**SPC Glossary**

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.

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.

Capability

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.

Cause-and-Effect Diagram

A quality control tool used to analyze potential causes of problems in a product or process. It is also called a fishbone diagram or an Ishikawa diagram after its developer.

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.

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

Statistically calculated control chart lines which indicate how the process is behaving and whether the process is 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, nearly all of the sample points fall within the control limits. Sometimes called the Natural Process Limits for the sample size.

Correlation

A measure of the linear relation between two variables. If both variables grow larger (or smaller) together, it is called positive correlation. If one variable becomes smaller as the other grows larger, it is called negative 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.

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 graph of the observed frequencies versus each value or range of values for a set of data. A histogram provides a graphical summary of the variation in the data.

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.

Mean

A measure of the location or center of data. Also called the average. The mean is calculated by summing all of the observations and dividing by the number of observations.

Median

The “middle” value of a group of observations, or the average of the two middle values.

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.

Nonconforming Unit

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

Nonconformity

A specified requirement that is not fulfilled, such as a blemish, defect or imperfection.

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 based on counting the number of defective units in each constant size subgroup. 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.

p-Chart

A control chart based on the proportion of nonconforming units per subgroup. The p-chart is based on the binomial distribution.

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.

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

A measure of the spread of the data, calculated as highest value minus lowest value. Range = R = x

_{max}– x_{min}

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.

Runs 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 the variable to be predicted and the x-axis being used for the variable to make the prediction.

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.

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. Negative skewness denotes more small observations, while positive skewness denotes more large observations. Skewed data may affect the validity of control charts and other statistical tests based on the normal distribution.

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

The written or engineering requirements for judging the acceptability of the output of a process.

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

A measure of the spread of a set of data from its mean.

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.

Stratified Sampling

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.

Tampering

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

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 based on counting the number of nonconformities or defects per inspection unit. The u-chart is based on the Poisson distribution.

Variables Data

Data values which are measurements of some quality or characteristic of the process. The data values are used to construct the control charts. This qualitative data is used for the x-bar, R-, s- and individuals charts, as well as the CUSUM and moving range charts.

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. Also called an individuals chart or I-chart.

X-bar Chart

A control chart used for processes in which the averages of subgroups of process data are plotted for analysis.

## 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.

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*by Statit Software, Inc.*

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