XBar R Charts
Six Sigma – iSixSigma › Forums › Old Forums › General › XBar R Charts
 This topic has 6 replies, 4 voices, and was last updated 14 years, 3 months ago by Almudena.

AuthorPosts

June 26, 2008 at 6:58 pm #50408
AlmudenaParticipant@Almudena Include @Almudena in your post and this person will
be notified via email.I have a destructive testing on the line and we took 3 piece sample, plot the average and range in an XBar R Chart to monitor weldstrength. The individual readings do not follow a normal distribution.
The process is incontrol, based on this fact we compute the Cpk however one of our managers challenge its validity because the distribution of the individual readings is not normal…
Our response was that that was the purpose of the central limit theorem, and that based upon the central limit theorem we could use the averages and ranges from the control chart to estimate the Cpk value.
What is wrong with the inference?
I would appreciate any comments and/or references.
Thanks
Almudena0June 27, 2008 at 1:27 am #173288
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.Hi.
I see several things wrong. First, you say that the process is in control because you compute the CpK…the two concepts of capability and control can’t be tied together through the capability index. Control indicates a stable process, while capability indicates that the specification can be met to some degree.
Second, the central limit theorem states that averages will be approximately normally idstributed regardless of the distribution of the individual observations. I don’t see how that relates to your problem at all.
Your manager is correct. CpK has an underlying assumprtion of normaility. My guess is that your data is skewed right. Since you are probably dealing with a singlesided specification, you should calculate the CpL (lower side of CpK) based on the individuals, not the average and range.
I am sure other people will elaborate more on this.0June 27, 2008 at 11:10 am #173295Normality IS NOT A REQUIREMENT when using Shewhart control Charts…This thought trail was misapplied in GE and somehow escaped into the general community.
Please help putting a stop to this falsehood.
Thanks0June 27, 2008 at 12:48 pm #173301
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.Ron, how does this comment (which is correct) apply to the question? Control charts work for any shape distribution, but the CpK is based on a normal distribution. Some software packages calculate it somehow. I have no idea what they use.
0June 27, 2008 at 1:33 pm #173303I generally agree with Michael.
One note is that you will never, I mean never, have a distribution that is perfectly normally distributed. The idea is that if your distribution somewhat resembles the bell curve, calculate things like Cpk in the usual fashion. So, if your distribution is significantly different from the normal, you might tell the software you are using to “Assume distribution is not normally distributed.”0June 27, 2008 at 4:55 pm #173306There is no correlation between constructing a control chart (Xbar &R) and Cpk. These are two very different concepts.
Cpk refers to the centering of a process around specification limits. Control Charts refer to Statistical Control Limits and represent the voice of the process.
Central limit theorem does not come into the discussion when referring to control charts. It does come into the discussion of Nortmailty which as previously stated is out of scope for control charts but germane to process capability.
So to answer your question since you asked two of them.
Normailty not required for control charts
Is required for process Cp calculations to be valid.0June 29, 2008 at 4:01 am #173334
AlmudenaParticipant@Almudena Include @Almudena in your post and this person will
be notified via email.Thank you Michael and Ron for your help, now I have a better undestanding of these concepts.
Regards,
Almudena0 
AuthorPosts
The forum ‘General’ is closed to new topics and replies.