Control charts, also known as
Shewhart charts or
process-behaviour charts, in
statistical process controlStatistical process control is an effective method of monitoring a process through the use of control charts. Control charts enable the use of objective criteria for distinguishing background variation from events of significance based on statistical techniques...
are tools used to determine whether a manufacturing or
business processA business process or business method is a collection of related, structured activities or tasks that produce a specific service or product for a particular customer or customers...
is in a state of statistical control or not.
Overview
If the chart indicates that the process is currently under control then it can be used with confidence to predict the future performance of the process. If the chart indicates that the process being monitored is not in control, the pattern it reveals can help determine the source of variation to be eliminated to bring the process back into control. A control chart is a specific kind of
run chartA run chart, also known as a run-sequence plot is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process.- Overview :...
that allows significant change to be differentiated from the natural variability of the process.
This is key to effective process control and improvement. On a practical level the control chart can be seen as part of an objective disciplined approach that facilitates the decision as to whether process performance warrants attention or not.
The control chart is one of the seven basic tools of
quality controlIn engineering and manufacturing, quality control and quality engineering are used in developing systems to ensure products or services are designed and produced to meet or exceed customer requirements....
(along with the
histogramIn statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories: it is a form of data binning. The categories are usually specified as non-overlapping intervals of some variable. The categories must...
,
Pareto chartA Pareto chart, named after Vilfredo Pareto, is a type of chart which contains both bars and a line graph. The bars display the values in descending order, and the line graph shows the cumulative totals of each category, left to right....
,
check sheetThe check sheet is a simple document that is used for collecting data in real-time and at the location where the data is generated. The document is typically a blank form that is designed for the quick, easy, and efficient recording of the desired information, which can be either quantitative or...
, cause-and-effect diagram,
flowchartA flowchart is a common type of diagram, that represents an algorithm or process, showing the steps as boxes of various kinds, and their order by connecting these with arrows...
, and scatter diagram).
History
The control chart was invented by
Walter A. ShewhartWalter Andrew Shewhart was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.W...
while working for
Bell LabsBell Laboratories is the research and development organization of Alcatel-Lucent and previously of the American Telephone & Telegraph Company .Bell Laboratories has had its headquarters at Murray Hill, New Jersey, and it has research and development facilities...
in the 1920s. The company's engineers had been seeking to improve the reliability of their
telephonyIn telecommunication, telephony encompasses the general use of equipment to provide voice communication over distances, specifically by connecting telephones to each other....
transmission systems. Because
amplifierGenerally, an amplifier or simply amp, is any device that changes, usually increases, the amplitude of a signal. The relationship of the input to the output of an amplifier—usually expressed as a function of the input frequency—is called the transfer function of the amplifier, and the magnitude of...
s and other equipment had to be buried underground, there was a business need to reduce the frequency of failures and repairs. By 1920 they had already realized the importance of reducing variation in a manufacturing process. Moreover, they had realized that continual process-adjustment in reaction to non-conformance actually increased variation and degraded quality. Shewhart framed the problem in terms of Common- and special-causes of variation and, on May 16 1924, wrote an internal memo introducing the control chart as a tool for distinguishing between the two. Dr. Shewhart's boss, George Edwards, recalled: "Dr. Shewhart prepared a little memorandum only about a page in length. About a third of that page was given over to a simple diagram which we would all recognize today as a schematic control chart. That diagram, and the short text which preceded and followed it, set forth all of the essential principles and considerations which are involved in what we know today as process quality control." Shewhart stressed that bringing a production process into a state of statistical control, where there is only common-cause variation, and keeping it in control, is necessary to predict future output and to manage a process economically.
Dr. Shewhart created the basis for the control chart and the concept of a state of statistical control by carefully designed experiments. While Dr. Shewhart drew from pure mathematical statistical theories, he understood data from physical processes never produce a "
normal distributionIn probability theory and statistics, the normal distribution or Gaussian distribution is a continuous probability distribution that describes data that cluster around a mean or average. The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known...
curve" (a Gaussian distribution, also commonly referred to as a "
bell curveBell curve can refer to:* Normal distribution, whose density function graph is a bell-shaped curve* The Bell Curve, a book by Richard J. Herrnstein and Charles Murray* Bell curve grading, a method of evaluating scholastic performance....
"). He discovered that observed variation in manufacturing data did not always behave the same way as data in nature (
Brownian motionBrownian motion is the seemingly random movement of particles suspended in a fluid or the mathematical model used to describe such random movements, often called a particle theory....
of particles). Dr. Shewhart concluded that while every process displays variation, some processes display controlled variation that is natural to the process, while others display uncontrolled variation that is not present in the process causal system at all times.
