# Control charts where the center line is a trend or slope?

#### bobdoering

##### Stop X-bar/R Madness!!
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We can agree to disagree.

That is true.

If measurement error is an issue, then multiple readings of the same part can minimize that effect.

Exactly, that is the technique employed in the X hi/lo –R chart.

The MSE from regression incorporates the inherent variability at any given time point.

Gage error always needs to be made statistically insignificant to not mask the process error. It is mandatory. But, gage error and measurement error are two different things. Measurement error is using a perfectly good gage incorrectly, such as measuring one diameter to represent an infinite number of diameters found in a circular feature.

The slope and intercept should give me the overall trend.

When prepared correctly – which is better with the X hi/lo chart since it removes the measurement error – the slope provides the tool wear rate. That is handy, but does not provide the more critical information an operator needs to control the process: when to make an adjustment so that no diameters are out of control (X hi/lo chart) and when to change the tool (the r chart is the leading indicator for the need to change a tool, as the range increases as the tool moves from cutting to burnishing.)

#### Statistical Steven

##### Statistician
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That is handy, but does not provide the more critical information an operator needs to control the process: when to make an adjustment so that no diameters are out of control (X hi/lo chart) and when to change the tool (the r chart is the leading indicator for the need to change a tool, as the range increases as the tool moves from cutting to burnishing.)

I would argue that using tolerance intervals on the regression curve and setting a threshold can be effective in determining when to replace the tool.

But I think BOTH methods provide vital information that when used correctly can help to control the process.

#### bobdoering

##### Stop X-bar/R Madness!!
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I would argue that using tolerance intervals on the regression curve and setting a threshold can be effective in determining when to replace the tool.

Data shows that the change in roundness is a better leading indicator. Its variance is buried in other lesser variances about the trend curve that hold little bearing on the tool wear. It is all defined in the Total Variance Equation, if one prepares it conscientiously.

Exactly, that is why they need to be directed not to adjust until the the need to (as in approaching but not exceeding the specification, and, yes, you NEED to then). If one just waits for an adjustment based on some odd special cause condition that exceeds the control limits about the trend line, the trend can easily continue past the specification - primarily because those limits do not relate to the trend itself - just the "noise" about it.

But I think BOTH methods provide vital information that when used correctly can help to control the process.

Perhaps. But the extra work of fabricating a trend chart does not tend to justify itself over the simplicity and benefits if the more straight forward X hi/lo-R chart. But, one may pick their poison as the see fit.

C

#### chalapathi

It is good that you reminded an important point. Control chart is just like hypothesis testing only. With every subgroup plotted, we are testing hypothesis that the process is in statistical control (Ho).
Trend control charts is not something new in AIAG manuals. You can see this method in one of the old classical books on quality - Grant and Leavenworth.
It is very useful for marketing applications also, apart from tool wear application in machining

#### bobdoering

##### Stop X-bar/R Madness!!
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It is good that you reminded an important point. Control chart is just like hypothesis testing only. With every subgroup plotted, we are testing hypothesis that the process is in statistical control (Ho).
Trend control charts is not something new in AIAG manuals. You can see this method in one of the old classical books on quality - Grant and Leavenworth.

It is correct, trend charts are not new - but their limitations in precision maching have not been clearly stated previously. Now that they have, the merit of the X hi/lo-R charting is clearer. But, the basis for this statement is far too long for a post - that is why it is in the blogs and book.

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#### Bev D

##### Heretical Statistician
Super Moderator
It is good that you reminded an important point. Control chart is just like hypothesis testing only. With every subgroup plotted, we are testing hypothesis that the process is in statistical control (Ho).
Trend control charts is not something new in AIAG manuals. You can see this method in one of the old classical books on quality - Grant and Leavenworth.
It is very useful for marketing applications also, apart from tool wear application in machining

first - control charts aren't really hypothesis tests. although I get the gist of what you are saying. they are useful only when they help us with the economic control of quality.

and a control chart with sloping limits has many useful applications. precision machining is only one area where it might be useful. the hi/lo chart is simple and therefore useful in controlling over adjustment in the presence of tool wear. but there are a myriad of situations and nothing is ever one size fits all.

#### bobdoering

##### Stop X-bar/R Madness!!
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first - control charts aren't really hypothesis tests. although I get the gist of what you are saying. they are useful only when they help us with the economic control of quality.... but there are a myriad of situations and nothing is ever one size fits all.

Absolutely - and the key is understand which factors of variance you are trying to monitor and how they participate in the total variance. Precision machining has tool wear that generates a trend - but its factors of variance are different than plating solution concentration, as it trends based on drag-in/drag-out, usage and its other participating variation, such as part size, configuration, plating thickness, etc., etc. Just noticing a trend exists and pulling out the trend chart is just a bit too elementary of an approach (although perhaps the most typical). As much as people would thrive on plug and chug, SPC really does not lend itself to that as much as people think.