I charts
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 This topic has 4 replies, 4 voices, and was last updated 18 years, 10 months ago by Gabriel.

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July 24, 2003 at 8:04 pm #32877
I have a question regarding control charts (specifically individual charts) I just ran one in minitab and came up with a negative LCL. How can this be since the value I am measuring is wait time. Also I have been told not to compare contol limits with specification limits but when everytime I run an individuals chart the UCL and LCL ranges are so wide that it looks like the process is in control even though logically it is not. Is it possible to put in the USL and LSL which I feel give a better indication if the process is in control? Thanks.
0July 24, 2003 at 8:16 pm #88306There is a big difference between “in spec” and “in control”. Being in spec doesn’t say anything about whether or not you are in control because spec limits can be arbitrarily placed. Being in control doesn’t tell you anything about whether you are in spec because the control limits are calculated independently of the specs. Besides, being in control is a good thing. It means that you can start to apply other six sigma tools, most of which should not be applied to out of control processes. Don’t confuse the two ideas of “in spec” and “in control”. My guess is that your process is logically out of spec, so you think your control chart should reflect that. But control charts are not telling you anything about how you are in relation to specs. That’s what capability analysis is for.
0July 24, 2003 at 8:26 pm #88307Also please note that you can (and should in your case) set the lower sigma bound at 0. It is clear that your elapsed time can never be less than zero.
Minitab in particular has a function within the Individuals menu to allow you to set this limit.0July 24, 2003 at 8:42 pm #88308Zilgo,
Thanks for the help.0July 24, 2003 at 9:12 pm #88309
GabrielParticipant@Gabriel Include @Gabriel in your post and this person will
be notified via email.About your first point: The standard way of calculating the control limits is +/ 3 sigmas of the charted parameter (in your case, individual values). In the normal distribution, that represents about 99.7% of the population. But the normal distribution is infinte to both sides. Many distributions are not infinite towards one or both sides. Your distribution can not be normally distributed since you have zero as a natural bound, and hence it is not infinite to the negative side.
Does it means that you cannot use these limits? No, it doesn’t mean that. After all, no process is actually normally distributed. Some are closer from normal, and some are farther. Which is the limit up to which these limits can be used despite of the lack of normality? I don’t know. Many people may tell you that if you reject normality with a normality test, then you shouldn’t use the standard +/3 sigma limits. I do not agree. Since no process is perfectly normal, give me enough data and I will rejcet normality for any process. Some will tell you that when you have a physical bound then you should use lognormal. Come on, all processes have a physical bound, closer or farther from the process average. You can’t turn a diamter to less than zero inches! It’s true that when the bound is close from the average, the distribution can be pretty nonnormal. But once again, how close is close?
Take for example the charts for ranges (R), standard deviation (s), defective rates (p). These parameters are always positive, and their distributions are clearly not normal. Yet, they use the standard +/3 sigma limits. How do they deal with lower limits that are negative if the charted value can never be negative? It is solved saying “If the LCL is negative then the LCL does not exist or is defaulted to zero”. In the practice, using the negative value, zero or no limit at all is the same thing. No point will fall below the LCL.
Do not despise this chart because of that. You lost the “below LCL” signal, but you still have a lot of other signals that can help you identify and eliminate special causes of variation.
Do I mean that the +/3 sigma limits can ALLWAYS be used despite the distribution shape. I wish I could say that, but I can’t. May be for some extreme distribution using +/3 sigma limits will give more problems than solutions. But I have to see such a case yet. I have used the +/3 sigma limits for distributions that I knew they were not normal and I didn’t found problems with that. But from that to saying that they can allways be used for any not notmal distribution there is a long way. And in your case? I don’t know. I would try to use the standard control limits and see how it works. Most probably, it will work fine.
About your second point: Mmmm… This seems to be yet another case of mixing stabilty with capability, let’s see. How on Earth do you get to conclude that your process is clearly out of control if from the chart it looks like it is in control? You should listen to that who told you not to mix specifications with control charts.0 
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