需要引用Neget包 MathNet.Numerics

公式

无偏常量 d2()、d3() 和 d4()
无偏常量 c4() 和 c5()
无偏常量 c4’()

代码

using MathNet.Numerics;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;namespace Spc.Core
{public static class SigmaConstants{private static readonly Dictionary<int, double> d2 = new(){{ 2, 1.128d },{ 3, 1.693d },{ 4, 2.059d },{ 5, 2.326d },{ 6, 2.534d },{ 7, 2.704d },{ 8, 2.847d },{ 9, 2.97d },{ 10, 3.078d },{ 11, 3.173d },{ 12, 3.258d },{ 13, 3.336d },{ 14, 3.407d },{ 15, 3.472d },{ 16, 3.532d },{ 17, 3.588d },{ 18, 3.64d },{ 19, 3.689d },{ 20, 3.735d },{ 21, 3.778d },{ 22, 3.819d },{ 23, 3.858d },{ 24, 3.895d },{ 25, 3.931d },{ 26, 3.964d },{ 27, 3.997d },{ 28, 4.027d },{ 29, 4.057d },{ 30, 4.086d },{ 31, 4.113d },{ 32, 4.139d },{ 33, 4.165d },{ 34, 4.189d },{ 35, 4.213d },{ 36, 4.236d },{ 37, 4.259d },{ 38, 4.28d },{ 39, 4.301d },{ 40, 4.322d },{ 41, 4.341d },{ 42, 4.361d },{ 43, 4.379d },{ 44, 4.398d },{ 45, 4.415d },{ 46, 4.433d },{ 47, 4.45d },{ 48, 4.466d },{ 49, 4.482d },{ 50, 4.498d }};private static readonly Dictionary<int, double> d3 = new(){{ 2, 0.8525d },{ 3, 0.8884d },{ 4, 0.8798d },{ 5, 0.8641d },{ 6, 0.848d },{ 7, 0.8332d },{ 8, 0.8198d },{ 9, 0.8078d },{ 10, 0.7971d },{ 11, 0.7873d },{ 12, 0.7785d },{ 13, 0.7704d },{ 14, 0.763d },{ 15, 0.7562d },{ 16, 0.7499d },{ 17, 0.7441d },{ 18, 0.7386d },{ 19, 0.7335d },{ 20, 0.7287d },{ 21, 0.7242d },{ 22, 0.7199d },{ 23, 0.7159d },{ 24, 0.7121d },{ 25, 0.7084d },};private static readonly Dictionary<int, double> d4 = new(){{ 2, 0.954d },{ 3, 1.588d },{ 4, 1.978d },{ 5, 2.257d },{ 6, 2.472d },{ 7, 2.645d },{ 8, 2.791d },{ 9, 2.915d },{ 10, 3.024d },{ 11, 3.121d },{ 12, 3.207d },{ 13, 3.285d },{ 14, 3.356d },{ 15, 3.422d },{ 16, 3.482d },{ 17, 3.538d },{ 18, 3.591d },{ 19, 3.64d },{ 20, 3.686d },{ 21, 3.73d },{ 22, 3.771d },{ 23, 3.811d },{ 24, 3.847d },{ 25, 3.883d },};private static readonly Dictionary<int, double> d4dian = new(){{ 2, 0.79785 },{ 3, 0.87153 },{ 4, 0.905763 },{ 5, 0.925222 },{ 6, 0.937892 },{ 7, 0.946837 },{ 8, 0.953503 },{ 9, 0.958669 },{ 10, 0.962793 },{ 11, 0.966163 },{ 12, 0.968968 },{ 13, 0.971341 },{ 14, 0.973375 },{ 15, 0.975137 },{ 16, 0.976679 },{ 17, 0.978039 },{ 18, 0.979249 },{ 19, 0.980331 },{ 20, 0.981305 },{ 21, 0.982187 },{ 22, 0.982988 },{ 23, 0.98372 },{ 24, 0.984391 },{ 25, 0.985009 },{ 26, 0.985579 },{ 27, 0.986107 },{ 28, 0.986597 },{ 29, 0.987054 },{ 30, 0.98748 },{ 31, 0.987878 },{ 32, 0.988252 },{ 33, 0.988603 },{ 34, 0.988934 },{ 35, 0.989246 },{ 36, 0.98954 },{ 37, 0.989819 },{ 38, 0.990083 },{ 39, 0.990333 },{ 40, 0.990571 },{ 41, 0.990797 },{ 42, 0.991013 },{ 43, 0.991218 },{ 44, 0.991415 },{ 45, 0.991602 },{ 46, 0.991782 },{ 47, 