Does the data in a control chart have to be normally distributed?

Tim Folkerts

Super Moderator
#21
Steve,

Now you made me go and think :mad:

Seriously, as you point out, there is a big danger of people over-interpreting "false positives" (specifically, being outside the 3 sigma limits) from control charts. :agree1: I have come to realize this evening that the odds of a false positive with an individual x chart can vary from about 10% down to exactly zero, depending on the distribution. The one advantage of having a normal distribution (or forcing a normal distribution by averaging seveal data points ala the central limit theorem) is that you have a pretty good idea of the odds of a false positive are close to 0.3%. That's not a great number, but it is at least it is known.

If the data is not normal, that throws the probabilities out the window. I can come up with distributions that have some basis in reality that will produce an individual x chart that vary anywhere from
* 10% of the data fall outside the 3 sigma limits (the worst-case Tchebychev limit)
* all of the data are within the 3 sigma limits (or even all of it withinin 1 sigma limits!)

The bottom line is that for individual x charts the odds of a "false positive" range anywhere from 10% (bad) down to exactly 0% (great). If people are worried about a 0.3% chance of false positive, imagine what they would think of a 10% chance! On the other hand, imagine the calm if they knew there was essentially 0% chance of a false positive.

I see the normal distribution as a happy medium. The odds of a false positive are not zero, but they aer sure to be small.



Tim

P.S. As I think a little more, averaging data makes bad distributions better (from 10% down toward 0.3%) and makes good distribution worse (from exactly 0% up toward 0.3%). I'm thinking there is a "best" number of data points to average - somewhere around three. The good distributions are still guaranteed to be within the 3 sigma limits, but the bad distributions have dropped close to 0.3%. But then, I haven't even thought about the range part of the charts!
 
Elsmar Forum Sponsor
D

dfirka

#22
Steve,

Sorry, let me explain myself a little bit more. Yes, Shewhart originally based his conclusions on experimental data and the Camp-Meidell theorem (extension to Tchebicheff Inequality). Shewhart's point of view, shared by no less than Dr. Wheeler (1) , is that we should not restrict control charts to normal distributions, or force averaging when we have non-normality.

Averaging a distribution, as Tim pointed out and according to the Central Limit Theorem, will create a distribution for means that tends to normality, so the probability of special causes will tend to 0.3 % as we increase sample size. Camp-Meidell covers 1/(2.25k^2) , so about 5%.

Regarding sensitivity, one argument is that averaging will give you more sensitivity to shifts in the mean of the distribution (the control limits for averages are closer to the mean than those for individual values, so a slight departure from the mean will produce a special signal faster on the graph)

I think another (maybe excesively fine) point is that Camp-Meidell requires an unimodal distribution, so is more restricting that CLT, which only requires that the first two moments should exist.

So when I see the data of my process very skewed, I feel more comfortable using averages, if possible.

I'm not statistician, so pls take this as an informed opinion.
Daniel

(1) Wheeler, D. J. (1995). Advanced Topics in Statistical Process Control, and
http://www.qualitydigest.com/sep96/spctool.html (mith 2)
 
B

bhandari80

#23
Re: XS chart for a subgroup size 25

Dear All,

Please help me out , i m trying to plot XS chart for Manufactured part
having 25 variable critical dimensions , is it posible to plot all the
25 dimensions in single XS chart taking subgroup size 25.

warm regards
:truce:MSB
 
A

Allattar

#24
Re: XS chart for a subgroup size 25

25 dimensions on one part, is that right?
If so it would not make sense to use the subgroup size as 25, it may make more sense to try and use a multivariate control chart instead of the XBar S becuase you are trying to visualise simultaneous control across multiple dimensions.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#25
Re: XS chart for a subgroup size 25

Dear All,

Please help me out , i m trying to plot XS chart for Manufactured part
having 25 variable critical dimensions , is it posible to plot all the
25 dimensions in single XS chart taking subgroup size 25.

warm regards
:truce:MSB

It is possible. You could do some form of difference between the specification and the measurement and sum that up in a chi square type calculation, or look a T-square http://en.wikipedia.org/wiki/Hotelling's_T-square_distribution. You do lose a lot of information by collapsing the data into one number, however.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#27
Yes, calculation of Cpk assumes normality. However, in case of non-normal data, you can use some transforms (Box-Cox, Pearson etc) to convert and 'normalize' the data.

