• 1. Glossary
    • 2. 4-Block …………………………… a error …………………………… a risk ……………………………… Accuracy ………………………… Active (opportunity or defect) … Advocacy Team ………………… Alternate Hypothesis ………… ANOVA …………………………… ANOVA method (Gauge R&R) … Assignable cause variation …… Attribute Chart ………………… Attribute data …………………… Average ………………………Graphical tool to show the relationship between process capability, control & technology. The error made if difference is claimed, when the reality is sameness (e.g. rejecting good parts; Producer’s Risk). The risk (probability) of making an a error (frequently set at 5%). How close measurements are, on average, to their target. An opportunity or defect that is being measured (a defect we are looking for). The group of people who have a stake in the Six Sigma project, including those who must keep it in control. See Ha Analysis of Variance. A statistical method of quantifying contributions of discrete levels of “X”s to the variation in a “Y” response. A Minitab selection for Gauge R&R that includes operator-part interaction in the calculation of variation contributions. The most accurate method for Gauge R&R. Removable variation in a process; variation due to outside influences. See ‘Black Noise’. Statistical Process Control (SPC) chart for discrete data. Includes p, np, c and u charts. Data that can be described by levels, integer values or categories only. See Discrete data. The sum of all data in a sample divided by the number of data points in the sample. See Mean.
    • 3. b error …………………………… b risk …………………………… Baselining ……………………… Benchmarking…………………… Black Belt ……………………… Black Noise ……………………… Boxplot ………………………… Brainstorming …………………… Centring ………………………… Centring of X variables ………… Central Limit Theorem ………… The error made if sameness is claimed, when the reality is difference (e.g. accepting bad parts - Consumer’s Risk). The risk (probability) of making a beta error (frequently set at 10%). Evaluating the capability of a process as it stands today, without “tweaking” - i.e. passive observation. Evaluating the capability of similar processes to quantify what constitutes ‘the Best’. A person whose full time job consists of application of Six Sigma tools/methods on projects. Process variation due to ‘outside influences’. See Assignable Cause Variation. Graph showing the portion of a distribution between the first and third percentiles within a ‘box’. The boxplot also shows the median of the distribution and the extreme values. Often used to compare population. A technique used by an Advocacy Team to, for e.g., develop a list of potential X’s at the beginning of project. A process characteristic describing how well the mean of the sample corresponds to the target value. A method used to transform X variables in DoE’s that develop higher order (quadratic) models; reduces correlation between X’s. A fundamental statistical theorem stating that the distribution of averages of a characteristic tends to be normal, even when the parent population is highly non-normal.
    • 4. Central Composite Design …… Champion ………………………… Champion Review ……………… Chi-Squared test ………………… Classical Yield …………………… Common Cause Variation ……… Components Search …………… Confidence ……………………… Confidence Interval ……………… Consumer ………………………… Continuous Data …………………A Design of Experiments (DoE) method where each X is tested at 5 levels (see ‘Star Points’). A CCD provides the capability to model a process with a quadratic equation OR a linear equation. Typically a director - someone who can support the Six Sigma project and has the authority to remove barriers and provide resources. Takes an active part in Project Review. A regular meeting to present Six Sigma projects, share experiences and remove roadblocks. Hypothesis test for discrete data. Evaluates the probability that counts in different cells are dependent on one another, or tests Goodness of Fit to some a priori probability distribution. See “First Pass Yield”. Good units produced divided by Total Units Produced. See “White Noise”. The inherent variation of a process, free from external influences. Usually measured over a short time period. A method of screening for Vital Few X’s in manufactured assemblies. Also known as ‘Part Swapping’. The complement of alpha risk. Confidence = 1-a. A range of plausible values for a population parameter, such as mean or standard deviation. The end user of a product (the homeowner, for e.g.). The consumer is external to the business. Data that can be meaningfully broken down into smaller and smaller increments - e.g. length, temperature etc.)