0.991953 },{ 48, 0.992118 },{ 49, 0.992276 },{ 50, 0.992427 },{ 51, 0.992573 },{ 52, 0.992713 },{ 53, 0.992848 },{ 54, 0.992978 },{ 55, 0.993103 },{ 56, 0.993224 },{ 57, 0.99334 },{ 58, 0.993452 },{ 59, 0.993561 },{ 60, 0.993666 },{ 61, 0.993767 },{ 62, 0.993866 },{ 63, 0.993961 },{ 64, 0.994053 },{ 65, 0.994142 },{ 66, 0.994229 },{ 67, 0.994313 },{ 68, 0.994395 },{ 69, 0.994474 },{ 70, 0.994551 },{ 71, 0.994626 },{ 72, 0.994699 },{ 73, 0.994769 },{ 74, 0.994838 },{ 75, 0.994905 },{ 76, 0.99497 },{ 77, 0.995034 },{ 78, 0.995096 },{ 79, 0.995156 },{ 80, 0.995215 },{ 81, 0.995272 },{ 82, 0.995328 },{ 83, 0.995383 },{ 84, 0.995436 },{ 85, 0.995489 },{ 86, 0.995539 },{ 87, 0.995589 },{ 88, 0.995638 },{ 89, 0.995685 },{ 90, 0.995732 },{ 91, 0.995777 },{ 92, 0.995822 },{ 93, 0.995865 },{ 94, 0.995908 },{ 95, 0.995949 },{ 96, 0.99599 },{ 97, 0.99603 },{ 98, 0.996069 },{ 99, 0.996108 },{ 100, 0.996145 },{ 101, 0.996182 },{ 102, 0.996218 },{ 103, 0.996253 },{ 104, 0.996288 },{ 105, 0.996322 },{ 106, 0.996356 },{ 107, 0.996389 },{ 108, 0.996421 },{ 109, 0.996452 },{ 110, 0.996483 },{ 111, 0.996514 },{ 112, 0.996544 },{ 113, 0.996573 },{ 114, 0.996602 },{ 115, 0.996631 },{ 116, 0.996658 },{ 117, 0.996686 },{ 118, 0.996713 },{ 119, 0.996739 },{ 120, 0.996765 },{ 121, 0.996791 },{ 122, 0.996816 },{ 123, 0.996841 },{ 124, 0.996865 },{ 125, 0.996889 },{ 126, 0.996913 },{ 127, 0.996936 },{ 128, 0.996959 },{ 129, 0.996982 },{ 130, 0.997004 },{ 131, 0.997026 },{ 132, 0.997047 },{ 133, 0.997069 },{ 134, 0.997089 },{ 135, 0.99711 },{ 136, 0.99713 },{ 137, 0.99715 },{ 138, 0.99717 },{ 139, 0.997189 },{ 140, 0.997209 },{ 141, 0.997227 },{ 142, 0.997246 },{ 143, 0.997264 },{ 144, 0.997282 },{ 145, 0.9973 },{ 146, 0.997318 },{ 147, 0.997335 },{ 148, 0.997352 },{ 149, 0.997369 },{ 150, 0.997386 },{ 151, 0.997402 },{ 152, 0.997419 },{ 153, 0.997435 },{ 154, 0.99745 },{ 155, 0.997466 },{ 156, 0.997481 },{ 157, 0.997497 },{ 158, 0.997512 },{ 159, 0.997526 },{ 160, 0.997541 },{ 161, 0.997555 },{ 162, 0.99757 },{ 163, 0.997584 },{ 164, 0.997598 },{ 165, 0.997612 },{ 166, 0.997625 },{ 167, 0.997639 },{ 168, 0.997652 },{ 169, 0.997665 },{ 170, 0.997678 },{ 171, 0.997691 },{ 172, 0.997703 },{ 173, 0.997716 },{ 174, 0.997728 },{ 175, 0.997741 },{ 176, 0.997753 },{ 177, 0.997765 },{ 178, 0.997776 },{ 179, 0.997788 },{ 180, 0.9978 },{ 181, 0.997811 },{ 182, 0.997822 },{ 183, 0.997834 },{ 184, 0.997845 },{ 185, 0.997856 },{ 186, 0.997866 },{ 187, 0.997877 },{ 188, 0.997888 },{ 189, 0.997898 },{ 190, 0.997909 },{ 191, 0.997919 },{ 192, 0.997929 },{ 193, 0.997939 },{ 194, 0.997949 },{ 195, 0.997959 },{ 196, 0.997969 },{ 197, 0.997978 },{ 198, 0.997988 },{ 199, 