Also see:
http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm
I rarely recommend using transformations, as they mask information found in the original distribution. When possible, it is best to analyze the original distribution directly. I find transformations are typically useful for "normalcentrics" that simply cannot handle data unless it is in a normal form. Any port in a storm - but not a good port...:cool:
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#28
Re: XS chart for a subgroup size 25

Dear All,

Please help me out , i m trying to plot XS chart for Manufactured part
having 25 variable critical dimensions , is it posible to plot all the
25 dimensions in single XS chart taking subgroup size 25.

warm regards
:truce:MSB
What kind of process is it? Knowing that makes a HUGE difference in the answer.:cool:
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#29
The act of control charting (per Dr. Shewhart originally) is not dependent upon the normal distribution. .
I agree, normality is not a criteria for control charting. But, it is an issue with picking control chart methodology. Using X-bar-R and its associated calculations for control limits (as well as the complete list of Western Electric Rules) is guaranteed to frustrate anyone implementing control charting for precision machining. Is also guarantees overcontrol. It is absolutely the worst methodology for controlling precision machining (defined as processes where the most significant process variation is from tool wear.)

But, there is a correct way to control chart - and it assures zero defects (with exception of special causes, such as broken tools).

In fact, it you see a normal distribution for a precision machining process (in lengths and diameters), it virtually assures that the process is out of control.

So yes, I absolutely agree that you can control chart without normality - but not necessarily the same way you would with normality.:cool:
 
L

Laura M

#30
But you need to know the process is 'in control' before establishing the control limits, regardless of the type of control chart. Knowing the distribution can help establish that. X-bar does help stablize a non-normal distribution because the averages tend to be normally distributed, even if the individual distribution is not. (Central limit theorem)

You need to know something about the process before just putting a control chart on it, including whether or not the process is in control or stable.

Trend charts have been used successfully for tool wear.
 