    • 5. Contour Plot ………………… Control Limits ……………… Cost of Quality ……………… Cp …………………………… Cpk …………………………… CQ …………………………… CTQ ………………………… Cube Plot …………………… Customer …………………… Data Window ………………… Defect ………………………… Dependent Variable …………A graph used to analyze experiments of a Central Composite Design. Two X’s comprise the axes, and levels of constant Y are shown in the body of graph. Resembles a topographical map. Lines on a Statistical Process Control (SPC) chart that represent decision criteria for taking action on the process. Lines are drawn +/- 3 standard deviations (s) from the mean. A financial reconciliation of all the costs associated with defects (scrap, rework, concessions etc.) Statistic used to measure Process Capability. Assumes data is centred on target. Similar in concept to Z.st Statistic used to measure Process Performance. Does not assume centred data. Similar in concept to Z.lt Commercial Quality. Used to categorize non-manufacturing projects that impact the consumer and/or customer. Critical-to-Quality characteristic. An aspect of the product or service that is important to the customer/consumer. A graph used for analysis of the results of a factorial designed experiment (DoE). Shows test conditions that optimize the response. The recipient of the output of a process. May be internal (e.g. Assembly is a customer of finishing shops), or external (e.g. Currys, Belling etc.) who then sell our products to consumers. The spreadsheet window in Minitab where data is entered for analysis. Any aspect of a part or process that does not conform to requirements. The output of a process. The “Y” response.
    • 6. Descriptive Statistics ……… Design of Experiments (DoE) Discrete Data ……………… Dotplot ……………………… DPMO ………………………… DPO ………………………… DPU ………………………… e (Exponential Function) …… Entitlement ………………… Executive Summary ……… F-test …………………………Mean, Standard Deviation, Variance and other values calculated from sample characteristics. Also includes assorted graphs. A statistical field of study where independent variables (X’s) are systematically manipulated and the response observed. Used to demonstrate which X’s are the Vital Few, and to optimize the response. Data that can only be described by levels, i.e. pass/fail, operator a/b/c, integer values (e.g. number of defects). Data that cannot be broken down into finer increments. Frequency diagram representing data by ‘dots’ along a horizontal axis. Generally used as an alternative to a histogram for small sample sizes. Defects Per Million Opportunities - 1,000,000 multiplied by total number of defects, divided by the total number of opportunities. A metric for defects equivalent to ppm used for defectives. Defects Per Opportunity - total number of defects divided by total number of opportunities. Used to enter the Normal Table to obtain Z values. Defects per unit - total number of defects divided by total number of units. Used primarily to calculate Rolled Throughput Yield (Y.rt) through the Poisson formula Y.rt = e-DPU. A mathematic constant roughly equal to 2.718 Mathematical identity: ln(e)=1 Z.st The best the process can be. What the process would look like if all Assignable Cause Variation was controlled. The first page of output from the Minitab Process Capability selection. A test to compare variances of 2 or more samples, and to compare the equality of two or more means (in ANOVA).
    • 7. Factorial Experiment ……… Fractional Factorial Experiment. First Pass Yield ……………… FMEA …………………………… Functional Owner …………… GaugeXBR method ………… Gantt Chart …………………… Gauge R&R …………………… Green Belt ……………………… Ha ……………………………… Ho ………………………………A designed experiment (DoE) which involves testing of all possible combinations of independent (X) variables. A designed experiment (DoE) which involves testing a fraction of all possible combinations of independent (X) variables in a full Factorial experiment. Results in fewer test runs. See ‘Classical Yield’. Equal to the number of good units produced divided by the total number of units produced. Failure Mode and Effects Analysis - a team-based procedure that identifies and documents all possible failure modes, effects, causes and associated corrective actions. The person with financial responsibility for the process under consideration. Gauge R&R method- an option in Minitab. A project management tool that graphs milestones vs. the calendar. Bars are used to indicate both planned and actual duration of tasks. A means of determining the acceptability of the variability in the gauging system for use in the process. A person who uses Six Sigma tools and methodology in the course of their work, and who always has a Six Sigma project active in their place of work. Alternate Hypothesis (hypothesis of difference). The hypothesis being proven in a statistical hypothesis test. Null hypothesis (hypothesis of sameness). The starting assumption in a statistical hypothesis test. NB. The null hypothesis cannot be proved!
    • 8. Histogram …………………… Homogeneity of Variance …… Hypothesis test ……………… I/MR Chart ……………………… Independent Variable ………… Inferential statistics …………… Inherent Process Capability … Interaction plot ………………A frequency diagram composed of rectangular bars whose relative heights indicate the number of counts (or relative frequency) at a particular level. A menu selection in Minitab under which the F-test (comparison of variances) is performed Any of several statistical tests of 2 or more samples from populations. Used to determine if the observed differences can be attributable to chance alone. The result of the test is to either accept or reject the alternate hypothesis (Ha). (t-test, F-test and Chi-Squared test are examples.) Individual/Moving Range chart - a Statistical Process Control (SPC) chart in which the upper graph is used to plot individual data points compared to calculated control limits; the lower graph (Moving Range) plots the difference between sequential data as points on the chart. Control limits are also calculated for this chart. Variables (X’s) that influence the response of a dependent variable (Y) Statistical analyses that quantify the risk of statements about populations, based on sample data. Inferential statistics are usually hypothesis tests or confidence intervals. The Best the process can be, with only variation due to white noise present. See Entitlement, Z.st A graph used to analyse factorial and fractional factorial designs of experiments. Indicates the effect on Y when two X’s are changed simultaneously. The greater the difference in slopes between the X’s, the greater the interaction.
