Control Chart

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 ?x ?x 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. 23 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 Institute of Quality and Reliability www. world-class-quality. com 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 ?x R d2 s c4 Page 1 of 3 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 ?x 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 . 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 Institute of Quality and Reliability www. world-class-qua lity. com 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 ?x 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 . 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 Page 2 of 3 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 umber / rate of units in a category p (1 ? p ) p (1 ? p ) n LCL p = p ? 3 p (1 ? p ) n CL = np np UCL np = 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 Institute of Quality and Reliability www. world-class-quality. com u ni u n Control Chart Factors Page 3 of 3