Setting Lower Control Limit on Attributes Charts

Bill McNeese

Involved In Discussions
#1
Wondering what others may think. I never have liked the practice of setting a lower control limit to zero for an attribute chart when that lower control limit is negative. I always simply say there is no lower control limit. There is a lower boundary of course - but not a lower control limit.

For example, you are charting occurrences (such as OSHA recordable injuries per month) using a c control chart. The average is 4. That gives a lower control limit of -2. Can't have negative injuries, so there should be on lower control limit - not setting it to 0.

A control limit is "special" in that it marks the realm of common cause of variation. In this example, there is nothing special about 0. You can easily have a month with no injuries and there is nothing "special" about it - although a lot of managers like people were being more careful that month.

So, I prefer to say there is no lower control limit for an attribute chart when it is less than zero. Not sure how the practice of setting it to zero started.
 
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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#2
Yes I prefer to say there is no lower control limit. However, even if you said the lower control limit was zero, since the rule is "outside the control limits" then you are still okay if a zero comes in.

By the way, there are some charts that can have negative numbers, so keep that in mind.
 
T

t.PoN

#3
Yes, you may use No Lower Control Limit.

but be careful, sometimes having too many zeros could be an indicator for something else.

for example: when you are starting to get many months with zero injuries while the previous history shows an average of 4 to 5 reported injuries. then you may want to check the reporting system. People might start hiding injuries reports. or may be your process is getting much much better, you need t set a new average
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#4
for example: when you are starting to get many months with zero injuries while the previous history shows an average of 4 to 5 reported injuries. then you may want to check the reporting system. People might start hiding injuries reports. or may be your process is getting much much better, you need t set a new average
In this case, you would still make use of other rules, such as 7 in a row below average, or 4 of 5 at one standard deviation below average to detect this, prior to establishing any new baselines.
 
D

DRAMMAN

#5
IMHO, setting the lower limit to zero and calling it the LCL simplifies it for everyone else. I used to try and explain to everyoe that it is not reallya LCL but the conversation just goes over heir head.
 

RoxaneB

Change Agent and Data Storyteller
Super Moderator
#6
It depends on the audience and who the message from the attributes chart is directed towards. Like Dramman, I prefer to keep it simple - especially if the target audience aren't into stats (i.e., are we within the range, yes or no?).

To start throwing in -2 for occurences instead of 0, will complicate the message, in my opinion. For behind-the-scenes activities, such as determining UCL and LCL in the future, feel free to use the -2 result, but for the message, one really does need to consider the audience and how the attribute and subsequent results are used.
 

Bill McNeese

Involved In Discussions
#7
To start throwing in -2 for occurences instead of 0, will complicate the message, in my opinion. .
I do not throw in a -2. The chart would not show anything below 0. There would simply be no lower control limit. Key is for folks to understand that a 0 is nothing special - just due to common causes.
 
D

DRAMMAN

#8
I will usually leave out details such as having a negative lower limit when a negative qty is impossible. I can think of many times where the audiences gets fixated on the negative number and it throws off an entire meeting. This usually happens when the audience are upper managers who are looking for any detail to complain about and the only thing they understand is a negative defect qty is not possible.
 
M

Matt33

#9
When the LCL is negative and a negative value is not possible, my preference is to show on the chart:
LCL = 0 or LCL = N/A
However, "behind" the chart, as a person working with the chart, I like to see what the actual calculated value is, even if it negative. I think I prefer this approach so that I can discuss the math and how the limits are symmetrical about the mean, but in this case, it doesn't make sense to show the LCL. Thus, setting it to 0 or N/A makes sense.
In summary, I like to separate the displayed chart from the mathematics.
The chart that your audience sees shows:
LCL = 0 or LCL = N/A
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#10
for me the point is that some processes DON'T have symmetrical limits. (certainly the r chart and the s chart don't)

if you have a p chart (categorical defect rates) then as your quality improves you certainly don't have a symmetrical distribution; more and more subgroups will have zero defects. you DO have a truncated distribution and that is not symmetrical.

And of course if the defect rate is small enough the p chart (or the np, c or u charts) isn't appropriate. Not because of any violation of Normality, but because the distributions deviate substantially from symmetrical.

PHYSICS matters...
 
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