    • 9. Kurtosis ………………………… L1 Spreadsheet ……………… L2 Spreadsheet …………… LCL (Lower Control Limit) … Leverage Variable …………… Linearity (gauge)……………… Long term data ………………… LSL ……………………………… m ………………………………… Macro …………………………… Main Effects Plot ……………… Master Black Belt ……………Comparison of the height of the peak of a distribution to the spread of the ‘tails’. The kurtosis value is 3 for a perfect normal distribution. Excel spreadsheet for discrete data that calculates subsystem Z values and ‘rolls’ them into a system-level Z value. Replaced by Product Report in Minitab release 11.2 Excel spreadsheet for continuous data that calculates Z.st and Z.lt Replaced by Process Reports in Minitab release 11.2 The lower control boundary on a Statistical Process Control (SPC) chart. A limit calculated as the mean minus 3 standard deviations. Note: SEM (Standard Error of the Mean) is used for s; stdev = s/sqrt(n). An X variable with a strong influence on the Y response. One of the Vital Few. The difference in the accuracy of the gauge from the low end to the high end of the test range. Data obtained in such a way that it contains assignable cause variation (‘black noise’). Lower Specification Limit The mean or average of a population A mini program within a software package designed to provide a particular output (e.g. Gauge R&R) A graph used to analyze factorial and fractional factorial designs of experiments. Compares the effect on Y of an X at the ‘high’ level vs. its effect at the ‘low’ level. Slope of the line on the graph indicates significance. A coach, mentor and trainer of the Six Sigma methodologies and tools.
    • 10. Mean …………………………… Measurements Systems Analysis ……………………… Median ………………………… Minitab ………………………… Normal Curve ………………… Normal Probability Plot ……… Normalize ……………………… Normalized Average Yield…… Null Hypothesis ……………… Orthogonal …………………… p-value ………………………… Pareto Analysis ………………The average. May be the average of a sample (x-bar), or the average of a population (m). See ‘Gauge R&R’. The middle value of a set of data (the 50th percentile). A statistical software package containing the majority of Six Sigma tools. A widely-used, commonly-seen distribution where data is symmetrically distributed around the mean (‘bell curve’). A graphical hypothesis test in which sample data is compared to a ‘perfect normal’ distribution. Ho: the sample data is the same as the ‘perfect normal’ distribution. Ha: the sample data is different (i.e. non-normal). The process of converting non-normal data through the use of a transformation function. The average yield of a process with multiple steps or operations. Y.na = (Y.rt)1/n See ‘Ho’. Literally, “right angles”. A feature of a well-defined experiment that allows main effects to be separated from 2-way and higher order interactions, as well as quadratic (squared) terms. The probability of making an alpha (a) error. A value used extensively in hypothesis testing. Also referred to as the ‘observed level of significance’. p-values are compared to the ‘acceptable’ level of alpha risk in order to make decisions in hypothesis tests. A problem solving tool that allows characteristics to be ranked in descending order of importance.
    • 11. Pareto Principle ……………… Passive (opportunity/defect) … Point of Inflexion ……………… Poisson Approximation ……… Population …………………… Power of the Test …………… ppm …………………………… Practical Problem …………… Practical Solution …………… Precision ……………………… Pre-Control …………………… Principle of Reverse Loading .. Probability of a defect p(d) …The “80-20” rule. The principle that 20% of the variables cause 80% of the variation. A defect or opportunity that is counted upon occurrence, but that is not part of the active monitoring process. Point on the normal curve where it changes from convex to concave. Mathematically defined by setting the third derivative to zero. A mathematical approximation for Rolled Throughput Yield, given DPU: Y.rt = e-DPU. All data of interest for a particular process, recorded or not. Usually modelled with samples. The likelihood of detecting beneficial change. Represented as 1-b. The probability of rejecting the null hypothesis. Parts per million defective. A discrete measurement of defectives for long term data The output of the Measure phase. A characterization of the Z value, centring and spread for Y. The output of the Control Phase. The optimised X levels and control plan to maintain the process at its highest Z value. How closely the data is clustered around their mean. Describes the spread of the data. A Statistical Process Control (SPC) method that allows an operator to take action on a process based on where the part measurements fall in a normal distribution. Parts are coded red, yellow or green. Planning ahead – Need to define what do you want to know, so what tool/test should be used, so what data do you need? The ‘tail’ area of the normal curve, beyond the specification limit(s).
