This article is about natural fluctuations in statistical processes. For process variation in semiconductor fabrication, see Process variation (semiconductor).
The following equations are used for an x-bar-control chart:
In the example, with n = 10 samples, the targeted mean, , and 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 the means should have a normal distribution, regardless of the distribution of the samples themselves.
The importance of knowing the natural process variation becomes clear when we apply statistical process control. 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 (UCL and LCL) is considered the natural variation of the process.
Usageedit
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 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.
Goaledit
The most important goal of understanding the principle of natural process variation is to consider the natural variance in the output before we make any changes to the process. Since SPC 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 helps us avoid making any unnecessary changes to the process, which might add variance to the process, instead of removing it.
Referencesedit
Douglas C. Montgomery, George C. Runger. Applied Statistics and Probability for Engineers, 4/e. Wiley, 2006. ISBN978-0-471-74589-1.
An Introduction to Understanding Variation
Respecting Natural Variation
April 12, 2024
natural, process, variation, this, article, about, natural, fluctuations, statistical, processes, process, variation, semiconductor, fabrication, process, variation, semiconductor, this, article, includes, list, references, related, reading, external, links, s. This article is about natural fluctuations in statistical processes For process variation in semiconductor fabrication see Process variation semiconductor This article includes a list of references related reading or external links but its sources remain unclear because it lacks inline citations Please help improve this article by introducing more precise citations April 2009 Learn how and when to remove this template message Natural process variation sometimes just called process variation is the statistical description of natural fluctuations in process outputs Contents 1 Equations 2 Usage 3 Goal 4 ReferencesEquations editThe following equations are used for an x bar control chart x i 1nxi n displaystyle bar x sum i 1 n x i n nbsp sx s n displaystyle sigma bar x sigma sqrt n nbsp In the example with n 10 samples the targeted mean x displaystyle bar x nbsp and standard error of the mean sx displaystyle sigma bar x nbsp are x 1 displaystyle bar x 1 nbsp sx 0 1 10 0 0316 displaystyle sigma bar x 0 1 sqrt 1 0 0 0316 nbsp 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 the means should have a normal distribution regardless of the distribution of the samples themselves The importance of knowing the natural process variation becomes clear when we apply statistical process control 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 UCL and LCL is considered the natural variation of the process Usage editWhen 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 rules conclude that the process is out of control if One point plots outside the 3s limits the UCL and LCL Two out of three consecutive points plot beyond a 2s limit Four out of five consecutive points plot at a distance of 1s or beyond from the centerline Eight consecutive points plot on one side of the center line Goal editThe most important goal of understanding the principle of natural process variation is to consider the natural variance in the output before we make any changes to the process Since SPC 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 helps us avoid making any unnecessary changes to the process which might add variance to the process instead of removing it References editDouglas 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 Respecting Natural Variation Retrieved from https en wikipedia org w index php title Natural process variation amp oldid 792274400, wikipedia, wiki, book, books, library,
