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LCL – Lower Control Limit

LCL, (Lower Control Limit), as it applies to X Bar, (mean), and R Bar, (range), control charts, is a formula that will calculate an lower most limit for samples to evaluate to. There is usually a UCL, (Upper Control Limit), that is also calculated. Used in SPC, (statistical process control).

You can also use Pre-Control to establish control limits on control charts.

To calculate the LCL, you use the factor table below. You need to know the number of samples and the number of observations, (subgroups using stratified sampling), labeled n, that were used. You must obtain the X Double Bar, (grand average), or average of the X Bar calculations. You must also obtain the R Bar calculation to calculate control limits.

A2 = a factor used in calculating the control limits for the X chart.
D4 = a factor used in calculating the upper control limit for the R chart.
D3 = a factor used in calculating the lower control limit for the R chart.

The factors A2, D4. and D3 vary with the size of the sample. Select the appropriate factor from the table shown below.

Control Limit Factor Table

Number of

X Chart.

R Chart. Factors

for Control Limits

Observa-

Factors for

tions in

Control

Sample

Limits

( n )

( A2 )

( D3 )

( D4 )

2

1.88

0

 

3.27

3

1.02

0

 

2.57

4

.73

0

 

2.28

5

.58

0

 

2.11

6

.48

0

 

2.00

7

.42

 

.08

1. 92

8

.37

 

.14

1.86

9

.34

 

.18

1.82

10

.31

 

.22

1. 78

X Bar Lower Control Limit, (XLCL), Formula

X Bar (XLCL)  =  X Double Bar –  (A2 Factor) * R Bar

XLCL  = X Double Bar – A2R Bar

R Bar Lower Control Limit, (RLCL), Formula

R Bar (RLCL)  =  D3 *  R Bar

RLCL  = D3R Bar

For an example of a X-Bar and R-Bar charts see our ZeroRejects features page. It makes doing statistical process control charts easy. And at only $150.00, (USD), our software can get you going quickly.

Also for more details on control limits and their usage, see X Bar and Range Control Charts.

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Last Updated: Saturday, 10-Jun-06 15:50:57 PDT

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