In 1924 or 1925, Shewhart's innovation came to the attention of
W. Edwards DemingWilliam Edwards Deming was an American statistician, professor, author, lecturer, and consultant. Deming is widely credited with improving production in the United States during the Cold War, although he is perhaps best known for his work in Japan...
, then working at the Hawthorne facility. Deming later worked at the
United States Department of AgricultureThe United States Department of Agriculture is the United States federal executive department responsible for developing and executing U.S. federal government policy on farming, agriculture, and food...
and then became the mathematical advisor to the
United States Census BureauThe United States Census Bureau is the government agency that is responsible for the United States Census. It also gathers other national demographic and economic data. As part of the United States Department of Commerce, the Census Bureau serves as the leading source of quality data about...
. Over the next half a century,
DemingWilliam Edwards Deming was an American statistician, professor, author, lecturer, and consultant. Deming is widely credited with improving production in the United States during the Cold War, although he is perhaps best known for his work in Japan...
became the foremost champion and proponent of Shewhart's work. After the defeat of
Japanis an island country in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, People's Republic of China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
at the close of
World War IIWorld War II, or the Second World War , was a global military conflict which involved a majority of the world's nations, including all great powers, organized into two opposing military alliances: the Allies and the Axis...
,
DemingWilliam Edwards Deming was an American statistician, professor, author, lecturer, and consultant. Deming is widely credited with improving production in the United States during the Cold War, although he is perhaps best known for his work in Japan...
served as statistical consultant to the
Supreme Commander of the Allied PowersSCAP may refer to:* Security Content Automation Protocol* Separation of Content and Presentation* Shackled City Adventure Path* SREBP cleavage activating protein* Supervisory Capital Assessment Program...
. His ensuing involvement in Japanese life, and long career as an industrial consultant there, spread Shewhart's thinking, and the use of the control chart, widely in Japanese manufacturing industry throughout the 1950s and 1960s.
Chart Details
A control chart consists of:
- Points representing measurements of a quality characteristic in samples taken from the process at different times [the data]
- A center line, drawn at the process characteristic mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
, which is calculated from the data
- Upper and lower control limits (sometimes called "natural process limits") that indicate the threshold at which the process output is considered statistically 'unlikely'
It may have other optional features, including:
- Upper and lower warning limits, drawn as separate lines, typically two standard deviations above and below the center line
- Division into zones, with the addition of rules governing frequencies of observations in each zone
- Annotation with events of interest, as determined by the Quality Engineer in charge of the process's quality
Chart usage
If the process is in control, all points will plot within the control limits. Any observations outside the limits, or systematic patterns within, suggest the introduction of a new (and likely unanticipated) source of variation, known as a special-cause variation. Since increased variation means increased
quality costsThe concept of quality costs is a means to quantify the total cost of quality-related efforts and deficiencies. It was first described by Armand V...
, a control chart "signaling" the presence of a special-cause requires immediate investigation.
This makes the control limits very important decision aids. The control limits tell you about process behavior and have no intrinsic relationship to any specification targets or engineering tolerance. In practice, the process mean (and hence the center line) may not coincide with the specified value (or target) of the quality characteristic because the process' design simply can't deliver the process characteristic at the desired level.
Control charts limit
specification limitsA specification is an explicit set of requirements to be satisfied by a material, product, or service. Should a material, product or service fail to meet one or more of the applicable specifications, it may be referred to as being out of specificiation;...
or targets because of the tendency of those involved with the process (e.g., machine operators) to focus on performing to specification when in fact the least-cost course of action is to keep process variation as low as possible. Attempting to make a process whose natural center is not the same as the target perform to target specification increases process variability and increases costs significantly and is the cause of much inefficiency in operations.
Process capabilityA process is a unique combination of tools, materials, methods, and people engaged in producing a measurable output; for example a manufacturing line for machine parts...
studies do examine the relationship between the natural process limits (the control limits) and specifications, however.
The purpose of control charts is to allow simple detection of events that are indicative of actual process change. This simple decision can be difficult where the process characteristic is continuously varying; the control chart provides statistically objective criteria of change. When change is detected and considered good its cause should be identified and possibly become the new way of working, where the change is bad then its cause should be identified and eliminated.
