# Quality Advisor

A free online reference for statistical process control, process capability analysis, measurement systems analysis,

control chart interpretation, and other quality metrics.

## Glossary

## A

### Alpha value

The risk of being wrong when completing a hypothesis test.

The chi-square table is computed in such as way that if the assumption of “normal data” is true for a given X-bar and sigma, the results of the chi-square test will be incorrectly rejected only 5% of the time. This calculation reflects the alpha value.

### Assignable cause

An assignable cause is a source of variation that is intermittent, not predictable. It is sometimes called “special cause” variation. On a control chart, an assignable cause is signaled by points beyond the control limits or nonrandom patterns within the control limits.

### Attributes data

Attributes data is data that can be classified and counted. There are two types of attributes data: counts of defects per item or group of items (nonconformities) and counts of defective items (nonconforming). For example, yes/no, good/bad, pass/fail, and go/no go.

### Average

Another term for a mean, it is an indicator of the center of a set of data points. It is found by adding all the individual values and dividing by the number of values.

## B

### Bell curve

Another term for the shape formed by a normal distribution when drawn as a histogram.

### Bias

Something that influences the selection of certain items when collecting a sample.

### Bimodal distribution

A distribution that has two modes. Drawn as a histogram, this condition is reflected by two peaks or high points.

## C

### Capability

The capability of a process is how the process performs when compared to specification limits or requirements. It uses a series of indices: Cp, Cpk, Cr, and Cpm.

### Capability analysis

A set of statistical calculations performed on a set of data to assess how the distribution formed by the data compares to specifications or requirements.

### Capable process

A process is said to be capable if nearly 100% of its output falls within specification limits.

### c-chart

An attributes control chart that is used to monitor the number of nonconformities, such as defects per subgroup. The subgroup size must remain constant for this type of chart.

### Central location

Central location is the center of a set of data points. Mean, median, and mode are the statistics used to describe it.

### Central tendency

Statistics such as the mean, median, and mode are said to be measures of central tendency.

### Characteristic

A distinguishing feature of a process or its output on which variables or attributes data can be collected.

### Chi-square

A goodness-of-fit-test statistic used to test the assumption that the distribution of a set of data is similar to the expected distribution, such as a normal distribution.

### Coefficient of variance

A ratio that measures the significance of the standard deviation in relation to the mean.

### Common cause

A source of variation that is inherent in a system and is predictable. A control chart identifies a system with only common causes of variation. Common causes of variation affect all individual values of a system, and can be eliminated only by a systemic change.

### Control chart

A control chart is a graphical representation of a characteristic of a process, showing plotted values of some statistic, a central line, and one or two control limits. It is used to determine whether a process has been operating in statistical control and is an aid to maintaining statistical control.

### Control limits

Lines on a control chart used as a basis for judging whether variation in data on a chart is due to special or common causes. These limits are calculated from data collected from the system, they are not specifications or limits set by customers or management.

### Cp

A capability index that compares the width of a two-sided specification with the variation in the process. Estimated standard deviation is used to calculate the process variation. A Cp larger than 1 indicates that the process variation is narrower than the specification.

### Cpk

Cpk is a capability index that tells how well a system can meet two-sided specification limits. Because it takes the target value into account, the system does not have to be centered on the target value for this index to be useful. It is calculated with estimated standard deviation. A Cpk greater than 1 indicates that the process can meet the specification.

### Cpl

A capability index that compares the variation in the process to the lower specification. Estimated standard deviation is used to calculate the process variation. A Cpl greater than 1 indicates the process is capable of meeting the lower specification.

### Cpm

Cpm is a capability index that shows how well the system can produce output within specifications while taking the target into account. Its calculation uses sigma calculated from the target value instead of the mean.

### Cpu

A capability index that compares the variation in the process to the upper specification. Estimated standard deviation is used to calculate the process variation. A Cpu greater than 1 indicates the process is capable of meeting the upper specification.

### Cr

Capability ratio compares the variation in a process with the width of a two-sided specification. Estimated standard deviation is used to calculate the process variation. It is the inverse of Cp.

## D

### Defect

An occurrence such as a blemish, scratch, burn, error, or omission that appears on an object. A defect does not necessarily make the object unusable or unacceptable.

