Process capability Analysis
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 This topic has 8 replies, 6 voices, and was last updated 16 years, 9 months ago by Joseph Banerjee.

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April 15, 2005 at 2:28 pm #39041
How to calculate the process capability if my data follows a lognormal /exponential distribution.
0April 15, 2005 at 2:46 pm #117840Do you really need to report the capability indexes? My suggestion is twofold:
1) Plot your data on a control chart and make sure everything is hunkydory; they don’t care if you’re “normal” or not
2) Make a histogram of your data and plot the upper & lower spec limits on this graph; no stats, just a visual
If everything is in control, the histogram will show you where your process sits relative to specs, how close you are to the nearest spec, how you should shift the process or decrease variation, etc. Isn’t this everything you need to know anyway?
0April 15, 2005 at 2:58 pm #117843Do you really need to report the capability indexes? My suggestion is twofold:
I would say yes, you do. At least report the Z value… As this quantifies your defect rate baseline. Hard to get an estimation of the defect rate from a picture alone… sample size is a huge factor that is hard to see in a histogram.
1) Plot your data on a control chart and make sure everything is hunkydory; they don’t care if you’re “normal” or not
Who doesn’t care if it’s normal or not??? Your MBB should. Normality is a critical thing, and will effect your estimates of capability.
2) Make a histogram of your data and plot the upper & lower spec limits on this graph; no stats, just a visual
I agree this will give you a visual picture of the problem but, the reason to report the capability stats is so you can quantify the defect rate / which quantifies the cost associated with the problem.
If everything is in control, the histogram will show you where your process sits relative to specs, how close you are to the nearest spec, how you should shift the process or decrease variation, etc. Isn’t this everything you need to know anyway? I think you are confusing “control” with “capability” they are two different things. Very hard to determine “control” from a histogram.0April 15, 2005 at 3:12 pm #117847I don’t wanna fight today, so here’s my nice responses:
1) Z values only apply to normal distributions; this isn’t normal
2) Control charts are robust to nonnormal data sets; OOC points are signals of unexpected variation, regardless of distribution type
3) Anyone who spouts off % defective, PPM, or cost of repair from a capability study is delusional; the resolution just doesn’t exist; if you want to know the cost, go count the number of parts in the scrap pile – there’s some real data!
5) You determine control from the control chart (hence the name); the histogram shows where your process sits relative to specs and has absolutely no statistics involved
6) If you made the histogram, you should know how many samples are in it!
Capability anaysis lets you look at the spec width versus the process in terms of process variation. If you’re telling me just reporting a Cp and Cpk (heaven forbid we start talking about Pp and Ppk) give you more process insight than this method, them’s fightin’ words!0April 15, 2005 at 3:16 pm #117848
facemanParticipant@faceman Include @faceman in your post and this person will
be notified via email.I would say yes, you do. At least report the Z value… As this quantifies your defect rate baseline. Hard to get an estimation of the defect rate from a picture alone… sample size is a huge factor that is hard to see in a histogram.
For this part you could get the parameters of the lognormal / exponential distribution that characterizes your process and the use that distributional assumption to caluclate the expected proportion outside the tolerance limits both tolerance limits and subtract that from one. You could then run that through the cumulative normal distribution (mean = 0, sd = 1) and you should have your Z score.
I think that should work if you don’t want to impose an assumption of normality. With something like minitab it shouldn’t take more than a couple of minutes.
Regards,
faceman0April 15, 2005 at 3:34 pm #117851Don’t think of it as “Z” – think of it as the distance from the process mean to the nearest spec. From your histogram, you know where your process mean is, you know which spec you’re closest to, and your range chart estimates sigma – figure out what this distance is in sigma units, and there’s your “score”.
Sample size is an issue whether the data is normal or not; what does that have to do with anything?
Go pick up Understanding Statistical Process Control by Wheeler. It has the details on all the topics I’m spouting. One reason I love this book is you don’t find too many statisticians who preach common sense more than stat! Wheeler didn’t really invent any tools, just good ways of explaining and analyzing them…
0April 15, 2005 at 4:11 pm #117859
Been There, Done ThatParticipant@BeenThere,DoneThat Include @BeenThere,DoneThat in your post and this person will
be notified via email.Joe:
There are all kinds of reasons why your data may follow a nonnormal distribution. Please check to see if you have overlapping or multiple processes first. If the data is too chunky because of the resolution of the gage, then it may look bellshaped, but still fail the AndersonDarling test of normality. If you have a rat’s breakfast of a mixture of processes, then turn the whole dataset into discrete data and count defect/nondefect. That is a robust way of reporting if your MBB has a check box for your reportout.
Caution – do not proceed unless you are sure you have a continuous, single nonnormal distribution.
There are times when your data is and must be nonnormal.
– Interarrival times are Weibull (special case of exponential)
– inventory and sales data are lognormal
– the number of paint defects per unit area are Poisson(?)
– the eccentricity of a hole is Rayleigh distributed.If you really know that you have a single, homogeneous process generating nonnormal data, then transform the entire set (including the spec limits) to normality and report the process capability based on the transformed data and spec limits.
For example, we did this for the particle count of hazardous material in a manufacturing plant. We transformed the particle count/unit area and the upper specification limit requiring for OHSA reporting. This had the extra advantage that we could use the usual statistical tools to test for difference of means and variance between two different configurations of fume hoods over the pelleting machine.
We have done similar things for financial processes.
BTDT0April 15, 2005 at 4:24 pm #117862Hmmm.. Ok, thanks for the nice responses! Pleasure discussing this with you! I agree all that matters is the control chart, and the histogram, everything else is useless in helping to undertand your process.
0April 15, 2005 at 4:31 pm #117864
Joseph BanerjeeParticipant@JosephBanerjee Include @JosephBanerjee in your post and this person will
be notified via email.Hi Been ,
Thankyou for the response i think it makes more sense to transform the data and use the process capability.
Thankyou people for your suggestions.
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