Natural process variation, sometimes just called process variation, is the
statistical
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industr ...
description of natural fluctuations in process outputs.
Equations
The following equations are used for an ''x''-bar-
control chart
Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1)
The hourly status is arranged on the graph, and the occurrence of abnormalit ...
:
:
:
In the example, with ''n'' = 10 samples, the targeted
mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set.
For a data set, the '' ari ...
,
, and
standard error
The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error ...
of the mean,
are:
:
:
That is, independent 10-sample means should themselves have a
standard deviation of 0.0316. It is natural that the means vary this much, for by the
central limit theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables thems ...
the means should have a
normal distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
:
f(x) = \frac e^
The parameter \mu i ...
, regardless of the distribution of the samples themselves.
The importance of knowing the natural process variation becomes clear when we apply
statistical process control
Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a production process. This helps to ensure that the process operates efficiently, producing ...
. In a stable process, the mean is on target; in the example, the target is the filling, set to 1 litre. The variation within the upper and lower
control limits
Process Window Index (PWI) is a statistical measure that quantifies the robustness of a manufacturing process, e.g. one which involves heating and cooling, known as a thermal process. In manufacturing industry, PWI values are used to calibrate th ...
(UCL and LCL) is considered the natural variation of the process.
Usage
When a sample average (size ''n'' = 10 in this case) is located outside the control limits, then this is an indication that the process is out of (statistical) control. To be more specific:
:The
Western Electric
The Western Electric Company was an American electrical engineering and manufacturing company officially founded in 1869. A wholly owned subsidiary of American Telephone & Telegraph for most of its lifespan, it served as the primary equipment ma ...
rules conclude that the process is out of control if:
:# One point plots outside the 3σ-limits (the UCL and LCL).
:# Two out of three consecutive points plot beyond a 2σ-limit.
:# Four out of five consecutive points plot at a distance of 1σ or beyond from the centerline.
:# Eight consecutive points plot on one side of the center line.
Goal
The most important goal of understanding the principle of natural
process variation
Natural process variation, sometimes just called process variation, is the statistical description of natural fluctuations in process outputs.
Equations
The following equations are used for an ''x''-bar-control chart:
:\bar x = \sum_^n x_i/n ...
is to consider the natural variance in the output before we make any changes to the process. Since
SPC
SPC may refer to:
Business and law
* Segregated Portfolio Company, a specialized form of offshore company
* Signature panel code, a credit or debit card security code
* Social Purpose Corporation, a company that considers social issues in its deci ...
tends to minimize the process variations in time, as we better understand the process and have more experience with running it, we try to reduce the variation of it. The knowledge of the principle of natural
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of number ...
helps us avoid making any unnecessary changes to the process, which might add variance to the process, instead of removing it.
References
* Douglas C. Montgomery, George C. Runger. ''Applied Statistics and Probability for Engineers, 4/e''. Wiley, 2006. {{ISBN, 978-0-471-74589-1.
An Introduction to Understanding Variation
Statistical process control