### Defective

A product or service flawed beyond use or acceptability.

### Discrimination

This refers to a description of the capability of a measurement system.

### Dispersion

Statistics such as the range and standard deviation (sigma) are said to be measures of dispersion.

### Distribution

Distribution is a way of describing the output from a system of variation. The distribution’s location, shape, and spread may be evaluated by statistics such as the mean, median, sigma, and range.

## E

### Estimated sigma

This is an estimate of the standard deviation calculated by dividing the average range by the tabular constant d2 (R-bar/d2).

## H

### Histogram

A histogram is a bar chart that represents the frequency distribution of data. The height of each bar corresponds to the number of items in the class or cell. The width of each bar represents a measurement interval. The histogram shows basic information such as central location, shape, and spread of the data being examined.

# I

### In control

A process is said to be “in control” or “stable” if it is in statistical control. If a process is in statistical control, a control chart will have no subgroups falling outside the control limits, no runs, and no nonrandom patterns.

### Individuals control chart

The individual portion of an X-MR control chart. The individual data points are plotted onto the chart and compared with control limits.

## K

### Kurtosis

Kurtosis is a statistic that is used to measure the “flatness” or “peakedness” of a set a of data. It represents a measure of the combined weight of the tails relative to the rest of a distribution. As the tails of a distribution become heavier, the kurtosis will increase. As the tails become lighter, the kurtosis value will decrease.

## L

### Lower control limit

A line on a control chart used as a basis for judging whether variation from the data on the chart is due to special or common causes. Any point beyond the lower control limit is an indication of a special cause occurring. This limit is calculated from data collected on the system, it is not a specification or limit set by customers or management. The symbol is LCL.

### Lower specification limit

The lower limit of a specification. This limit is set as an aim for a system or process, it is usually set by the customer of the process, engineering, or management. The symbol for the lower specification is LSL – lower specification limit.

## M

### Maximum acceptable subgroup size

When a varying sample size is being used in a p or u-control chart, the maximum acceptable sample size is usually a sample size that is twenty-five percent larger than the average sample size. Any subgroup with a sample size larger than the maximum acceptable subgroup size has to have control limits calculated specifically for that subgroup.

### Mean

Another term for average, it is an indicator of the central location of a set of data. It is found by adding all the individual values and dividing by the number of values.

### Measurement system

A measurement system consists of the people, procedures, systems, and devices used to take measurements.

### Median

The middle number in a set of data when it is ranked from lowest to highest, it is an indicator of central location in a data set.

### Minimum acceptable subgroup size

When a varying sample size is being used in a p or u-control chart, the minimum acceptable sample size is usually a sample size that is twenty-five percent smaller than the average sample size. Any subgroup with a sample size smaller than the minimum acceptable subgroup size has to have control limits calculated specifically for that subgroup.

### Mode

Is the number that occurs most frequently in a data set. It is usually an indicator of central location.

### Moving range

The difference between consecutive subgroup values on an X-MR control chart. The moving range is used as a measure of variability.

### Moving range chart

The moving range portion of an individuals and moving range control chart. The moving ranges are plotted on the chart and compared with control limits.

## N

### Negatively skewed distribution

A distribution of data where most of the data appears on the right hand side of the distribution and then tails off to the left. Also known as a skewed left distribution.

### Nonconforming

Nonconforming data is a count of defective units. It is often described as go/no go, pass/fail, or yes/no, since there are only two possible outcomes to any given check. You can track either the number of defective units or the number of nondefective units.

### Nonconformities

Nonconformities data is a count of defects per unit or group of units. It can refer to defects or occurrences that should not be present but are, or any characteristic that should be present but is not.

### Nonnormal data

Data that does not form a normal distribution.

### Nonnormal data distribution

Any data set that does not show a normal, bell-shaped distribution.

### Nonrandom pattern

A pattern in data that is repeating, or is not due to normal variation.

### Normal curve

This bell-shaped curve is used to illustrate the shape of a normal distribution.

### Normal distribution

A data distribution that is bell shaped and symmetrical, the normal distribution is the basis for control chart and capability analysis.