    • 12. Problem Statement …………… Process Capability …………… Process Characterization …… Process Map ………………… Process Optimisation ………… Project Hopper ……………… QFD …………………………… Quartiles ……………………… R-bar/d ……………………… Random Cause Variation …… Range ………………………… Rational Subgrouping ………A brief but succinct description of the issue under investigation. Includes the practical and business reasons for the project. A statistic that numerically describes how well the process could perform in the absence of ‘black noise’. Examples: Z.st, Cp Understanding the Y’s and X’s in a process. Developed through the tools of the Define, Measure and Analyse phases. A problem solving tool that graphically describes each step or phase in a process. Defining the best operating point for X’s in a process. Developed through tools of the Improve/Control phases. A stack of potential Six Sigma projects, to be picked up by Black Belts or Green Belts when resources allow. Quality Function Deployment. A rigorous method of determining technical requirements and CTQ’s from the definition of Consumer Cues. ‘Quarters’ of a population. 1/4 of the data fall below the first quartile, 1/4 of the data fall above the 3rd quartile. An estimate of standard deviation using the range of the data and tabled adjustment factors. Used in calculation of control limits in Minitab Gauge R&R Xbar graphical output. See ‘White Noise’. The inherent variation of the process, free from external influences. The largest value in a data set minus the smallest value in the data set. A data collection technique that allows the separation of short term variation from long term variation.
    • 13. Regression …………………… Repeatability (Gauge) ……… Repetition ……………………… Reproducibility (Gauge) ……… Response Surface Experiment Resolution (Gauge) ………… Resolution (Fractional Factorial) ………………… Rolled Throughput Yield …… A statistical modelling tool that allows data to be represented by an equation. Used for continuous Y responses, usually with continuous X inputs. (There is special technique within Minitab called Logistic Regression which handles special forms of discrete X’s.) Ability of a gauge to consistently measure the same part with the same results. Part of the output of a Gauge R&R study. Collecting multiple data points sequentially from a process, without re-setting the process Ability of operators of a gauge to generate consistent measurements. Part of the output of a Gauge R&R study. A designed experiment (DoE) that allows the Y response to be modelled as a function of continuous X variables. See Regression also. The ability of a gauge to discriminate increments of a continuous measurement. Gauge resolution is usually required to be ten times greater than the measurement of interest; i.e., a feature specified with a specification to one decimal place would require a gauge with a resolution of two decimal places etc. A roman numeral that indicates the degree of confounding in a fractional factorial design. Higher resolution indicates less confounding - i.e. less ambiguity in the source of effects. Y.rt The product of yields at each step of a process. Can be estimated using the Poisson Approximation.
    • 14. s ………………………………… Sample ……………………… Session Window …………… Shift …………………………… Short term data …………… Sigma (s) ……………………… Six Sigma Team Member …… Skewness …………………… Specification ………………… Spread ………………………… Stability (Gauge) ……………… Standard Deviation …………The standard deviation of a sample. A measure of spread (or variability) of the data. s=sqrt[S(x-xbar)/(n-1)] A collection (subset) of data intended to represent the characteristics of the parent population. One of the 4 Minitab windows. Used for command entry and data output. The difference between short-term and long-term process variation. Z.shift = Z.st - Z.lt Data obtained in such a way that it contains NO assignable cause variation (‘black noise’). Only the inherent process variation is represented, which allows calculation of Z.st The standard deviation of a population. A stakeholder in the Six Sigma process. A person who needs to have an understanding of the methodology, but does not formally use the tools. Evaluation of the symmetry of a distribution. Skewness=0 for perfect symmetry; skewness is negative if the distribution is shifted to the right, positive if shifted to the left. The requirements of a design, usually expressed as a target (or nominal) value with an associated allowable tolerance for variation (e.g. 5.00cm +/- 0.05 cm) How far the data is distributed away from their mean. Consistency of measurement values obtained with the same gauge on the same set of parts, with measurements taken at different times. Gauge instability can lead to calibration issues. A statistical measure of spread or dispersion from a mean value.
