SPC Software - Graphical Presentation & p-chart LCL formula

I am working with a developer who is working on a SPC software development project. I received the following explanation on Xbar R charts from him which states:

"This is a combination of 2 graphs that are lined up atop one another. The Range graph is on top, as it is the most important of the 2 graphs, and the X-Bar graph is shown directly below the R graph".

and

"The difference between what we currently offer with the INDIVIDUAL chart and an XBAR-R chart, is that both the XBAR and R charts are shown atop one another".

I have never seen a Xbar R chart with the range on top. Is this becoming more common? Comments on the two statements?

One other question: Is the following calculation correct for the LCL on a p-Chart? LCLp = MAX(0,pBar - (3 * (SQRT((pBar*(1-pBar) / nj)))
pBar is the Average Percent and nj is the sample size per sample.

I, in my limited experience, have not seen the calculation expressed in this manner.

Thank you in advance for your response.

war-eagle said:

I am working with a developer who is working on a SPC software development project. I received the following explanation on Xbar R charts from him which states:

"This is a combination of 2 graphs that are lined up atop one another. The Range graph is on top, as it is the most important of the 2 graphs, and the X-Bar graph is shown directly below the R graph".

and

"The difference between what we currently offer with the INDIVIDUAL chart and an XBAR-R chart, is that both the XBAR and R charts are shown atop one another".

I have never seen a Xbar R chart with the range on top. Is this becoming more common? Comments on the two statements?

Thank you in advance for your response.

Click to expand...

I have not seen this approach with an X-bar/R chart, but the X hi/lo-R chart does show the range in the X chart area, but still has a separate chart to evaluate the Range values against the UCL for the range. This chart is used for precision machining, where the X-barR and X-MR charts are ineffective...actually, they are simply wrong...:mg:

See Statistical process control for precision machining for more information on the X hi/lo-R chart.

The developer doesn't know what he's talking about.
The Range chart is not the most important chart - they are both of equal importance as they graph two seprate components of variation. The convention has been and still is that the Average chart goes on top. I have never seen it any other way. However, there is no violation of a law of physics if the positions are reversed. The only dilemma is that because of the conventional display protocol people who look at a different protocol may be easily confused as they would expect the average chart to be on top.

Not sure exactly what part of the LCL formual you are concerned about so I'll address the two most likely parts:

1. The logical format you presented for a p chart is fairly typical as you can't have less than 0 defects. So the p chart is correctly truncated at zero when the mathematical calculation yields a negative Lower Control Limit.
2. Correcting the control limits for each subgroup for it's variable sample size (nj) should be done when variable sizes are used and that is the correct formula for doing so.

I'd lean towards the statement that the Range is more important that the xbar chart. This is documented in Acheson Duncan's Quality Control and Industrial Statistics. The reason I believe Range is more important is that the Range chart must be stable and in control before the control limits on the xbar chart have any meaning. So, if I had to choose putting the Range on top in a presentation or the xbar chart, I'd choose putting the Range on top.

The pchart formula does appear to be correct.

perhaps it's semantics. It's true during the limit calculation period, that unless the within subgroup variation is stable, the between subgroup calculations are not 'correct'. However to say that one chart is 'more important' than another to me means that we could do without the less important chart. yes there is a precedent - subsequent relationship to calculating the limits and judging that they are useful for asssessing future results, but that while determining the limits not while using the limits. The Range chart does not provide all of the information necessary to assess control once limits have been set. And a loss of control in the Range is not "more harmful" than a loss of control in the average. In fact either chart can indicate a loss of control while the other chart is perfectly stable. You need both to assess control.

I guess I'd ask if you've ever put the Range chart on top of the Xbar chart in your presentations? (which was the OPs first question) I've never seen it done it that way. (not that it can't be, just that the typical style is Xbar on top...)