### Normal probability plot

A normal probability plot is a graphical method for showing a frequency distribution. The scaling is set up so that if the distribution is normal, a straight line will result.

### np-chart

An attributes control chart that plots the number of items that are defective or possess a characteristic of interest. The subgroup size must remain constant for this type of chart to be used.

## O

### Observation

An observation is a single piece of data, usually a count or a measurement. It is also known as a reading.

### Operational definition

When applied to data collection, it is a clear, concise, and detailed definition of a measure. It ensures that those collecting data do so consistently.

### Outlier

An outlier is a point on a chart that does not fall into the pattern of the rest of the data.

### Out-of-control

When applied to a control chart, out of control means that at least one special cause of variation is present.

### Overcontrol

Over reaction to a set of data. For example, in a control chart, it would be reacting to a common cause as if it were a special cause.

## P

### Pareto chart

A Pareto chart is a bar chart for ranking aspects of a problem. Typically, a few aspects make up a significant portion of the problem while many trivial aspects exist.

### p-chart

An attributes control chart that plots the number of items possessing a characteristic of interest. The subgroup size may vary.

### Positively skewed distribution

A distribution of data where most of the data appears on the left hand side of the distribution and then tails off to the right. Also known as a skewed right distribution.

### Pp

Pp is a capability index, similar to Cp, that is a measure of process performance. Pp tells how well a system can meet two-sided specification limits, assuming that the average is centered on the target value. It is calculated with the actual sigma (using the actual individual values) rather than the estimated sigma. A Pp larger than 1 indicates that the process variation is narrower than the specification.

### Ppk

Similar to Cpk, Ppk is a capability index that indicates whether a process is capable of meeting two-sided specification limits. However, Ppk uses actual standard deviation to calculate the process variation, whereas Cpk uses an estimated standard deviation. The target value is taken into account with Ppk, so the system does not have be center on the target value to be useful. A Ppk greater than 1 indicates that the process can meet the specification.

### Ppl

A capability index similar to Cpl in that it compares the variation in the process to the lower specification. However, Ppl uses standard deviation to calculate the process variation, whereas Cpl uses an estimated standard deviation. A Ppl greater than 1 indicates the process is capable of meeting the lower specification.

### Ppu

A capability index similar to Cpu in that it compares the variation in the process to the upper specification. However, Ppu uses standard deviation to calculate the process variation, whereas Cpu uses an estimated standard deviation. A Ppu greater than 1 indicates the process is capable of meeting the upper specification.

### Pr

A capability ratio similar to Cr in that it compares the variation in a process with the width of a two-sided specification. However, Pr uses standard deviation to calculate the process variation, whereas Cr uses an estimated standard deviation. It is the inverse of Pp.

### Process

A process is the combination of people, equipment, materials, methods, and environment that produce output—a given product or service. The words process and system are often used interchangeably.

### Process capability

Process capability is the 6 sigma range of common cause variation for statistically stable processes only. Sigma is usually estimated by R-bar/d2.

### Process performance

The process performance is the 6 sigma range of inherent variation for statistically stable processes only, where sigma is usually estimated by the sample standard deviation.

## R

### Random distribution

A distribution that forms no particular shape.

### Random sample

A sample that allows every item in a population to have an equal chance of being selected, with no bias.

### Range

Range is an estimate of spread in a set of data points; the difference between the highest and lowest values in the data set.

### Repeatability

Repeatability refers to variation in a series of measurements that have been taken with one gage measuring one characteristic of the same item by the same person.

### Reproducibility

Reproducibility refers to variation in a series of measurements that have been taken with one gage measuring one characteristic of the same item by different people.

### Run chart

A run chart is a simple line chart that plots one characteristic over time. It is used to plot individual observations and detect patterns in the data.

## S

### Sample

A sample is a collection of one or more observations used to analyze the performance of a process, as opposed to the total populations. It is intended to represent the characteristics of the population. Sample is a synonym for “subgroup” in process control applications.

### Sample size

The number of pieces of data taken at one time. For example five boxes are checked for stiffness every hour, the sample size in this case is five. If the temperature of a room is taken every hour, only one number is collected every hour, so the sample size is one.