0.997997 },{ 200, 0.998007 },{ 201, 0.998016 },{ 202, 0.998025 },{ 203, 0.998034 },{ 204, 0.998043 },{ 205, 0.998052 },{ 206, 0.998061 },{ 207, 0.99807 },{ 208, 0.998078 },{ 209, 0.998087 },{ 210, 0.998095 },{ 211, 0.998104 },{ 212, 0.998112 },{ 213, 0.99812 },{ 214, 0.998128 },{ 215, 0.998137 },{ 216, 0.998145 },{ 217, 0.998152 },{ 218, 0.99816 },{ 219, 0.998168 },{ 220, 0.998176 },{ 221, 0.998184 },{ 222, 0.998191 },{ 223, 0.998199 },{ 224, 0.998206 },{ 225, 0.998214 },{ 226, 0.998221 },{ 227, 0.998228 },{ 228, 0.998235 },{ 229, 0.998242 },{ 230, 0.99825 },{ 231, 0.998257 },{ 232, 0.998263 },{ 233, 0.99827 },{ 234, 0.998277 },{ 235, 0.998284 },{ 236, 0.998291 },{ 237, 0.998297 },{ 238, 0.998304 },{ 239, 0.998311 },{ 240, 0.998317 },{ 241, 0.998323 },{ 242, 0.99833 },{ 243, 0.998336 },{ 244, 0.998342 },{ 245, 0.998349 },{ 246, 0.998355 },{ 247, 0.998361 },{ 248, 0.998367 },{ 249, 0.998373 },{ 250, 0.998379 },{ 251, 0.998385 },{ 252, 0.998391 },{ 253, 0.998397 },{ 254, 0.998403 },{ 255, 0.998408 },{ 256, 0.998414 },{ 257, 0.99842 },{ 258, 0.998425 },{ 259, 0.998431 },{ 260, 0.998436 },{ 261, 0.998442 },{ 262, 0.998447 },{ 263, 0.998453 },{ 264, 0.998458 },{ 265, 0.998463 },{ 266, 0.998469 },{ 267, 0.998474 },{ 268, 0.998479 },{ 269, 0.998484 },{ 270, 0.998489 },{ 271, 0.998495 },{ 272, 0.9985 },{ 273, 0.998505 },{ 274, 0.99851 },{ 275, 0.998515 },{ 276, 0.998519 },{ 277, 0.998524 },{ 278, 0.998529 },{ 279, 0.998534 },{ 280, 0.998539 },{ 281, 0.998544 },{ 282, 0.998548 },{ 283, 0.998553 },{ 284, 0.998558 },{ 285, 0.998562 },{ 286, 0.998567 },{ 287, 0.998571 },{ 288, 0.998576 },{ 289, 0.99858 },{ 290, 0.998585 },{ 291, 0.998589 },{ 292, 0.998593 },{ 293, 0.998598 },{ 294, 0.998602 },{ 295, 0.998606 },{ 296, 0.998611 },{ 297, 0.998615 },{ 298, 0.998619 },{ 299, 0.998623 },{ 300, 0.998627 },{ 301, 0.998632 },{ 302, 0.998636 },{ 303, 0.99864 },{ 304, 0.998644 },{ 305, 0.998648 },{ 306, 0.998652 },{ 307, 0.998656 },{ 308, 0.99866 },{ 309, 0.998664 },{ 310, 0.998668 },{ 311, 0.998671 },{ 312, 0.998675 },{ 313, 0.998679 },{ 314, 0.998683 },{ 315, 0.998687 },{ 316, 0.99869 },{ 317, 0.998694 },{ 318, 0.998698 },{ 319, 0.998701 },{ 320, 0.998705 },{ 321, 0.998709 },{ 322, 0.998712 },{ 323, 0.998716 },{ 324, 0.99872 },{ 325, 0.998723 },{ 326, 0.998727 },{ 327, 0.99873 },{ 328, 0.998734 },{ 329, 0.998737 },{ 330, 0.99874 },{ 331, 0.998744 },{ 332, 0.998747 },{ 333, 0.998751 },{ 334, 0.998754 },{ 335, 0.998757 },{ 336, 0.998761 },{ 337, 0.998764 },{ 338, 0.998767 },{ 339, 0.99877 },{ 340, 0.998774 },{ 341, 0.998777 },{ 342, 0.99878 },{ 343, 0.998783 },{ 344, 0.998786 },{ 345, 0.99879 },{ 346, 0.998793 },{ 347, 0.998796 },{ 348, 0.998799 },{ 349, 0.998802 },{ 350, 0.998805 },{ 351, 0.998808 },{ 352, 0.998811 },{ 353, 0.998814 },{ 354, 0.998817 },{ 355, 0.99882 },{ 356, 0.998823 },{ 357, 0.998826 },{ 358, 0.998829 },{ 359, 0.998832 },{ 360, 0.998835 },{ 361, 0.998837 },{ 362, 0.99884 },{ 363, 0.998843 },{ 364, 0.998846 },{ 365, 0.998849 },{ 366, 0.998851 },{ 367, 0.998854 },{ 368, 0.998857 },{ 369, 0.99886 },{ 370, 0.998862 },{ 371, 0.998865 },{ 372, 0.998868 },{ 373, 0.998871 },{ 374, 0.998873 },{ 375, 0.998876 },{ 376, 0.998879 },{ 377, 0.998881 },{ 378, 0.998884 },{ 379, 0.998886 },{ 380, 0.998889 },{ 381, 0.998892 },{ 382, 0.998894 },{ 383, 0.998897 },{ 384, 0.998899 },{ 385, 0.998902 },{ 386, 0.998904 },{ 387, 0.998907 },{ 388, 0.998909 },{ 389, 0.998912 },{ 390, 0.998914 },{ 391, 0.998917 },{ 392, 0.998919 },{ 393, 0.998921 },{ 394, 0.998924 },{ 395, 0.998926 },{ 396, 0.998929 },{ 397, 0.998931 },{ 398, 0.998933 },{ 399, 0.998936 },{ 400, 0.998938 },{ 401, 0.99894 },{ 402, 0.998943 },{ 403, 0.998945 },{ 404, 0.998947 },{ 405, 0.99895 },{ 406, 0.998952 },{ 407, 0.998954 },{ 408, 0.998956 },{ 409, 0.998959 },{ 410, 0.998961 },{ 411, 0.998963 },{ 412, 0.998965 },{ 413, 0.998967 },{ 414, 0.99897 },{ 415, 0.998972 },{ 416, 0.998974 },{ 417, 0.998976 },{ 418, 0.998978 },{ 419, 0.99898 },{ 420, 0.998982 },{ 421, 0.998985 },{ 422, 0.998987 },{ 423, 0.998989 },{ 424, 0.998991 },{ 425, 0.998993 },{ 426, 0.998995 },{ 427, 0.998997 },{ 428, 0.998999 },{ 429, 0.999001 },{ 430, 0.999003 },{ 431, 0.999005 },{ 432, 0.999007 },{ 433, 0.999009 },{ 434, 0.999011 },{ 435, 0.999013 },{ 436, 0.999015 },{ 437, 0.999017 },{ 438, 0.999019 },{ 439, 0.999021 },{ 440, 0.999023 },{ 441, 0.999025 },{ 442, 0.999027 },{ 443, 0.999028 },{ 444, 0.99903 },{ 445, 0.999032 },{ 446, 0.999034 },{ 447, 0.999036 },{ 448, 0.999038 },{ 449, 0.99904 },{ 450, 0.999042 },{ 451, 0.999043 },{ 452, 0.999045 },{ 453, 0.999047 },{ 454, 0.999049 },{ 455, 0.999051 },{ 456, 0.999052 },{ 457, 0.999054 },{ 458, 0.999056 },{ 459, 0.999058 },{ 460, 0.99906 },{ 461, 0.999061 },{ 462, 0.999063 },{ 463, 0.999065 },{ 464, 0.999067 },{ 465, 0.999068 },{ 466, 0.99907 },{ 467, 0.999072 },{ 468, 0.999073 },{ 469, 0.999075 },{ 470, 0.999077 },{ 471, 0.999078 },{ 472, 0.99908 },{ 473, 0.999082 },{ 474, 0.999084 },{ 475, 0.999085 },{ 476, 0.999087 },{ 477, 0.999088 },{ 478, 0.99909 },{ 479, 0.999092 },{ 480, 0.999093 },{ 481, 0.999095 },{ 482, 0.999097 },{ 483, 0.999098 },{ 484, 0.9991 },{ 485, 0.999101 },{ 486, 0.999103 },{ 487, 0.999104 },{ 488, 0.999106 },{ 489, 0.999108 },{ 490, 0.999109 },{ 491, 0.999111 },{ 492, 0.999112 },{ 493, 0.999114 },{ 494, 0.999115 },{ 495, 0.999117 },{ 496, 0.999118 },{ 497, 0.99912 },{ 498, 