The purpose in adding warning limits or subdividing the control chart into zones is to provide early notification if something is amiss. Instead of immediately launching a process improvement effort to determine whether special causes are present, the Quality Engineer may temporarily increase the rate at which samples are taken from the process output until it's clear that the process is truly in control. Note that with three sigma limits, one expects to be signaled approximately once out of every 370 points on average, just due to common-causes.
Choice of limits
Shewhart set
3-sigma limits on the following basis.
- The coarse result of Chebyshev's inequality
In probability theory, Chebyshev's inequality states that in any data sample or probability distribution, nearly all the values are close to the mean value, and provides a quantitative description of "nearly all" and "close to".More precisely, no more than...
that, for any probability distributionIn probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval...
, the probabilityProbability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy...
of an outcome greater than k standard deviationIn probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though...
s from the meanIn statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
is at most 1/k2.
- The finer result of the Vysochanskii-Petunin inequality
In probability theory, the Vysochanskij–Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away....
, that for any unimodalIn mathematics, a monotonic function is a function which preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory....
probability distributionIn probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval...
, the probabilityProbability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy...
of an outcome greater than k standard deviationIn probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though...
s from the meanIn statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
is at most 4/(9k2).
- The empirical investigation of sundry probability distribution
In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval...
s reveals that at least 99% of observations occurred within three standard deviationIn probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though...
s of the meanIn statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
.
Shewhart summarized the conclusions by saying:
... the fact that the criterion which we happen to use has a fine ancestry in highbrow statistical theorems does not justify its use. Such justification must come from empirical evidence that it works. As the practical engineer might say, the proof of the pudding is in the eating.
Though he initially experimented with limits based on
probability distributionIn probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval...
s, Shewhart ultimately wrote:
Some of the earliest attempts to characterize a state of statistical control were inspired by the belief that there existed a special form of frequency function f and it was early argued that the normal law characterized such a state. When the normal law was found to be inadequate, then generalized functional forms were tried. Today, however, all hopes of finding a unique functional form f are blasted.
The control chart is intended as a heuristic.
DemingWilliam Edwards Deming was an American statistician, professor, author, lecturer, and consultant. Deming is widely credited with improving production in the United States during the Cold War, although he is perhaps best known for his work in Japan...
insisted that it is not a hypothesis test and is not motivated by the
Neyman-Pearson lemmaIn statistics, the Neyman-Pearson lemma states that when performing a hypothesis test between two point hypotheses H0: θ = θ0 and H1: θ = θ1, then the likelihood-ratio test which rejects H0 in favour of...
. He contended that the disjoint nature of population and sampling frame in most industrial situations compromised the use of conventional statistical techniques.
DemingWilliam Edwards Deming was an American statistician, professor, author, lecturer, and consultant. Deming is widely credited with improving production in the United States during the Cold War, although he is perhaps best known for his work in Japan...
's intention was to seek insights into the cause system of a process
...under a wide range of unknowable circumstances, future and past .... He claimed that, under such conditions,
3-sigma limits provided
... a rational and economic guide to minimum economic loss... from the two errors:
- Ascribe a variation or a mistake to a special cause when in fact the cause belongs to the system (common cause). (Also known as a Type I error
In statistics, the terms type I error and type II error are used to describe possible errors made in a statistical decision process...
)
- Ascribe a variation or a mistake to the system (common causes) when in fact the cause was special. (Also known as a Type II error
In statistics, the terms type I error and type II error are used to describe possible errors made in a statistical decision process...
)
Calculation of standard deviation
As for the calculation of control limits, the
standard deviationIn probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though...
required is that of the common-cause variation in the process. Hence, the usual
estimatorIn statistics, an estimator is a statistic that is used to estimate an unknown population parameter ; an estimate is the result from the actual application of the function to a particular sample of data...
, in terms of sample variance, is not used as this estimates the total squared-error loss from both common- and special-causes of variation.
An alternative method is to use the relationship between the
rangeIn descriptive statistics, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observation from the greatest and provides an indication of statistical dispersion.It is measured in the same units as the data...
of a sample and its
standard deviationIn probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though...
derived by
Leonard H. C. TippettLeonard Henry Caleb Tippett was an English physicist and statistician.Born in London, Tippett graduated in physics in the early 1920s at Imperial College. He studied for his MSc in statistics under Professor Karl Pearson at the Galton Laboratory, University College London and R. A. Fisher at...
, an estimator which tends to be less influenced by the extreme observations which typify special-causes.
