AVEVA™ Manufacturing Execution System

Sigma

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Sigma

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Last UpdatedMar 19, 2016
3 minute read

The CL, LCL, and UCL are calculated based on the sigma setting for a characteristic. The tables below contain the formulas used to calculate CL, LCL, and UCL for a chart point.

The examples given below illustrate the control limits calculated for the chart point 0.01663.

Use Tables (sigma est = 0)
Formula	Example
Sample Size = Size of a sample CL = Estimated Standard Deviation * C4 [Sample Size] LCL = CL – (3 * Estimated Standard Deviation * ) UCL = CL + (3 * Estimated Standard Deviation * ) if LCL < 0 then 0; otherwise LCL	CL = 0.02100 * 0.92132 = 0.01935 The estimated standard deviation calculated from the data is 0.02100 and the C4 factor value for a sample size of 4, obtained from the last sample is 0.92132. LCL = 0.01935 – (3 * 0.02100 * )= – 0.00515 Since LCL is less than 0, LCL = 0 UCL = 0.01935 + (3 * 0.02100 * ) = 0.04384

Use Tables (sigma est = 0)

Formula

Example

Sample Size = Size of a sample

CL = Estimated Standard Deviation * C4 [Sample Size]

LCL = CL – (3 * Estimated Standard Deviation *
ControlRuleVioSigmaEq1 )

UCL = CL + (3 * Estimated Standard Deviation *
ControlRuleVioSigmaEq1 )

if LCL < 0 then 0; otherwise LCL

CL = 0.02100 * 0.92132 = 0.01935

The estimated standard deviation calculated from the data is 0.02100 and the C4 factor value for a sample size of 4, obtained from the last sample is 0.92132.

LCL = 0.01935 – (3 * 0.02100 * ControlRuleVioSigmaEq2 )= – 0.00515

Since LCL is less than 0, LCL = 0

UCL = 0.01935 + (3 * 0.02100 * ControlRuleVioSigmaEq2 ) = 0.04384

Use Std. Dev. (sigma est = 1)
Formula	Example
Sample Size = Size of a sample CL = Standard Deviation * C4 [Sample Size] LCL = CL – (3 * Standard Deviation * ) UCL = CL + (3 * Standard Deviation * ) if LCL < 0 then 0; otherwise LCL	CL = 0.02025 * 0.92132 = 0.01866 The standard deviation calculated from the data is 0.02025 and the C4 factor value for a sample size of 4, which is obtained from the last sample is 0.92132. LCL = (0.01866) – (3 * 0.02025 * ) = –0.00496 Since LCL is less than 0, LCL = 0 UCL = (0.01866) + (3 * 0.02025 * ) = 0.04229

Use Std. Dev. (sigma est = 1)

Formula

Example

Sample Size = Size of a sample

CL = Standard Deviation * C4 [Sample Size]

LCL = CL – (3 *
Standard Deviation * ControlRuleVioSigmaEq1 )

UCL = CL + (3 *
Standard Deviation * ControlRuleVioSigmaEq1 )

if LCL < 0 then 0; otherwise LCL

CL = 0.02025 * 0.92132 = 0.01866

The standard deviation calculated from the data is 0.02025 and the C4 factor value for a sample size of 4, which is obtained from the last sample is 0.92132.

LCL = (0.01866) – (3 * 0.02025 * ControlRuleVioSigmaEq2 ) = –0.00496

Since LCL is less than 0, LCL = 0

UCL = (0.01866) + (3 * 0.02025 * ControlRuleVioSigmaEq2 ) = 0.04229

The following tables show examples of control limits and sigma limits for all the chart points using all the data.

Label	Chart Point	Use Tables (sigma est = 0)
Label	Chart Point	LCL	CL	UCL	Lower σ	Upper σ
1	0.026077	0	0.019738	0.041232	0.006579	0.007165
2	0.030035	0	0.018609	0.047790	0.006203	0.009727
3	0.003819	0	0.018609	0.047790	0.006203	0.009727
4	0.016630	0	0.019346	0.043838	0.006449	0.008164

Label	Chart Point	Use Std. Dev. (sigma est = 1)
Label	Chart Point	LCL	CL	UCL	Lower σ	Upper σ
1	0.026077	0	0.019039	0.039772	0.026077	0.052154
2	0.030035	0	0.017950	0.046098	0.030035	0.06007
3	0.003819	0	0.017950	0.046098	0.003819	0.007638
4	0.016630	0	0.018661	0.042286	0.016630	0.03326

AVEVA™ Manufacturing Execution System

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