**SPC Glossary**

Unsure of a certain SPC term? Use this page to find the technical definition you’re after.

Accuracy

Accuracy of measurements refers to the closeness of agreement between observed values and a known reference standard. Any offset from the known standard is called bias.

Assignable Cause

A cause of process variation that isn’t random or inherent and that is attributable to some identifiable and controllable influence. A dulled cutting tool, for example, could be an assignable cause for a cutting process’s increased variation.

Attribute data

Qualitative data that can be counted for recording and analysis. Examples include: number of defects, number of errors in a document, number of rejected items in a sample, presence of paint flaws. Attribute data are analyzed using the p-, np-, c- and u-charts.

Average

See

*mean*.

Average Run Length (ARL)

Short for average run length, ARL is the interval between out-of-control events that can be expected. For example, is a common out-of-control event chosen to determine a process’ ARL. When an out-of-control event appears on a control chart, an analyst can examine the interval between that event and the previous out-of-control event. If the interval matches or exceeds the process’ ARL value: a) the process can probably be classified as still in-control, b) the violation can probably be attributed to typical process variation, and c) a search for an assignable cause can probably be considered unwarranted. The inverses of these statements are likely true if the interval between out-of-control events is smaller than the ARL value.

Bias

The offset of a measured value from the true population value.

Binomial Distribution

A discrete probability distribution used for counting the number of successes and failures, or conforming and nonconforming units. This distribution underlies the p-chart and the np-chart.

Box and Whisker Plot

A graphical display of data tat shows the median and upper and lower quartiles, along with extreme points and any outliers.

Brainstorming

In the field of SPC as it is applied to manufacturing, a recognized strategy for identifying manufacturing problems and solutions.

Capability

A measure of the amount of variation inherent in a stable process. Capability can be determined using data from control charts and histograms and is often quantified using the C

_{p}and C_{pk}indices. A process is said to be capable when all of its output is in-spec.

Cause-and-Effect Diagram

A quality-control tool used to analyze potential causes of problems in a product or process. It organizes potential problems into four groups: man, method, machine, and material. It is also called a fishbone diagram or an Ishikawa diagram, after its developer.

c-Chart

A control chart based on counting the number of defects per constant size subgroup. Also known as a Count of Nonconformities chart. The c-chart is based on the Poisson distribution.

Center Line (CL)

The line on the control chart that represents the long-run expected, or average value, of the quality characteristic that corresponds to the in-control state which occurs when only chance causes are present.

Central Limit Theorem

An important statistical theorem that states that subgroup averages tend to be normally distributed even if the output as a whole is not. This allows control charts to be widely used for process control, even if the underlying process is not normally distributed.

Check Sheet

In the field of SPC, a simple user-friendly form for collecting data over a period of time. Originally, it was a paper form but today it is often found integrated into SPC software.

Coefficient of Correlation

See

*Correlation*below.

Common Causes

Problems with the system itself that are always present, influencing all of the production until found and removed. These are “common” to all manufacturing or production output. Also called chance causes, system causes, or chronic problems. Compare

*common causes*to*special causes*.

Continuous Improvement

The ongoing improvement of products, services, or processes through incremental and breakthrough improvements.

Control Chart

A graphical mechanism for deciding whether the underlying process has changed based on sample data from the process. Control charts help determine which causes are “special” and thus should be investigated for possible correction. Control charts contain the plotted values of some statistical measure for a series of samples or subgroups, along with the upper and lower control limits for the process.

Control Limits

Numerical limits, often represented on control charts as horizontal lines, which indicate whether the process is statistically in control. There is typically an upper control limit (UCL) and a lower control limit (LCL). If the process is in control and only common causes are present, and nearly all of the sample points fall within the control limits.

Correlation

A measure of the relationship between two variables. If both variables grow larger (or smaller) together, they have a positive correlation. If one variable becomes smaller as the other grows larger, they have a negative correlation. Correlation values range from -1 to 1, with -1 indicating a negative correlation and 1 indicating a positive correlation.

Count Data

See

*attribute data*.

