## SPC Definitions for Statistical Process Control

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3 Sigma (N)

This approximates the control limits using ± 3 standard deviations with N degrees of freedom. This method should only be used to calculate control limits if you are certain that your process is stable and in control.

3 Sigma (N-1)

This approximates the control limits using ± 3 standard deviations with N-1 degrees of freedom. This method should only be used to calculate control limits if you are certain that your process is stable and in control.

3 User-Defined-Sigma

This approximates the control limits using ± 3 times a standard deviation you provide.

This method might be used in an attempt to reduce the variability of a stable, in-control process. Several types of short run control charts eliminate any need for this technique.

Bar Chart

Bar Charts are a very simple way of illustrating the nature of process data. A bar chart simply illustrates the relative frequencies or magnitude of data that can be broken down into distinct categories.

Beta

The shape parameter in the Weibull distribution.

C

Average count per subgroup

C Chart

C is the average count per subgroup. The C control chart displays the number of defects that appear in samples of fixed size. C charts are based on a Poisson distribution.

A C control chart is used in dealing with the number of defects that appear in fixed unit samples. The data for a C Chart should consist of the counts of the total number of nonconformities (defects) of a given type.

Capability Statistics

Indices that define the degree to which the process is or is not meeting the specifications.

These include Cpl, Cpu, Cpk, and Cp.

CDF – Cumulative Distribution Function

The cumulative distribution function for a random variable X defined for any real x by the probability X<x. An Ogive is the graph of a cumulative distribution function.

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Center/Center Line

A horizontal graphical line designating the mean or median of the process measurements.

Control Chart

A tool for detecting uncontrolled variation. There are based on the laws of probability and statistics and are effective at detecting the presence of uncontrolled variation in any process. Typical software control charts include X (Run), XBAR-R, X Moving Range, XBAR-S, PN, P, C, U, XBAR, R, S and Moving Range.

Correlation

The degree to which one variable is related to another. This statistic can either be negative or positive depending on the slope of the line.

Cp

A process capability index that is a ratio of the specification range (USL-LSL) to the standard deviation of the process.

Cpk

This statistic is the minimum of the Cpl and Cpu statistics. It indicates whether or not the process being analyzed is capable of producing little or no defects. The higher the number, the less likely it will be that defectives are produced.

Cpl

This statistic relates the difference between the center line and the LSL to the standard deviation.

Cpu

This statistic relates the difference between the USL and the center line to the standard deviation.

Cyclic

A cycle is a sequence of points that alternate up and down. A process that is in control (only natural causes of variation) should have values that are randomly above and below the preceding value.

Data Bin

This is a group or class of data points. Each bar on a histogram represents a data bin.

Decreasing Trend

A decreasing trend is a sequence of points for which each is lower/smaller than the previous. A process that is in control (only natural causes of variation) should have values that are randomly above and below the preceding value.

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Distribution Graph

A representation of the data where points are plotted according to the value and frequency of occurrence. Distribution graphs include histograms, frequency polygons and CDFs (Ogives).

F Value

A ratio of the regression mean square to the error mean square. It is used to make inferences as to whether or not a relationship exists between x and y based on the analysis of variance approach.

Frequency Polygon

A line graph connecting the midpoints of each class in a data set plotted at a height corresponding to the frequency of the curve. For an XBAR chart, this will reflect the distribution of the sample averages. The frequency polygon is a graphical display of a frequency distribution (histogram). It consists of a series of straight lines joining small circles that are plotted at cell midpoints with a height proportional to cell frequencies.

Gamma

The location parameter in the Weibull distribution.

Graduated Scale

A y-axis labeling convention where the y-axis is labeled in incremental units.

Histogram

A histogram is a series of rectangles, each proportional in width to the range of values within a class and proportional in height to the number of items falling in the class. A histogram reveals the amount of variation that any process has within it. The histogram is useful because it emphasizes and clarifies trends that are not readily discernible in tables. For an XBAR chart, this will reflect the distribution of the sample averages.

Increasing Trend

An increasing trend is a sequence of points for which each is higher/larger than the previous.

A process that is in control (only natural causes of variation) should have values that are randomly above and below the preceding value.

Individuals Histogram

For an XBAR chart, this will reflect the distribution of the individual data samples.

Individual Moving Range (XMR) Chart

A chart produced by continuously plotting the range between current and previous individual measurements.

Individuals Ogive (CDF)

For an XBAR chart, this will reflect the distribution of the individual data samples.

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Individuals Polygon

For an XBAR chart, this will reflect the distribution of the individual data samples.

LCL – Lower Control Limit

A statistically determined value that appears as a horizontal dashed line below the process average. Generally considered to be three times the standard deviation of the process measurements.

LSL – Lower Specifications Limit

A user-defined quantity that identifies the lowest acceptable value of a product attribute.

Limits

Boundaries that indicate the acceptable ranges for a product attribute. These limits are either provided by the user or calculated based on the process measurements.

