Why the difference in control limit value when using different calculation methods?

L

limeho

#1
Hi all,

I am running a process where we take measurements on 5 pcs of product every 2 hours. So far, I have 221 sets of measurements (each set has 5 measurements).

I am planning to implement X-bar R chart on this process. I calculated the control chart limits using these 2 different methods:

Method 1: Use the control limit formula

Control Limits = (Average of X-bars) +/- (A2) x (Average of Rs)
= 2.376 +/- (0.577) x (0.097)

Result, UCL = 2.432, LCL = 2.320

Method 2: Use Excel's built-in formula STDEV()

Control limits = (Average of X-bars) +/- 3 x STDEV(all the individual Xs)
= 2.376 +/- 3 x (0.101)

Result, UCL = 2.679, LCL = 2.073

I find the difference between the 2 methods to be too much. Does anyone know what might be the problem?

Thanks.
 
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Miner

Forum Moderator
Staff member
Admin
#2
Re: Why the difference in control limit value when using different calculation method

Method 1 is the correct approach. It is using the within-subgroup (short-term) variation to establish control limits.

Method 2 measures the total variation (short and long-term) variation resulting in wider limits.

SPC was based on economically identifying when long-term (between subgroup) variation exceeds short-term (within subgroup) variation. This requires that control limits be based on the within subgroup variation (i.e., Method 1).
 
D

Darius

#3
Re: Why the difference in control limit value when using different calculation method

Agree with Miner
Method 1 - within group variation
Method 2 - total variation

there could be a Method 3 - between group variation.

SPC uses within group variation - the minimum "natural" variation

Method 2 consideres the trend accross the time + between group variation + within group variation

The Method 3 is the variation between subgoups, like between shift1 and shift2 workers (if every shift take several samples and shift1 and shift2 could be different) or between production lots (several samples of the same lot, possible differences between lots).

It is spected that

Variation within < Variation between < Total Variation

And remember each statistic is just an estimate and each estimate type has it's uses, so all are usefull but for their specific application.
 
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