### Sigma of the individuals

Sigma of the individuals is standard deviation calculated from the individual data values in a data set. It is also known as actual or calculated sigma.

### Sigma

Sigma is the Greek symbol, , used to denote standard deviation. It is a measure of the variation or spread within a set of data.

### Skewed distribution

A distribution that tails off to one side, either to the left or right.

### Skewness

Skewness is a statistic that is used to measure the symmetry of the distribution for a set of data. A process that is skewed tails off to the left or to the right.

### Special cause

Special cause variation is a source of variation that is intermittent, not predictable. Sometimes it is called “assignable cause” variation. On a control chart, a special cause is signaled by points beyond the control limits, runs, or nonrandom patterns within the control limits. A process that has special cause variation is said to be out-of-control, unstable, or unpredictable.

### Specification limits

Specifications are boundaries, usually set by management, engineering, or customers, within which a system must operate. They are sometimes called engineering tolerances.

### Spread

Spread is the range of data from the lowest value to the highest value.

### Stable process

A system, analysed by a control chart, with no special causes of variation present, this system is also said to be in control. Variation within a stable system is due to common causes, and is predictable.

### Standard deviation

A statistic that describes the variation or spread within a data set. It can be used to indicate the variation in a process and to compare with specifications.

### Statistical control

Statistical control is a condition describing a process from which all special causes of variation have been removed and only common causes of variation remain. On a control chart, processes that are in statistical control show no subgroups outside the control limits, no runs, and no nonrandom patterns. This condition is also referred to as in control, stable, or predictable.

### Subgroup

A subgroup is one or more occurrences or measurements taken at one time. Multiple subgroups are used to analyze the performance of a process. Subgroup is used as a synonym for “sample.”

### Symmetrical distribution

A distribution that if cut in half, shows each side is the mirror of the other.

## T

### Target value

The exact value at which customers, engineering, or management want the system to operate.

### Trial limits

On a control chart, trial limits are calculated when there is insufficient data to calculate control limits. These give a temporary guide until sufficient data has been collected.

## U

### u-chart

An attributes control chart that is used to monitor the number of nonconformities per unit, such as defects per item. The subgroup size may vary.

### Undercontrol

Not reacting to a set of data when the data is showing an issue or problem. For example, in a control chart, it would be ignoring a special cause of variation.

### Uniform distribution

A distribution, when drawn as a histogram, has each bar at a similar frequency.

### Unstable system

A system that contains special and common causes of variation; this system is also said to be out of control. An unstable system is unpredictable.

### Upper control limit

A line on a control chart used as a basis for judging whether variation from the data on the chart is due to special or common causes. Any point beyond the upper control limit is an indication of a special cause occurring. This limit is calculated from data collected on the system, it is not a specification or limit set by customers or management. Its symbol is UCL.

### Upper specification limit

The upper limit of a specification. This limit is set as an aim for a system or process, it is usually set by the customer of the process, engineering, or management. The symbol for the upper specification is USL–upper specification limit.

## V

### Variability

Variability refers to the differences among individual outputs of a process. In control chart pairs, it refers to the differences between individual observations and is analyzed in range, sigma, and moving range charts.

### Variables

Variables data is data that is acquired through measurements, such as length, time, diameter, strength, weight, temperature, density, thickness, pressure, and height. X-bar and range, X-bar and sigma, and individuals and moving range charts are used to analyze variables data.

### Variation

Variation is the inevitable differences that occur among individual outputs of a process. Sources of variation may be grouped into two major categories: common causes and special causes.

## X

### X-bar

X-bar is the average or mean of values in a group of observations.

### X-bar chart

The X-bar chart is a variables control chart that shows the subgroup averages. The subgroup size for this chart must be larger than one and consistent.

## Z

### Zlower

The symbol for the Z value for the lower specification limit. It represents the number of standard deviations between the average and the lower specification limit.

### Zmin

The minimum of the Z values, either Z_{upper} or Z_{lower}. It is used to calculate the Cpk index in capability analysis.

### Zupper

The symbol for the Z value for the upper specification limit. It represents the number of standard deviations between the average and the upper specification limit.

### Z value

Used in capability analysis, it is the symbol for the number of standard deviations between the average and a specification limit for a normal distribution.