Max – Maximum

The greatest quantity or value measured.

Mean (Average)

The arithmetic average of a set of numbers. Use the average of the data points to calculate the center line. This is the most common method used to determine the process center line.

Median

The dividing point where exactly half of the data values are above and half are below.

Use the median of the data points to calculate the center line. This method is often used to minimize the effect of outliers and unusual data values on the process center calculation.

The median is the value for which an equal number of data values fall above and below.

Min – Minimum

The least quantity or value measured.

Mixture

A mixture is a sequence of points that are more than 1 sigma above or below the center line. A normally distributed process that is in control (only natural causes of variation) should have about 68% of its values within ± 1 sigma (standard deviation) of its average (mean).

Moving Range (MR) Chart

A chart produced by continuously plotting the range between the current and previous sample means.

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MR – Moving Range

Moving Range Chart

MR is a range chart made of the range of the last two individual measurements.

Mu

A parameter that refers to the mean of a distribution.

Nominal

The user-defined target value of a process.

Ogive

An ogive is the graph of a cumulative distribution function (CDF). For an XBAR chart, this will reflect the distribution of the sample averages. An ogive is the graphical representation of a cumulative frequency distribution. A cumulative frequency distribution enables the user to see how many observations lie above or below certain values rather than merely recording the numbers of items within intervals.

Outlier

A data point that lies outside the relevant range. This can be an indication of a severe disturbance in the process or a data entry problem. Marking an item as an outlier can serve as a flag to the user that something is potentially wrong.

P

Fraction Defective

PN

Percent Defective

Pareto Diagram

A Pareto chart is a special form of a vertical bar chart that helps to focus efforts on the problems offering the greatest potential for improvement. The basic structure for a Pareto is the same as a histogram. The ability of the Pareto chart to focus attention on the problem that is associated with the greatest cost or the greatest incidence is most effective when the ordering of the problems is not changing over time.

Patterns

Traits or other observable features characterizing a data set. These include runs, outliers, outlier patterns, stratification, trends, shifts and cycles.

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P Chart

P is the fraction of defectives in each group. The P Chart is based on a running record of the proportion of defective product in a subgroup. It shows the characteristics of both the mean (average) and dispersion (spread) of the process. The P Chart is based on a running record that is made up of the subgroup proportions of nonconforming product. A P chart shows the fraction defective (p). It is used when the number of items varies and the statistic of interest is the fraction (or percent) rejected. A P chart shows the characteristics of both the mean (average) and dispersion (spread) of the process. It is used with discrete data sets and may be applied to the results of any inspection that accepts or rejects individual items. The P Chart is an extremely useful aid in giving information as to when and where to exert pressure for quality improvement. It is based on a binomial distribution.

Pie Chart

Pie charts are simply graphs in which the entire circle represents 100% of the data to be displayed. The circle (pie) is divided into percentage slices that clearly show the largest shares of data. The pie chart is generally easy to understand and is widely used to display data in the media.

PN Chart

PN Charts show the number of defectives in identical groups. They are used whenever the data is binomially distributed and the sample size is constant. PN Charts show the characteristics of both the mean (average) and dispersion (spread) of the process. PN charts show the number of defectives (pn). It is used whenever the count data appear to be binomially distributed and the size of the subgroup (sample size) is constant. PN charts show the characteristics of both mean and dispersion of the process. They are used with discrete data sets.

Pop Sigma (n-1)

The standard deviation of all the individual measurements.

Population

A collection of all the items under study.

Process Specifications

Values used to identify the acceptable ranges for product attributes. These include LSL, USL and nominal.

R

Range

r2 – Sample coefficient of determination

It can be interpreted as the proportionate reduction of the total variation associated with the independent variable.

Range

The difference between the largest and smallest of a data set.

R Chart

R is the range of the data in each sample. The R Chart shows changes in the dispersion (spread) of the process. R is the range of the data in each sample or lot. The R Chart is for measurable characteristics and shows any changes in the dispersion of the process.

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Regression Statistics

The statistics that are associated with regression analysis. Regression analysis is the general process of predicting one variable from another.

The regression statistics include the regression line, the coefficient of determination (r2), F-value and t-value.

Regression Formula

Often referred to as the regression line or fitted line. The formula describing the “best” line that minimizes the distance between that line and the process data points.

Rel Var – Relative Variation

A ratio of the sample’s unbiased standard deviation to its mean. Often used as a comparison between processes which have the same mean.

Run

A run is a sequence of points that all fall on the same side of the center line. A process that is in control (only natural causes of variation) should have values randomly above and below the centerline.

Run Chart

Run Charts are employed to visually represent data. They are used to monitor a process to see whether or not the long range average is changing. Run charts are the simplest tool to construct and use. Points are plotted on the graph in the order in which they become available.

