Notation: Variables Data (x and R Control Charts) * Control Chart UCL = LCL = CL = Capability Study R Control Chart UCL =R D4 LCL = RD3 CL =

R UCL Upper Control Limit LCL Lower Control Limit CL Center Line CL C₂ = (USL LSL)/(66); where ô = Rld₂ UCL n Sample Size PCR Process Capability Ratio Ô Process Standard Deviation + A₂R -A₂R LCL Attribute Data (p, np, c, and u Control Charts) Notes p (fraction) P p+3, P-3₁ P(1-P) n SPC Calculations for Control Limit P(1-P) n If n varies, use or individual ni np (number of nonconforming) np np + 3√ np(1-P) np - 3√√np(1-P) n n must be a constant 2 3 4 5 6 7 8 9 10 X F R R Control Chart Formulas USL LSL A₂ 1.88 1.02 0.72 0.57 0.48 0.41 0.37 0.33 0.30 c (cou nonconfo C c+: C-3 n mu a con QUALITY CONTROL FOR OPERATORS & FOREMEN s 0 Z Area Under Standard Normal Curve Outside Z 0.07 Z Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 3.5 .00023 .00022 .00022 .00021 .00020 .00019 .00019 .0001 3.4 .00034 .00033 .00031 .00030 .00029 .00028 .00027 .0002 3.3 .00048 .00047 00045 .00043 .00042 00040 .00039 .0003 3.2 .00069 .00066 .00064 .00062 00060 00058 .00056 .0005 3.1 .00097 .00094 .00090 .00087 00085 .00082 .00079 .0007 1.5 .0668 .0655 .0643 1.4 .0808 .0793 .0778 1.3 .0968 .0951 .0934 1.2 .1151 .1131 .1112 1.1 .1357 .1335 .1314 3.0 .00135 .00131 .00126 .00122 .00118 .00114 .00111 .0010 2.9 .0019 .0018 .0017 .0017 .0016 .0016 .0015 .001! 2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .002¹ 2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0021 2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0031 2.5 .0062 .0060 .0059 2.4 .0082 .0080 .0078 2.3 .0107 .0104 .0102 .0099 2.2 .0139 .0136 .0132 .0129 2.1 .0179 .0174 .0170 .0166 -Pz .0057 .0055 .0054 .0075 .0073 .0071 .0052 .005 .0069 .0061 .0096 .0094 .0091 .008! .0125 .0122 .0119 .0111 .0162 .0158 .0154 .015 2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .019 1.9 .0287 .0281 .0274 0268 .0262 .0256 .0250 .024 1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .030 1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .038 1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .047 1.0 .1587 .1562 .1539 .1515 0.9 .1841 .1814 .1788 0.8 2119 2090 2061 .2389 .2358 .2709 .2676 0.7 2420 0.6 .2743 .0630 .0618 .0606 .0594 .0764 .0749 .0735 .0721 .0918 .0901 .0885 .0869 .1093 .1075 .1057 .1038 .1292 .1271 .1251 .1230 .1492 .1469 .1446 1762 1736 .1711 .1685 .2033 .2005 .1977 .1949 .2327 .2643 .058 .070 .085 .102 .121 142 .16€ .192 .2297 .2266 .2236 .22( .2611 .2578 .2546 .25* 0.5 .3085 .3050 3015 .2981 2946 2912 .2877 .28 0.4 .3446 .3409 .3372 .3336 3300 .3264 .3228 .31! 0.3 .3821 .3783 3745 3707 .3669 .3632 .3594 .351 0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .39 0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .431 0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .471 UCL = USL TABLE 9.1 NORMAL TABLES -(28-3³1) 0 -(28-3271) 0 √n LCL = LSL + Zs ts Average of Measurements Average of Averages Range Average of Ranges Upper Specification Limit Lower Specification Limit 10 13 19 7 13 9 3 7 18 int of rmances) ī 3√√6 We ist be istant D3 0.000 0.000 0.000 0.000 0.000 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 u (count of nonconformances/unit) ū ū +3, u-3 u n И n d₂ 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 If n varies, use or individual n 720 ΑΡΡΕΝΙ Factors for Co Observations in Sample, n 234567899 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 For n > 25. 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.08 0.09 18 .00017 .00017 26 .00025 .00024 38 .00036 .00035 54 .00052 .00050 76 .00074 .00071 07 .00104 .00100 5 .0014 .0014 1 .0020 .0019 B .0027 .0026 8 .0037 .0036 18960 .0049 .0048 .0066 .0064 .0084 .0113 .0110 .0146 .0143 9 .0087 .0188 .0183 .0239 0233 .0301 .0294 14 .0375 .0367 .0465 .0455 24745 12 .0571 .0559 18 .0694 .0681 53 .0838 .0823 20 .1003 .0985 10 .1190 .1170 23 .1401 .1379 50 .1635 .1611 .1894 1867 22 07 .2177 .2148 14 .2483 .2451 43 .2810 .2776 92 .3156 3121 57 .3520 3483 36 .3897 .3859 25 .4286 4247 21 .4681 .4641 UCLP= P'+3* ((P'*(1-I S= CLP = Pbar LCLP= P¹-3* ((P¹*(1-P'))/N)^ : the sample stan n Σ(x₁ - x)² i=1 n-1 Consequently, we may write th Note that B4 B6/c4 and B3 = 1 = able. In this case, we should use a weigl the number of observations in the ith sar EWIENI