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Control Limits & Capability Analysis

The document provides equations and notation for calculating control limits for variables and attributes data in statistical process control. For variables data, it gives the formulas to calculate the upper control limit, center line, and lower control limit for x-bar and R control charts using average, range, and sample size values. For attributes data, it lists the formulas to determine control limits for p, np, c, and u charts using fraction, sample size, count of nonconformances, and count of nonconformances per unit. It also gives notes on handling varying sample sizes.

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Divya Khan
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77 views1 page

Control Limits & Capability Analysis

The document provides equations and notation for calculating control limits for variables and attributes data in statistical process control. For variables data, it gives the formulas to calculate the upper control limit, center line, and lower control limit for x-bar and R control charts using average, range, and sample size values. For attributes data, it lists the formulas to determine control limits for p, np, c, and u charts using fraction, sample size, count of nonconformances, and count of nonconformances per unit. It also gives notes on handling varying sample sizes.

Uploaded by

Divya Khan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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SPC

Calculations for Control Limits

Notation: UCL Upper Control Limit x Average of Measurements


LCL Lower Control Limit =x Average of Averages
CL Center Line R Range

n Sample Size R Average of Ranges
PCR Process Capability Ratio USL Upper Specification Limit
Process Standard Deviation LSL Lower Specification Limit

Variables Data (x and R Control Charts)


x Control Chart n A2 D3 D4 d2

UCL = =x + A2R 2 1.880 0.000 3.267 1.128

LCL = =x A2R 3 1.023 0.000 2.574 1.693
CL = =x 4 0.729 0.000 2.282 2.059
5 0.577 0.000 2.114 2.326
R Control Chart 6 0.483 0.000 2.004 2.534

UCL = R D4 7 0.419 0.076 1.924 2.704

LCL = R D3 8 0.373 0.136 1.864 2.847

CL = R 9 0.337 0.184 1.816 2.970
10 0.308 0.223 1.777 3.078
Capability Study

Cp = (USL LSL)/(6 ); where = R/d2

Attribute Data (p, np, c, and u Control Charts)

Control Chart Formulas

np (number of c (count of u (count of


p (fraction) nonconforming) nonconformances) nonconformances/unit)
CL p np c u

p (1 p ) u
UCL p+3 np + 3 np(1 p ) c +3 c u +3
n n

p (1 p ) u
p3 np 3 np(1 p ) c 3 c u 3
LCL n n

Notes If n varies, use n n must be n must be If n varies, use n


or individual ni a constant a constant or individual ni

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