S – Standard Deviation

Sample

A representative collection of some but not all of the items of the population. Samples are used in describing the population.

S Chart

S is the sample standard deviation. The S Chart shows changes in the dispersion (spread) of the measurements. S is the standard deviation of the data in each sample or lot. The S Chart is for measurable characteristics and shows any changes in the dispersion of the process. Sample sizes of ten or more are recommended for an S Chart.

Scatter Diagram

A Scatter Diagram is used to study the possible relationship between one variable and another. It is a graph of the observed data and is used to test for possible cause and effect relationships.It cannot prove that one variable causes the other but it does make it clear whether a relationship exists and the strength of that relationship. A Scatter Diagram is set up whereby the horizontal axis (x-axis) represents the measurement values of one variable and the vertical axis (y-axis) represents the measurement values of a second variable.

Shift Up

A shift-up is a sequence of points for which the first half is below the center line and the second half is above the center line. A process that is in control (only natural causes of variation) should have values that are randomly above and below the center line.

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Shift Down

A shift-down is a sequence of points for which the first half is above the center line and the second half is below the center line. A process that is in control (only natural causes of variation) should have values that are randomly above and below the center line.

Sigma (n)

The biased standard deviation estimator. Bias implies n degrees of freedom. Generally, sigma (n) is used unless the sample size is small in relation to the population as a whole.

Sigma (n-1)

The unbiased standard deviation estimator. The estimator has n-1 degrees of freedom.

Sigma (n-1) is used when the sample size is small in relation to the population as a whole.

Skewness

This statistic measures the asymmetry of a process. This occurs when values in the frequency distribution are concentrated at either the low end or high end of the measurement scale on the horizontal axis.

SPC – SPC definitions for “Statistical Process Control”

The use of statistical techniques to analyze a process or its output so as to take appropriate actions to achieve and maintain a state of statistical control and to improve the capability of the process.

Stats – Statistics

Statistics

A branch of mathematics dealing with the collection, analysis, interpretation and presentation of masses of numerical data.

Stratification

Stratification is a sequence of points that are all within ± 1 sigma of the center line.

A normally distributed process that is in control (only natural causes of variation) should have about 32% of its values more than 1 sigma (standard deviation) above or below its average (mean).

Summary Statistics

The basic statistics associated with the process. These include the mean, median, max, min, sigma, etc.

T – Time

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t Value

A ratio of the slope of the fitted regression line to its standard deviation. Generally used as a test statistic to determine whether or not the true slope of the process equals some specified non-zero value.

Table

A table is a systematic arrangement of data usually in rows and columns for ready reference.

U

Average rate of defects per unit

U Chart

U is the average rate of defects per unit. The U Chart displays a rate of defects when sample size is not constant. The chart may or may not be based on a Poisson distribution.U is the average rate of nonconformities (defects) per unit. A U chart is used when the number of defectives in the material being inspected is not constant in area and length such as the unevenness of woven materials or pin holes in enamel wire. The sample size can vary and the data set is discrete. The chart may or may not be based on a Poisson distribution.

UCL – Upper Control Limit

A statistically determined measurement that appears as a horizontal dashed line above the process average. Generally considered to be three times the standard deviation of the process measurements.

Upper Specifications Limit (USL)

A user-defined quantity that identifies the highest acceptable value of a product attribute.

USL – Upper Specification Limit

XBAR

XBAR is the mean (average) of X

XBAR Chart

XBAR is the sample mean. The XBAR Chart shows changes in the mean value of the process. XBAR is the sample mean (or average). An XBAR Chart is for measurable characteristics and shows any changes in the mean value of the process.

XBAR-R Chart

The XBAR-R control chart shows both the mean value (XBAR) and the range (R) of a sample. This is the most common type of control chart using indiscrete or continuous values.The XBAR portion of the chart shows any changes in the mean value of the process while the R portion shows any changes in the dispersion of the process. This chart is particularly useful because it shows changes in mean value and dispersion of the process at the same time, making it a very effective method for checking abnormalities in the process.

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XBAR-S Chart

The XBAR-S control chart shows both the mean value (XBAR) Chart and the standard deviation (S) Chart. They should be used when the logical group size is larger than ten.The XBAR-S chart is identical to the XBAR-R chart except that the R (range) is replaced by an S (standard deviation). XBAR-S charts should be used when the logical group size is larger than 10 (ten).

X Moving Range Chart

Sometimes collecting enough data to produce a XBAR-R chart is impossible or at least impractical. Sometimes the natural subgroup size should be one (1) like when a measurement represents a lot or batch. In this case we need to be able to look at just a single measurement as a subgroup, hence an individuals chart. But what about the fact that the range is based on the variation between subgroup members? In this case, we use a range chart made of the range of the last two individuals or a moving range chart.

XMR

Individual Moving Range

Zones

Areas between the 1, 2 and 3 sigma lines above and below the center line.

### SPC Definitions for Statistical Process Control

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