C

_{p}A measure of the capability of a process to produce output within the specifications. The measurement is made without regard to the centering of the process.

C

_{pk}A measure of the capability of the process to produce output within the specifications. The centering of the process is taken into consideration by looking at the minimum of the upper specification limit capability and the lower specification limit capability. C

_{pk}= min (C_{pu}, C_{pl}).

CUSUM

A control chart designed to detect small process shifts by looking at the Cumulative SUMs of the deviations of successive samples from a target value.

Design of Experiments

A branch of applied statistics dealing with planning, conducting, analyzing, and interpreting controlled tests which are used to identify and evaluate the factors that control a value of a parameter of interest.

Defect

An occurrence of a defect type (see below) in a manufactured part. A part can have multiple defect types and each type can have multiple occurrences.

Defective Unit

A part that is determined to be defective, without detailing what makes the part defective.

Defect Type

A type of defect that may be observed in a part; for example, scratched. Each defect type may have multiple occurrences.

Detection Model

A method of quality control that only inspects a process’s output. It is considered inferior to a prevention method, as it tends to result in more output needing to be scrapped or reworked. In contrast, a prevention method anticipates scrap and rework and makes process adjustments accordingly.

Distribution

A mathematical model that relates the value of a variable with the probability of the occurrence of that value in the population.

EWMA charts

An Exponentially Weighted Moving Average control chart that uses current and historical data to detect small changes in the process. Typically, the most recent data is given the most weight, and progressively smaller weights are given to older data.

Histogram

A bar graph representing the frequency of different measurements in a set of data. The graph is divided into ranges, such as 1-5, 6-10, 11-15, 16-20, and 21-25. Each range is represented by a bar, the height of which indicates the number of measurements in the set of data fall within that range.

Hypothesis Testing

A procedure that is used on a sample from a population to investigate the applicability of an assertion (inference) to the entire population. Hypothesis testing can also be used to test assertions about multiple populations using multiple samples.

In-Control Process

A process in which the quality characteristic being evaluated is in a state of statistical control. This means that the variation among the observed samples can all be attributed to common causes, and that no special causes are influencing the process.

Individual

A single unit or a single measurement of a quality characteristic, usually denoted as X. This measurement is analyzed using an individuals chart, CUSUM or EWMA chart.

Individuals Chart

A control chart for processes in which individual measurements of the process are plotted for analysis. Also called an I-chart or X-chart.

Kurtosis

The degree of peakedness, or flatness, of a histogram’s distribution curve.

Mean

The average of the individual values in a subgroup.

Median

The “middle” value in a group of values. If the number of values is even, by convention, the median is determined by averaging the two middle values.

Mixture

A pattern on a control chart that indicates data is coming from different systems or processes. The pattern consists of 8 consecutive points that occupy both sides of the center line in Zone B or beyond but not Zone C.

Mixing

A generally improper sampling technique that arises in practice when the output from several processes is first thoroughly mixed and then random samples are drawn from the mixture. This may increase the sample variability and make the control chart less sensitive to process changes. This action violates the fundamental rule of rational sampling.

Mode

The observation that occurs most frequently in a sample. The data can have no mode, be unimodal, bimodal, etc.

Moving Range

A measure used to help calculate the variance of a population based on differences in consecutive data. Two consecutive individual data values are compared and the absolute value of their difference is recorded on the moving range chart. The moving range chart is typically used with an Individuals (X) chart for single measurements.

Non-conforming Unit

A unit with one or more nonconformities or defects. Also called a reject or defective unit.

Non-conformity

A defect or an occurrence of something that violates a requirement, such as a scratch or dent.

Normal Distribution

A continuous, symmetrical, bell-shaped frequency distribution for variables data that is the basis for control charts for variables, such as x-bar and individuals charts. For normally distributed values, 99.73% of the population lies within ± 3 standard deviations of the mean. According to the Central Limit Theorem, subgroup averages tend to be normally distributed even if the output as a whole is not.

np-Chart

A control chart that plots the number of defective units in a lot. Only used when the lot size is fixed. The np-chart is based on the binomial distribution.

