Table of Constants for Control Charts - DFX

Table 8 C Attribute Data ref : AIAG manual for SPC Centerline np chart for number / rate of units in a category c chart for number of incidences in on...

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Tables of Constants for Control charts Table 8A - Variable Data

ref : AIAG manual for SPC

X bar and R Charts Chart for Averages Control Limits Factor Subgroup size (n) 2 3 4 5 6 7 8 9 10 15 25

A2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.223 0.153

Chart for Averages Chart for Standard Deviation (s) Chart for Ranges (R) Divisors Divisors to to Control Estimate Factors for Control estimate Factors for Control Limits Factor Limits Limits σx σx

d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.472 3.931

D3 0.076 0.136 0.184 0.223 0.347 0.459

Centerline X bar and R Charts

CL X = X CLR = R

X bar and s Charts

X bar and s charts

CLX = X

CL s = s

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D4 3.267 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777 1.653 1.541

A3 2.659 1.954 1.628 1.427 1.287 1.182 1.099 1.032 0.975 0.789 0.606

c4 0.7979 0.8862 0.9213 0.9400 0.9515 0.9594 0.9650 0.9693 0.9727 0.9823 0.9896

B3 0.030 0.118 0.185 0.239 0.284 0.428 0.565

Control Limits UCLX = X + A2 R

LCL

UCLR = D4 R

LCL R = D3 R

UCLX = X + A3 S

LCL X = X − A3 S

UCL s = B4 s

LCL s = B 3 s

Control Chart Factors

X

= X − A2 R

B4 3.267 2.568 2.266 2.089 1.970 1.882 1.815 1.761 1.716 1.572 1.435

σx R d2

s c4

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Tables of Constants for Control charts Table 8B Variable Data

ref : AIAG manual for SPC

Median Charts Chart for Medians

Charts for Individuals Chart for Individuals

Chart for Ranges (R)

Control Divisors to Limits Estimate Factors for Control Factor Limits σx Subgroup size 2 3 4 5 6 7 8 9 10

~ A2 1.880 1.187 0.796 0.691 0.548 0.508 0.433 0.412 0.362

d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078

D3 0.076 0.136 0.184 0.223

D4 3.267 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777

Centerline CL

Median Charts

~ X

~ = X

CLR = R

Charts for Individuals

CL

X

= X

CLR = R

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Control Limits Factor E2 2.660 1.772 1.457 1.290 1.184 1.109 1.054 1.010 0.975

Chart for Moving Range (R) Divisors to Estimate Factors for Control σx Limits d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078

D3 0.076 0.136 0.184 0.223

D4 3.267 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777

Control Limits UCL

~ X

~ ~ = X + A2 R

UCLR = D4 R

UCL X = X + E 2 R

UCLR = D4 R

Control Chart Factors

LCL

~ X

~ = X − A2 R

LCL R = D3 R

LCL X = X − E 2 R

LCL R = D3 R

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Tables of Formulas for Control charts Table 8 C Attribute Data

ref : AIAG manual for SPC

Centerline

Control Limits Samples not necessarily of constant size

UCL p chart for CL p = p proportions of units in a category

pi

= p+3

c chart for number of incidences in one or more categories

ni

LCL p i = p − 3

p (1 − p ) ni

If the Sample size is constant (n)

UCL p = p + 3

np chart for number / rate of units in a category

p (1 − p )

p (1 − p ) n

LCL p = p − 3

p (1 − p ) n

CLnp = np

UCLnp = np + 3 np(1 − p)

LCLnp = np − 3 np(1 − p)

CL c = c

UCLc = c + 3 c

LCLc = c − 3 c

Samples not necessarily of constant size

CLu = u u chart for number of incidences per unit in one or more categories

UCLu = u + 3

LCLu = u − 3

u ni

UCL u = u − 3

u n

UCL u = u − 3

u n

using average sample size UCL u = u + 3

u n

If the sample size is constant (n) UCL u = u + 3

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u ni

u n

Control Chart Factors

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