产品
需要引用Neget包 MathNet.Numerics
公式
[无偏常量 d2()、d3() 和 d4()](https://support.minitab.com/zh-cn/minitab/18/quality-and-process-improvement/control-charts/how-to/variables-charts-for-subgroups/i-mr-r-s-chart/methods-and-formulas/unbiasing-constants-d2-d3-and-d4/)
[无偏常量 c4() 和 c5()](https://support.minitab.com/zh-cn/minitab/18/quality-and-process-improvement/control-charts/how-to/variables-charts-for-subgroups/i-mr-r-s-chart/methods-and-formulas/unbiasing-constants-c4-and-c5/)
[无偏常量 c4'()](https://support.minitab.com/zh-cn/minitab/18/quality-and-process-improvement/control-charts/how-to/variables-charts-for-subgroups/i-mr-r-s-chart/methods-and-formulas/unbiasing-constant-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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