Outliers

Unusually large or small observations relative to the rest of the data.

Over-control

An element often introduced into a process by a well-meaning operator or controller who considers any appreciable deviation from the target value as a special cause. In this case, the operator is incorrectly viewing common-cause variation as a fault in the process. Over control of a process can actually increase the variability of the process and is viewed as a form of tampering.

Pareto Chart

A problem-solving tool that involves ranking all potential problem areas or sources of variation according to their contribution to cost or total variation. Typically, 80% of the effects come from 20% of the possible causes, so efforts are best spent on these “vital few” causes, temporarily ignoring the “trivial many” causes.

Pareto Principle

The principle that 80% of the problems are due to 20% of the causes. Also known as the 80/20 rule.

p-Chart

A control chart that plots the proportion of nonconforming units per lot.

Percentiles

Percentiles divide the ordered data into 100 equal groups. The k

^{th}percentile p_{k}is a value such that at least k% of the observations are at or below this value and (100-k)% of the observations are at or above this value.

Poisson Distribution

A probability distribution used to count the number of occurrences of relatively rare events. The Poisson distribution is used in constructing the c-chart and the u-chart.

Precision

Precision of measurements refers to their long-run variation (s

^{2}). It is a measure of the closeness between several individual readings.

Prevention Model

A method of quality control that proactively adjusts a process using SPC so that scrap and rework are prevented. It is considered superior to a detection model, which only inspects a process’s output.

Process Capability

A measure of the ability of a process to produce output that meets the process specifications.

Quartile

Quartiles divide the ordered data into 4 equal groups. The second quartile (Q2) is the median of the data.

Random Sampling

A subset of the population chosen such that each member of the population has an equal probability of being included in the sample.

Range

The difference between the highest and lowest values in a subgroup. For example, if a subgroup contains the values 1, 2, 6, 4, and 5, the range is the difference between 6 and 1, which is 5.

Rational Subgroups

A principle of sampling which states that the variation between subgroups or samples should be solely attributable to the common causes in the system rather than the sampling method. Rational subgroups are usually chosen so that the variation represented within each subgroup is as small as feasible for the process, so that any changes in the process, or special causes, appear as differences between subgroups. Rational subgroups are typically made up of consecutive pieces, although random samples are sometimes used.

R-Chart

A control chart based on the range (R) of a subgroup, typically used in conjunction with an x-bar chart.

Run

A consecutive number of points consistently increasing or decreasing, or above or below the centerline. A run can be evidence of the existence of special causes of variation that should be investigated.

Run Chart

A simple graphic representation of a characteristic of a process which shows plotted values of some statistic gathered from the process. The graphic can be analyzed for trends or other unusual patterns.

S-Chart

A control chart based on the standard deviation, s, of a subgroup. The s-chart is typically used in conjunction with an x-bar chart.

Sample

A subset of data from a population that can be analyzed to make inferences about the entire population.

Sampling Distribution

The probability distribution of a statistic. Common sampling distributions include t, chi-square (c

^{2}), and F.

Scatter Plots

A graphical technique used to visually analyze the relationship between two variables. Two sets of data are plotted on a graph, with the y-axis being used for one variable and the x-axis being used for the other.

Sensitizing Rules

Control chart interpretation rules that are designed to increase the responsiveness of a control chart to out-of-control conditions by looking for patterns of points that would rarely happen if the process has not changed.

Short-run Techniques

Adaptations made to control charts to help determine meaningful control limits in situations when only a limited number of parts are produced or when a limited number of services are performed. Short-run techniques usually look at the deviation of a quality characteristic from a target value.

Sigma

The Greek letter used to designate a standard deviation.

Six Sigma

A high-performance, data-driven approach to analyzing the root causes of business problems and solving them. Six-sigma techniques were championed by Motorola.

Skewness

The tendency of the data distribution to be non-symmetrical. Skewness can be positive or negative and may affect the validity of control charts and other statistical tests based on the normal distribution.

SPC

Statistical Process Control, a proven and comprehensive methodology for achieving and maintaining manufacturing quality.