Rules for detecting signals
The most common sets are:
- The Western Electric rules
In Statistical Process Control, the Western Electric Rules are decision rules for detecting "out-of-control" or non-random conditions on control charts. Locations of the observations relative to the control chart control limits and centerline indicate whether the process in question should be...
- The Wheeler
Donald J. Wheeler graduated from the University of Texas with a Bachelor's degree in Physics and Mathematics and holds M.S. and Ph.D degrees in Statistics from Southern Methodist University. From 1970 to 1982 he taught in the Statistics Department at the University of Tennessee where he was an...
rules (equivalent to the Western Electric zone tests
- The Nelson rules
Nelson rules are a method in process control of determining if some measured variable is out of control . Rules, for detecting "out-of-control" or non-random conditions were first postulated by Walter A. Shewhart in the 1920s...
There has been particular controversy as to how long a run of observations, all on the same side of the centre line, should count as a signal, with 7, 8 and 9 all being advocated by various writers.
The most important principle for choosing a set of rules is that the choice be made before the data is inspected. Choosing rules once the data have been seen tends to increase the Type I error rate owing to testing effects suggested by the dataIn statistics, hypotheses suggested by the data must be tested differently from hypotheses formed independently of the data.-How to do it wrongly:...
.
Alternative bases
In 1935, the British Standards Institution, under the influence of Egon PearsonEgon Sharpe Pearson was the only son of Karl Pearson, and like his father, a leading British statistician. He went to Winchester School and Trinity College, Cambridge, and succeeded his father as professor of statistics at University College London and as editor of the journal Biometrika...
and against Shewhart's spirit, adopted control charts, replacing 3-sigma limits with limits based on percentileA percentile is the value of a variable below which a certain percent of observations fall. So the 20th percentile is the value below which 20 percent of the observations may be found...
s of the normal distributionIn probability theory and statistics, the normal distribution or Gaussian distribution is a continuous probability distribution that describes data that cluster around a mean or average. The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known...
. This move continues to be represented by John Oakland and others but has been widely deprecated by writers in the Shewhart-Deming tradition.
Performance of control charts
When a point falls outside of the limits established for a given control chart, those responsible for the underlying process are expected to determine whether a special cause has occurred. If one has, then that cause should be eliminated if possible. It is known that even when a process is in control (that is, no special causes are present in the system), there is approximately a 0.27% probability of a point exceeding 3-sigma control limits. Since the control limits are evaluated each time a point is added to the chart, it readily follows that every control chart will eventually signal the possible presence of a special cause, even though one may not have actually occurred. For a Shewhart control chart using 3-sigma limits, this false alarm occurs on average once every 1/0.0027 or 370.4 observations. Therefore, the in-control average run length (or in-control ARL) of a Shewhart chart is 370.4.
Meanwhile, if a special cause does occur, it may not be of sufficient magnitude for the chart to produce an immediate alarm condition. If a special cause occurs, one can describe that cause by measuring the change in the mean and/or variance of the process in question. When those changes are quantified, it is possible to determine the out-of-control ARL for the chart.
It turns out that Shewhart charts are quite good at detecting large changes in the process mean or variance, as their out-of-control ARLs are fairly short in these cases. However, for smaller changes (such as a 1- or 2-sigma change in the mean), the Shewhart chart does not detect these changes efficiently. Other types of control charts have been developed, such as the EWMA chartIn quality control, the EWMA chart is a type of control chart used to monitor either variables or attributes-type data using the monitored process's entire history of output.
and the CUSUMCUSUM is a sequential analysis technique due to E. S. Page of the University of Cambridge. It is typically used for monitoring change detection. CUSUM was announced in Biometrika a few years after the publication of Wald's SPRT algorithm....
chart, which detect smaller changes more efficiently by making use of information from observations collected prior to the most recent data point.
Criticisms
Several authors have criticised the control chart on the grounds that it violates the likelihood principleIn statistics,the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a sample is contained in the likelihood function....
. However, the principle is itself controversial and supporters of control charts further argue that, in general, it is impossible to specify a likelihood functionIn statistics, the likelihood function is a function of the parameters of a statistical model that plays a key role in statistical inference....
for a process not in statistical control, especially where knowledge about the cause system of the process is weak.
Some authors have criticised the use of average run lengths (ARLs) for comparing control chart performance, because that average usually follows a geometric distributionIn probability theory and statistics, the geometric distribution is either of two discrete probability distributions:* The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...}...
