Hello,

I am developng a control chart that tracks warranty returns. Obviously, the desired level is "0". I would like the control chart to reflect this. Is there any way to set the LCL to ) in Minitab?

Thanks in advance.

George

I am developng a control chart that tracks warranty returns. Obviously, the desired level is "0". I would like the control chart to reflect this. Is there any way to set the LCL to ) in Minitab?

Thanks in advance.

George

Welcome to the Cove. :bigwave:
That would be the lower specification limit, not control limit, and you should be able to set the spec limit wherever you want it. The control limits are calculated from the input data.

The poster may have a point, I think Minitab sometimes calculates and displays a negative LCL. Although mathematically correct, it makes no sense in the real world. I think IMR charts do this?

I'll have to check when I get in to work, oddly enough as much as I love SPC, I don't have a copy of MiniTab here at home!

So now I'll ask an expert, does anyone know how to set CL breaks in Mintab?

True, if you are getting a negative LCL when negative numbers are not possible, there is no reason to display the negative LCL, or perhaps overide it to zero. But - you would need to keep in mind where one standard deviation below average and two standard deviations below average are in case you are using them as part of detection rules.

I assume the original question asker had a LCL greater than zero, but wanted to show the LCL at zero since that was the desired specification. As properly pointed out, that would not be a good idea. One reason why not is - let us say this is a counting of bad things happening chart (injuries, defects, events, etc). The fact that the LCL is greater than zero means that we need to be realistic and say by the current process that we will most likely have a non-zero rate. That doesn't make it good or bad, but we need to acknowledge what the process is currently capable of.

And, by realizing the LCL is greater than zero, we know that if we do receive a time interval with zero items counted, then something special has indeed happened, and we may have a basis for celebration. Unless of course the method by which we got to zero was we said - "The next person to report a bad thing gets fired".

Thanks to everone who replied. Yes, Minitab did produce a negative LCL, and zero is the lowest possible (we are measuring units returned for warranty credit).

This is receiving further discussion here. There is some concern that showing the process as being within control limits will cause some to believe the current level is acceptable (not true). We do not have an upper specification limit for returns. We are thinking of establishing a target, which would be less than the mean to explain the expectations.

G

Just wondering if using a proportion chart would be a better application here?

I can also hazard a guess that the lower bound at zero makes the data non-normal. In that case to display correctly on an I-MR chart you may want to transform the data to a normal distribution.

It also sounds like it is just binomial data, and whilst a binomial distribution can be applied to an I-MR chart, it should probably only be used where the distribution approximates a normal one.

Just wondering if using a proportion chart would be a better application here?

I can also hazard a guess that the lower bound at zero makes the data non-normal. In that case to display correctly on an I-MR chart you may want to transform the data to a normal distribution.

It also sounds like it is just binomial data, and whilst a binomial distribution can be applied to an I-MR chart, it should probably only be used where the distribution approximates a normal one.

Control charting will work regardless of the distribution. Dr. Shewhart documented the Tchebychev Inequality (see other discussions on the Cove about that) and tested control charting with the normal distribution, and two non-normal distributions. I-MR (and my preference, I-sigma) can be used effectively even if the distribution is non-normal.

If what is being plotted is indeed binomial (I can't tell from what has been posted so far), I would recommend going to the p-chart control chart.

I quite happily understand that Individuals charts work for non normal data. However the control limits are going to be in slightly odd places. At least for an individuals chart calculated this way.

This is then where you get a negative control limit.

Control charting will work regardless of the distribution. Dr. Shewhart documented the Tchebychev Inequality (see other discussions on the Cove about that) and tested control charting with the normal distribution, and two non-normal distributions. I-MR (and my preference, I-sigma) can be used effectively even if the distribution is non-normal.

If what is being plotted is indeed binomial (I can't tell from what has been posted so far), I would recommend going to the p-chart control chart.

I argee with it.

FROM:V.J.BRAHMAIAH
BANGALORE-INDIA

Control limits for spc control charts are not related to your desired tolerance limits.The LCL & UCL are strictly based on the actual process variation.A trial run of the stable process is a must to determin the control limits.
No manipulation OF CONTROL LIMITS is permIted in an SPC CHART.

V.J.BRAHMAIAH :agree:

I quite happily understand that Individuals charts work for non normal data. However the control limits are going to be in slightly odd places. At least for an individuals chart calculated this way.

This is then where you get a negative control limit.

In Minitab you can change the lower boundary to requested limit bound.
I'm attaching the view of the option and two charts - one with "zero" enabled and one without boundary specification.

Hope this helps

:)

Dave

That is one way of handling the lower bound going below zero.
Problem is even though I-MR charts can work with non normal data, I will stick my neck out and say it isnt the most appropriate chart to use.
Certainly if the data is binomial, and your expected number of defectives is low then your better using the proportion chart.

If you are using the I-MR you do have to understand that your risk of finding a point outside of the limits changes.
With a normal distribution a proportion of 0.00135 is expected outside of 3 standard deviations.

Now I simulated a lognormal distribution with location 0 scale 1. This would give if fitted with a normal distribution a mean of 1.6269 and a standard deviation of 2. Plus 3 standard deviations is at 7.6269. The proportion above 7.6269 on the lognormal distribution is 0.0211.

Very roughly speaking your going from expecting 1 point in every thousand above the upper control limit to 2 parts in every hundred.
If you take the test for two points out of 3 more than 2 standard deviations from the mean as an example.

On the upper side we would expect 0.0228 more than 2 std dev away in a normal distribution. Which works out as roughly a 0.0015 chance of happening randomly.
Whereas if the data follows the lognormal, we would expect 0.042 above 2 standard deviations. Which roughly works out as 0.00507 chance of seeing 2 out of 3 points more than 2 standard deviations from the mean on the upper side.

Now test 2 works out quite nicely, 9 points in a row on the same side of the centre line. Has a probability of 0.0039 (2*0.05^9)
The lognormal distribution above has 0.313 above 1.6269, and 0.687 below.
The prob of this then, check this for correctness, I think should be 0.313^9 + 0.687^9.
Thats 0.000029 + 0.03409. Roughly speaking we go from an event likely to happen just under 4 times in a thousand to just under 3 and a half times in a hundred.

Surely the danger here is if the person viewing the chart is unaware of the fact that random data can flag up a test sooner.
The other issue is surely if you have all 8 tests in Minitab switched on the overall chance of seeing any test broken in a group rapidly increases.

I will agree that you can use an I-MR chart, but you must be aware how it changes the probabilities of common cause variation flagging up as special cause. If not you could end up chasing a lot of noise for a reason.

For the 2 out of 3 points I worked this out using a probability tree.

0
/ \
/ \
.9772 0.0228

There are three places with 2 points above 2 std devs, and one below. 3 * 0.0228^2 * .9772.
Plus one point with three points more than 2 std devs away on one side. 0.0228^3

Do the same for the lognormal distribution.
3* 0.042^2 *0.958 + 0.042^3