Thread starter Similar threads Forum Replies Date
H Does Powerway's APQP - PPAP fulfill TS16949 document and data control requirements? Customer and Company Specific Requirements 2
L How to evaluate the process capability of a data set that is non-normal (cannot be transformed and does not fit any known distribution)? Capability, Accuracy and Stability - Processes, Machines, etc. 12
I 510k Performance Testing Studies (Raw Data) - What does the FDA expect 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 4
shimonv Does 510(k) submission need to include UDI Data Other US Medical Device Regulations 6
S Does anyone know what a healthcare GDSN data pool actually looks like? Hospitals, Clinics & other Health Care Providers 2
M Does anyone here have experience implementing PCI DSS (Data Security Standard) IEC 27001 - Information Security Management Systems (ISMS) 10
K What does Data Logger Accuracy = ? 0.25% of Full scale ? 1 Digit Mean? General Measurement Device and Calibration Topics 4
C Who does the Analysis of Nonconformances and other Data Analysis? Nonconformance and Corrective Action 23
E Does anyone have a P-chart template for operator data collection? Statistical Analysis Tools, Techniques and SPC 1
I 510k Approval - Does the FDA look for Clinical Data 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 4
P Plug Gage Calibration Report does not include actual data - ISO 9001:2000 section 7.6 General Measurement Device and Calibration Topics 3
J Fitting an Equation to a set of data? Does minitab have the capability? Using Minitab Software 4
D Ppk Sampling Method - Does data for Ppk have to been continuous? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
B Calibration Certificates - Does 17025 require that all 'As Found' data be recorded? ISO 17025 related Discussions 7
D ISO 9001 - Gigantic waste or Beneficial? Why does ISO 9001 exist? Got data/facts? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 235
G Gloss Fade - Does anyone have any data on the fade of gloss on wood? Manufacturing and Related Processes 1
D Number of Distinct Data Categories:nDC: Where does the constant 1.41 come from? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
lanley liao Does all of the suppliers need to integrated into the supplier list qualified of the company? Oil and Gas Industry Standards and Regulations 2
0 To which part of 13485 does this refer? ISO 13485:2016 - Medical Device Quality Management Systems 3
A Medical Device Contract Manufacturer - Does the CM need to register with FDA? 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 3
J Records Control - Does each individual record need to be numbered? Records and Data - Quality, Legal and Other Evidence 2
lanley liao Does the customer`s trademark belong to customer-supplied property? Oil and Gas Industry Standards and Regulations 2
H How does a gas turbine work on diesel fuel? Oil and Gas Industry Standards and Regulations 12
G What does performance specification include? US Food and Drug Administration (FDA) 1
W Where does a coatings and paint company fall in IATF? IATF 16949 - Automotive Quality Systems Standard 5
A How much does a complete biocompatibility test package cost? Other ISO and International Standards and European Regulations 1
B Does anybody know how to get older versions of Minitab to work in Windows 10? Quality Tools, Improvement and Analysis 9
M Does the ISO 9001:2015 standard require a disaster recovery plan or emergency response plan ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 16
C Does an accessory need an IFU if it use is discussed in the Parent device IFU? 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 5
S How long does it take to register a product with MHRA? UK Medical Device Regulations 3
M Quality Manual - Where does Revision History Section go? Document Control Systems, Procedures, Forms and Templates 8
U Does *anyone* know a lab that will test to EN 455-4 Medical Gloves shelf life determination? EU Medical Device Regulations 1
A Brexit When does the UK responsible person need to be in place? UK Medical Device Regulations 10
M How does IEC-60601-1 apply to a non-medical device in the patient vicinity? IEC 60601 - Medical Electrical Equipment Safety Standards Series 1
N Does anyone have experience of GB/T 34986-2017? China Medical Device Regulations 1
Z Does anyone have experience with EN ISO 17664 ? IEC 62366 - Medical Device Usability Engineering 9
F Does anyone have an ESD quality/cooler talk to share? Training - Internal, External, Online and Distance Learning 4
A What does this line from MDCG 2020-3 (MDR art. 120 substantial change) mean to you? EU Medical Device Regulations 4
D Change Approval Requirements - Does every change need formal customer approval? Design and Development of Products and Processes 17
T What does AS9100 mean when it says you must establish a process to do X? AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 24
L Does a backdate form format can be changed if wrong revision is used? Document Control Systems, Procedures, Forms and Templates 8
B General Motors and Honda Alliance - What does this mean to suppliers? IATF 16949 - Automotive Quality Systems Standard 3
C ISO 13485 :2016 - CAPA - Does every CAPA need to be checked by regulations? ISO 13485:2016 - Medical Device Quality Management Systems 9
A Does ISO 9001:2015 cover all the requirements of ISO 10012:2003? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 6
N FDA UDI - Label vs. Labeling - Does the insert need to include UDI? Other US Medical Device Regulations 1
A Does anyone have a checklist of API Spec 650 13th Edition? Oil and Gas Industry Standards and Regulations 0
D Does Manufacture can submit CE mark application under MDD with NB for his New product after May 2020? EU Medical Device Regulations 3
A What does this sentence "this symbol shall be used in the orientation shown" mean in ISO 780:2015? Other Medical Device Related Standards 4
L Turkish Requirements - Does the Software need to be translated? CE Marking (Conformité Européene) / CB Scheme 2
R Where does IATF 16949 address Process mapping? IATF 16949 - Automotive Quality Systems Standard 3

Similar threads

Top Bottom