, which has high variability and difficulties
Types of charts
! Chart
! Process observation
! Process observations relationships
! Process observations type
! Size of shift to detect>
| XbarR chart An X-bar/R chart is a specific member of a family of control charts. A control chart is a tool used in quality control, specifically SPC or statistical process control, as originally developed by Walter A...
|
Quality characteristic measurement within one subgroup |
Independent |
Variables |
Large (≥ 1.5σ) |
| XbarS chart An Xbar-S chart is a specific type of control chart that depicts the variability of average characteristics of a process over time when variables are collected in sub-groups. Xbar-S charts are generally employed for plotting variability of sub-groups with sizes greater than 10...
|
Quality characteristic measurement within one subgroup |
Independent |
Variables |
Large (≥ 1.5σ) |
| Shewhart individuals control chart In statistical process control, the individual/moving-range chart is a type of control chart used to monitor variables data for which it is impractical to use rational subgroups.
(ImR chart or XmR chart) |
Quality characteristic measurement for one observation |
Independent |
Variables |
Large (≥ 1.5σ) |
| Three-way chart |
Quality characteristic measurement within one subgroup |
Independent |
Variables |
Large (≥ 1.5σ) |
| p-chart In industrial statistics, the p-chart is a type of control chart that monitors the proportion of nonconforming units in a sample. The appropriate data for p-charts are attribute data...
|
Fraction nonconforming within one subgroup |
Independent |
Attributes |
Large (≥ 1.5σ) |
| np-chart In industrial statistics, the NP chart is a type of control chart that is very similar to the p-chart except that the statistic being plotted is a number count rather than a sample proportion of items. An NP Chart records the number of defective units found per sample when sample sizes are constant...
|
Number nonconforming within one subgroup |
Independent |
Attributes |
Large (≥ 1.5σ) |
| c-chart In industrial statistics, the c-chart is a type of control chart used to monitor "count"-type data, typically total number of nonconformities per unit.
|
Number of nonconformances within one subgroup |
Independent |
Attributes |
Large (≥ 1.5σ) |
| u-chart In industrial statistics, the u-chart is a type of control chart used to monitor "count"-type data where the sample size is greater than one, typically the average number of nonconformities per unit....
|
Nonconformances per unit within one subgroup |
Independent |
Attributes |
Large (≥ 1.5σ) |
| EWMA chart In quality control, the EWMA chart is a type of control chart used to monitor either variables or attributes-type data using the monitored process's entire history of output.
|
Exponentially weighted moving average of quality characteristic measurement within one subgroup |
Independent |
Attributes or variables |
Small (< 1.5σ) |
| CUSUM CUSUM is a sequential analysis technique due to E. S. Page of the University of Cambridge. It is typically used for monitoring change detection. CUSUM was announced in Biometrika a few years after the publication of Wald's SPRT algorithm....
chart |
Cumulative sum of quality characteristic measurement within one subgroup |
Independent |
Attributes or variables |
Small (< 1.5σ) |
| Time series In statistics, signal processing, and many other fields, a time series is a sequence of data points, measured typically at successive times, spaced at time intervals...
model |
Quality characteristic measurement within one subgroup |
Autocorrelated |
Attributes or variables |
N/A |
| Regression Control Chart |
Quality characteristic measurement within one subgroup |
Dependent of process control variables |
Variables |
Large (≥ 1.5σ) |
See also
- Common cause and special cause
Common- and special-causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. However, it can be argued that they were recognised and discussed as early as 1703 by Gottfried Leibniz and are...
- Analytic and enumerative statistical studies
In Some Theory of Sampling , W. Edwards Deming introduced concepts he labeled Analytic and enumerative statistical studies. In any statistical study the ultimate aim is to provide a rational basis for action. Enumerative and analytic studies differ by where the action is taken...
- W. Edwards Deming
William Edwards Deming was an American statistician, professor, author, lecturer, and consultant. Deming is widely credited with improving production in the United States during the Cold War, although he is perhaps best known for his work in Japan...
- Statistical process control
Statistical process control is an effective method of monitoring a process through the use of control charts. Control charts enable the use of objective criteria for distinguishing background variation from events of significance based on statistical techniques...
- Total Quality Management
Total quality management is a business management strategy aimed at embedding awareness of quality in all organizational processes...
- Six Sigma
Six Sigma is a business management strategy originally developed by Motorola. it enjoys widespread application in many sectors of industry, although its application is not without controversy....
- Process capability
A process is a unique combination of tools, materials, methods, and people engaged in producing a measurable output; for example a manufacturing line for machine parts...
External links
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