entire group.
Population Variance
The average of the squared deviation of each individual data points from the population mean for all values of an entire group.
Positional Variation
Within piece variation.
Power
The probability of detecting a real difference, or 100% minus the Beta risk, the risk of incorrectly concluding that there is no difference.
Ppk
The distance between the mean and the nearest specification limit divided by (3 x long term standard deviation ).
Precision
The total variation due to the measurement system.
Pre-control
A technique of controlling processes that do not run at steady state.
Primary Metric
A gauge used to measure project progress (dpu, RTY, etc.).
Process
Consists of input, value-add, and output.
Process Flow Diagram
A detailed map of every step in the process, including hidden factory steps.
Process Improvement
Successful projects will improve quality, delight the customer, enhance employee development, increase process effectiveness & efficiency, and result in greater corporate profit, and a higher return on investment (ROI).
Project Team
Performs the process improvement tasks.
Process Improvement Methodology
The tactics of Six Sigma methodology.
Pure Error
The variation in the data that is estimated by repeat runs.
Randomized Block Design
An experiment containing two sets of categorical inputs, one set of which consists of noise variable(s).
Range
The numerical distance between the highest and lowest values in a data set.
Red Tagging
A technique used for sorting the necessary from the unnecessary.
Reduced Model
The best-fit predictive equation using only the statistically significant factors and interactions.
Region of Curvature
The region where one or more significant inputs no longer conforms to a linear model.
Regression Equation
A prediction equation which allows values of inputs to be used to predict the value of outputs.
Repeatability
The inherent variability of the measurement device. The variability of measurements under similar conditions such as the same operator and same measurement device.
Repeats
Experimental runs using the same combination of treatments, run consecutively without new setups.
Replicates
The number of times the entire experiment is repeated. Combinations are not run consecutively.
Reproducibility
The variability of a measurement device when measurements are made under different conditions such as with different operators or different measurement devices.
Residuals
The difference between the expected value from a model and the experimental data value.
Response Surface
The surface of the expected value of an output or response modeled as a function of significant inputs.
Risk Priority Number
An index used in FMEA (Failure Modes and Effects Analysis) to prioritize possible failure conditions, calculated as the product of Severity x Occurrence x Detection Difficulty. If Severity, Probability of Occurrence and Detection difficulty are each evaluated on a 1-10 scale, then the Risk Priority Number can range from 1 to 1000.
Sample Size
The amount of data the experimenter needs to answer a statistical question. Varies with alpha risk, beta risk & the associated difference to be detected.
Sample Statistic
A value derived from a sample from a population that is used to estimate the value of a population parameter or group characteristic.
Screening Experiments
Lower resolution designed experiments (DOE) for investigating main effects, usually involving several factors. Screening experiments often use Fractional Factorial designs.
Secondary Metric
Used to measure unintended consequences of process/product changes.
Shewhart
The inventor of control charts.
Shift
A sudden change in a process characteristic.
Six Sigma
Motorola Corporation originated Six Sigma during the 1980s as a quality management methodology, strategy, and tactics to enhance customer satisfaction, employee development, and continuously improve processes to increase corporate profits, shareholder value, and achieve corporate excellence.
Simple Regression
A method for determining an optimal equation (least-squared difference between observed and predicted values for the response) for a response as a function of just one input variable: Y= b0 + b1 X + error.
Special Cause Variation
Intermittent variation attributed to assignable events. Control charts are often used to distinguish between special cause variation and common cause variation.
Specification Limits
Requirements based on the customer requirements or expectations.
Stability of a Measurement System
A measure of the variation in accuracy or precision of a measurement system over time.
Standard Deviation
The square root of the variance.
Star and Axial Points
Levels of inputs in a Central Composite Design experiment used to determine the second order terms in Response Surface Modeling.
Steepest Ascent or Descent
A procedure for moving along the direction or combination of input factor values that most rapidly increases or decreases the value of the response.
Surface Plot
A plot for a Response or z-variable based on a mesh determined from two input factors, an x-variable and a y-variable.
Taguchi Quality Philosophy
The idea that any deviation from the target imparts a loss to society.
t-Distribution
Used for determining the confidence interval for means or for determining whether two means are significantly different. Developed by Gossett under the pseudonym "Student; hence, also referred to as Student's t-distribution.
Temporal Variation
Time-to-time variation.
Transition Action Plan
The actions required to move the project from the Black Belt's control to the functional organization's control.
Treatment
A single level assigned to a single factor.
Treatment Combination
An experiment run using a set of the specific levels of each input variable.
Type I Error
Finding an imagined difference where none actually exists.
Type II Error
Failing to find a difference when one actually exists.
Value-Added
An operation that transforms the product in a way that is meaningful to the customer.
VOB
Voice of the Business.
VOC
Voice of the Customer.
VOP
Voice of the Process.
Z-score
The distance of a particular value from the sample mean in units of standard deviations.
