Calculating Process Average Targets for LSL (Lower Specification Limit) Only

[cleverfox]

I have many processes where there is only a lower spec limit. The process averages are close to the spec limit. My control limits are narrow and also too close to the spec limit. Many single points of data are below the limit.

I know that I have to have the process average adjusted away from the lower spec limit, but is there a mathematical way to calculate a target for the process average? I can do it with characteristics with both a lower and an upper spec limit, centered that is.

You may ask why do this? Because statistically many of our process averages and control limits are typically closer to one of the spec limits. I have an excel worksheet that graphs the data on X bar R charts and I want to show manufacturing where, graphically, their process should be running.

Thanks

[Mike S.]

I always preface my statistical advice by saying I'm no expert on this stuff. However, I'll take a stab since no one else has, FWIW.

I think you're after Cpl -- preferably it should be > 1.33 (higher the better, though). Cpl = (process average - LSL) / 3 sigma hat where sigma hat is rbar/d2

I think your answer is this question: Where should your process average be so that Cpl is > 1.33?

Make sense?

Anyone else?

[cleverfox]

Mike,

I am definately not an expert on SPC . However, I am not after the Cpl, at least not until I have more data. I am after something a little easier. Like I said above, I want to plot the actual process average (a straight dotted line on the x-bar chart) against the best possible or "target" process average.

The problem is that I am not sure how to calculate this to plot it on the chart which only has a lower spec limit.

I know how to do it for characteristics that have an upper and a lower spec limit.

I was hoping someone may have some idea or may have done this in the past and could explain it to me.

Not sure if I must determine for myself using my own judgement, or if there is a more sound way to do it.

Thanks though for taking a stab at it.

[Mike S.]

Perhaps I don't understand your need. Here's what I'm thinking with a simple made-up example.

Let's say your LSL is 10 (spec. >/= 10). Your control chart subgroup size is 5, process average is 12, and your r-bar (avg. of subgroup ranges) is 3, and so you have some points out of spec. (too low). You want to know where to tell the mfg. guys their process average should be so that, if the variation stays the same, they don't make bad parts.

Current Cpl = (12-10)/ 3.869 = 0.517 (not good)

If your process average was raised to 15.2 and the variation stayed the same, Cpl would be (15.2 - 10)/3.869 = 1.344, in which case you should have very few points out of spec. (many companies set > 1.33 as a target for Cpl or Cpk)

Of course, you could achieve fewer rejects by also lowering the variation in the process, but you say you want to change the process average. This is how I would calculate where that average should be.

[Ravi Khare]

To start with, you could move the setting by a distance that would give you a Cpl of 1.33.
On obtaining more samples, at this setting, you can perform the t-test to find out whether you are sufficiantly away from the LSL. If the different between the observed mean and the LSL comes out statistically significant in the t-test, you are safely away from the LSL. t-test works well for small samples.
At the risk of telling you what you already know, I would put down A few points to note.
1. The t-statistic has its own 'alfa' risk. So if you refer to a 5% alfa risk t-table your decision can go wrong 5% of the times.
2.Control charts denote stability, and not reflect on Quality. You can have a situation where a control chart shows all points within control limits, yet rejection at a substantial level. If you use subgroup sizes above 1, the assumption of normality of raw data too cannot be verified, since averages are automatically normally distributed by the virtue of the Central Limit Theorem. Control charts for one sided tolerances will have both the control limits.
3. I would suggest, Look at the Cpk(lower) and verify your adjustment using the t-test.

[Darius]

The use of Cpl sounds OK, but I tink that if there is a few data points you should take it in account to calculate the Cpl minimum estimated value (in my opinion CPK IS NOT A VALUE BUT A RANGE).

http://www.qualitydigest.com/may00/html/lastword.html

A must see article.

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There is also other way to se the situation, as PreControl, in the cale of one spec limit, the target can be specificated using "the best value" away from the limit. In many cases "the best value" is no other but the value farther from the limit.

[Bill Ryan]

Cleverfox

Do you have enough data to compute a standard deviation (sigma hat)?? If so, in order to maintain a Cpk of 1.33 you would need to have your process mean at 4 sigma away from the LSL (this is without going into all the "normality" discussions). That is the simplest "formula" I can think of. (If you wish to maintain a Cpk of 1.67 or 2.00, you're mean would need to be 5 or 6 (resp.) sigma from the LSL).

Hope that helps (although it may be too simplistic??)

Bill

[cleverfox]

Bill,

Your idea is simple, which is what I wanted. I do have enough data to calculate std deviation. I should have thought to reverse calculate from the desired 1.33.

Thanks