0.999121 },{ 499, 0.999123 },{ 500, 0.999124 }};public static double D2(int N){if (N > 100){throw new Exception("N值大于100!");}if (N <= 1){throw new Exception("N值不能小于2!");}if (N >= 2 && N <= 50){return d2[N];}//https://support.minitab.com/zh-cn/minitab/18/help-and-how-to/quality-and-process-improvement/control-charts/how-to/variables-charts-for-subgroups/xbar-chart/methods-and-formulas/estimating-sigma/return 3.4873.Add(0.0250141.Mul(N)).Sub(0.00009823.Mul(Math.Pow(N, 2)));//3.4873 + (0.0250141 * N) - (0.00009823 * Math.Pow(N, 2));//return (double)((decimal)3.4873 + ((decimal)0.0250141 * N) - ((decimal)0.00009823 * (decimal)Math.Pow(N, 2)));}public static double D3(int N){if (N > 100){throw new Exception("N值大于100!");}if (N <= 1){throw new Exception("N值不能小于2!");}if (N >= 2 && N <= 25){return d3[N];}return 0.80818.Sub(0.0051871.Mul(0.00005098).Mul(Math.Pow(N, 2))).Sub(0.00000019.Mul(Math.Pow(N, 3)));//0.80818 - (0.0051871 * 0.00005098 * Math.Pow(N, 2)) - (0.00000019 * Math.Pow(N, 3))//return (double)((decimal)0.80818 - (decimal)0.0051871 * (decimal)0.00005098 * (decimal)Math.Pow(N, 2) - (decimal)0.00000019 * (decimal)Math.Pow(N, 3));}public static double D4(int N){if (N > 100){throw new Exception("N值大于100!");}if (N <= 1){throw new Exception("N值不能小于2!");}if (N >= 2 && N <= 25){return d4[N];}return 2.88606.Add(0.051313.Mul(N)).Sub(0.00049243.Mul(Math.Pow(N, 2))).Add(0.00000188.Mul(Math.Pow(N, 3)));//2.88606 + 0.051313 * N - 0.00049243 * Math.Pow(N, 2) + 0.00000188 * Math.Pow(N, 3))//return (double)((decimal)2.88606 + (decimal)0.051313 * N - (decimal)0.00049243 * (decimal)Math.Pow(N, 2) + (decimal)0.00000188 * (decimal)Math.Pow(N, 3));}public static double C4(int N){return Math.Sqrt(2 / N - 1).Mul(SpecialFunctions.Gamma(N / 2)).Div(SpecialFunctions.Gamma(N - 1 / 2));//Math.Sqrt(2 / N - 1) * (SpecialFunctions.Gamma(N / 2) / SpecialFunctions.Gamma(N - 1 / 2));//return (double)((decimal)Math.Sqrt(2 / N - 1) * ((decimal)(SpecialFunctions.Gamma(N / 2)) / (decimal)SpecialFunctions.Gamma(N - 1 / 2)));}public static double C4AddOne(int d){return Math.Sqrt(2 / d).Mul(SpecialFunctions.Gamma(d + 1 / 2)).Div(SpecialFunctions.Gamma(d / 2));//return (double)((decimal)Math.Sqrt(2 / d) * ((decimal)SpecialFunctions.Gamma((d + 1) / 2) / (decimal)SpecialFunctions.Gamma(d / 2)));}public static double C4Dian(int N){if (N < 2 || N > 500){throw new Exception("N不在2-500范围内!");}return d4dian[N];}public static double C5(int N){return Math.Sqrt((double)(1 - (decimal)Math.Pow(C4(N), 2)));}}
}

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C# Minitab Sigma 无偏常量

需要引用Neget包 MathNet.Numerics

公式

代码

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