    • 15. Standard Error of the Mean … Standard Normal Deviate …… Standard Order ……………… Star Point(s) …………………… Statistical Problem …………… Statistical Process Control … Statistical Solution …………… Statistics ……………………… Stepwise Regression ………… Structure Tree ………………The standard deviation of xbar, based on a sample size of n. (Also a correction factor for standard deviation of relatively small sample sizes (<30).) Reduces the standard deviation of the sample by sqrt(n). SEM = s/sqrt(n). See “Z transform”. A feature of factorial Design of Experiments (DoE) that determines the order of the high/low settings of the X’s for each run of an experiment by using a pre-determined pattern of +1’s and -1’s for each X. Extreme test points in a Central Composite Design of Experiments. Found by taking the fourth root of the number of ‘Cube points’ (factorial points) in the design and adding/subtracting this value from the Centre Point. The outcome of the Analyze phase. Is the problem centring, spread or both? SPC. A graphical method of monitoring a process and determining statistically when the process requires attention by comparing it to a historical mean and calculated control limits at +/- 3 sigma. Output of the Improve phase. Where do the X’s need to be set to control the Y? The study of variation, including methods of describing, quantifying and reducing variation, as well as estimating risks. A regression technique where the model is developed one step at a time, adding X variables one at a time to the model in order of their contribution to changes in Y. A problem solving tool listing the characteristics of interest on one side of the page, and showing contributing factors to the characteristics as branches.
    • 16. Subgroup ……………………… Sustained Process Capability t-test …………………………… Target ………………………… Technical Requirement ……… Test Sensitivity (d/s) ………… Tolerance ……………………… TOP (Total Opportunities) …… Transfer ……………………… Transform …………………… Trivial Many X’s ……………… UCL (Upper Control Limit) …… Unit …………………………… A sample of like parts or related data taken consecutively that contains only inherent process variation (‘white noise’) Capability of a process in the long term Z.lt A statistical test used to compare two means, or to compare a mean to a standard value. The specified or desired average of a process Physical or process characteristic that must be controlled to address a Consumer Cue - also known as “The Gap”. A statistic used to determine sample size for hypothesis testing. Compares the difference in means to the spread of the data. The amount of variation allowable by design in a process. Tolerance = USL-LSL. Number of opportunities per unit times the number of units. The last phase of a Six Sigma project, where knowledge gained is transferred to all other similar processes - ie synergy. Any mathematical relationship used to translate data of one space into data of another space (e.g. transforms to convert non-normal data to normal data; log, reciprocal, power functions etc.) The 80% of the independent variables (X’s) that generate only 20% of the total process variation. Variables that influence the process, but at a much less significant level than the ‘Vital Few’. The upper control boundary on a Statistical Process Control (SPC) chart. A limit calculated as the mean plus 3 standard deviations. NOTE: SEM (Standard Error of the Mean) is used for s: stdev = s/sqrt(n) A user-defined quantity representing the output of a process. May be a part, system
    • 17. Unit …………………………… USL …………………………… Variance ……………………… Vital Few X’s ………………… White Noise …………………… X ……………………………… X-bar ………………………… X-bar/R chart ………………… Y response…………………… Y.ft …………………………… Y.na …………………………… Y.rt ……………………………… Z.bench ………………………A user-defined quantity representing the output of a process. May be a part, system, component of a part or a sub-system. Upper Specification Limit (Standard Deviation)2 The 20% of the independent variables that generate 80% of the total process variation. These are X’s which must be controlled to bring a process to Six Sigma levels of performance. See ‘Common Cause Variation’. The natural variation within the process, free of external influences. The independent variable(s), or input(s), of a process. The mean or average of a sample. The sum of all data in the sample divided by the number of samples. A Statistical Process Control (SPC) chart in which the upper graph is used to plot subgroup averages compared to calculated control limits; the lower graph (Range) plots the difference between the high and low value of the subgroup. Control limits are also used on the Range chart. The dependent variable, or output, of a process. ‘First Time’ or ‘First Pass’ Yield. Classical Yield. Number of good units/total produced. ‘Normalized Average Yield’. (Rolled Throughput Yield)1/n. Average yield at each step of the process. ‘Rolled Throughput Yield’. Yields of all steps of the process multiplied together. The reported process capability. A value derived by combining all defects into one tail of the distribution, then reading the Z value
    • 18. Z.bench ……………………… Z transform …………………… Z.lt ……………………………… Z.st …………………………… The reported process capability. A value derived by combining all defects into one tail of the distribution, then reading the Z value from a Normal table. May be short term or long term (must quote which). A statistic that converts any normal distribution into the ‘standard normal’ distribution (mean=0, standard deviation=1. Z=(X-m)/s Long-term process capability. Indicates process performance, including the shift and drift of the process. Short-term process capability. Indicates “process entitlement”.