Special Causes

Causes of variation which arise periodically in a somewhat unpredictable fashion. Also called assignable causes, local faults, or sporadic problems. Contrast to common causes. The presence of special causes indicates an out-of-control process.

Specification Limits

The upper and lower limits within which a process’s output must fall in order for that output to be acceptable.

Spread

The amount of variability in a sample or population.

Stability

A process is considered stable if it is free from the influences of special causes. A stable process is said to be in control.

Standard Deviation

Deviation is the distance far process measurements deviate from the process mean. Standard deviation is a standardized distance that is calculated from process data.

Statistic

A value calculated from, or based on, sample data which is used to make inferences about the population from which the sample came. Sample mean, median, range, variance, and standard deviation are commonly calculated statistics.

Statistical Control

The condition describing a process from which all special causes of variation have been removed and only common causes remain.

Statistical Process Control (SPC)

A collection of problem solving tools useful in achieving process stability and improving capability through the reduction of variability. SPC includes using control charts to analyze a process to identify appropriate actions that can be taken to achieve and maintain a state of statistical control and to improve the capability of the process.

Statistical Quality Control (SQC)

Another name commonly used to describe statistical process control techniques.

Stratification

Stratification arises in practice when samples are collected by drawing from each of several processes, for example machines, filling heads or spindles. Stratified sampling can increase the variability of the sample data and make the resulting control chart less sensitive to changes in the process.

Subgroup

Another name for a sample from the population. Subgroups consist of individual measurements or readings and the number of measurements or readings is referred to as the subgroup size. A common subgroup size is 5, which means each subgroup consists of 5 measurements or readings.

Tampering

An action taken to compensate for variation within the control limits of a stable system. Tampering increases rather than decreases variation.

Target

The ideal or aimed-for measurement of a process. It is typically mid-way between the upper and lower specification limits but does not have to be.

Type I Error

Occurs when a true hypothesis about the population is incorrectly rejected. Also called false alarm. The probability of a Type I error occurring is designated by a.

Type II Error

Occurs when a false hypothesis about the population is incorrectly accepted. Also called lack of alarm. The probability of a Type II error occurring is designated by b.

u-Chart

A control chart that plots the number of non-conformities or defects per inspection unit. It is used when the lot size is not fixed.

Variable Data

Measurements, such as diameter or weight, that are taken from a measuring instrument, such as calipers or a scale. It contrasts with attribute data, which consists of defects that are observed by a human. An example of attribute data is scratches or dents.

Variation

The differences among individual results or output of a machine or process. Variation is classified in two ways: variation due to common causes and variation due to special causes.

X Chart

A control chart used for process in which individual measurements of the process are plotted for analysis, as opposed to being grouped into subgroups and averaged. Also called an individuals chart or I-chart.

Xbar Chart

A control chart for variable data that plots the average of each subgroup.

Xbar-R Chart

Two control charts that are viewed together. Usually, the X-bar chart is positioned above the R chart. Both charts are for variable data. The X-bar chart plots the average of each subgroup. The R chart plots the range of each subgroup and is typically used when the subgroup size is 7 or less.

Xbar-S Chart

Same as Xbar-R but typically used when the subgroup size is 8 or more.

Zone A

The outermost one-third of the area between the center line and the upper and lower limits on a control chart.

Zone B

The center one-third of the area between the center line and the upper and lower limits on a control chart.

Zone C

The innermost one-third of the area between the center line and the upper and lower limits on a control chart.

## Bibliography

Nelson, Loyd S. (1985), “Interpreting Shewhart X Control Charts”, Journal of Quality Technology, 17:114-16.

Steel, R. G. D. and J. H. Torrie (1980), Principles and Procedures of Statistics.New York: McGraw-Hill.

Western Electric Company (1956), Statistical Quality Control Handbook, available from ATT Technologies, Commercial Sales Clerk, Select Code 700-444, P.O. Box 19901, Indianapolis, IN 46219, 1-800-432-6600.

* *

*by Statit Software, Inc.*

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