C# 标准偏差STDEV与CPK的计算

C# 偏差STDEV与CPK的计算 最近由于在做一个检测的项目，客户要求报必须生成CPK，以前对CPK一点概念都没有，经过查资料，做出CPK相关的函数.     根据百度百科：     标准偏差公式：S = Sqrt[(∑(xi-x拨)^2) /（N-1）]公式中∑代表总和，x拨代表x的均值，^2代表二次方，Sqrt代表平方根。   例：有一组数字分别是200、50、100、200，求它们的标准偏差。   x拨 = (200+50+100+200)/4 = 550/4 = 137.5   S^2 = [(200-137.5)^2+(50-137.5)^2+(100-137.5)^2+(200-137.5)^2]/(4-1)   标准偏差 S = Sqrt(S^2)   STDEV基于样本估算标准偏差。标准偏差反映数值相对于平均值 (mean) 的离散程度。       其中：           Cpk:制程能力指标 要求1.33以上           Cp: 技术能力指标 要求1.0以上           k:  管理能力指标 要求0.25以下           Mean:平均值           s:  标准差,值越大，数据越散乱           USL:规格上限           LSL:规格下限           n:  数据数目(30~50)         下面是计算CPK会用到的类： using System; using System.Collections.Generic; using System.Text; namespace CPKClass {     class ProCPK     {         public static float StDev(float[] arrData) //计算标准偏差         {             float xSum = 0F;             float xAvg = 0F;             float sSum = 0F;             float tmpStDev = 0F;             int arrNum = arrData.Length;             for (int i = 0; i < arrNum; i++)             {                 xSum += arrData[i];             }             xAvg = xSum / arrNum;             for (int j = 0; j < arrNum; j++)             {                 sSum += ((arrData[j] - xAvg) * (arrData[j] - xAvg));             }             tmpStDev = Convert.ToSingle(Math.Sqrt((sSum / (arrNum - 1))).ToString());             return tmpStDev;         }         public static float Cp(float UpperLimit, float LowerLimit, float StDev) /         {             float tmpV = 0F;             tmpV = UpperLimit - LowerLimit;             return Math.Abs(tmpV / (6 * StDev));         }         public static float Avage(float[] arrData)         {             float tmpSum = 0F;             for (int i = 0; i < arrData.Length; i++)             {                 tmpSum += arrData[i];             }             return tmpSum / arrData.Length;         }         public static float Max(float[] arrData)         {             float tmpMax = 0;             for (int i = 0; i < arrData.Length; i++)             {                 if (tmpMax < arrData[i])                 {                     tmpMax = arrData[i];                 }             }             return tmpMax;         }         public static float Min(float[] arrData)         {             float tmpMin = arrData[0];             for (int i = 1; i < arrData.Length; i++)             {                 if (tmpMin > arrData[i])                 {                     tmpMin = arrData[i];                 }             }             return tmpMin;         }         public static float CpkU(float UpperLimit, float Avage, float StDev)         {             float tmpV = 0F;             tmpV = UpperLimit - Avage;             return tmpV / (3 * StDev);         }         public static float CpkL(float LowerLimit, float Avage, float StDev)         {             float tmpV = 0F;             tmpV = Avage - LowerLimit;             return tmpV / (3 * StDev);         }         public static float Cpk(float CpkU, float CpkL)         {             return Math.Abs(Math.Min(CpkU, CpkL));         }         private void button1_Click(object sender, EventArgs e)         {             float[] k = { 0.03F, 0.06F, 0.05F, 0.03F, 0.04F, 0.04F, 0.03F, 0.04F, 0.04F, 0.04F, 0.04F, 0.04F, 0.04F, 0.03F, 0.01F, 0.03F, 0.01F, 0.03F, 0.04F, 0.04F, 0.04F, 0.05F, 0.02F, 0.04F, 0.05F, 0.05F, 0.05F, 0.05F, 0.03F, 0.05F, 0.05F, 0.03F, 0.02F, 0.04F, 0.04F, 0.02F, 0.06F, 0.04F, 0.02F, 0.03F, 0.04F, 0.02F, 0.05F, 0.06F, 0.07F, 0.02F, 0.04F, 0.04F, 0.03F, 0.03F };              float Nomial = 0.05F;             float UpperLimit = 0.12F;             float LowerLimit =0F;             textBox1.Text = "检测点:" + k.Length.ToString()+"/r/n";             textBox1.Text += "Nominal:"+Nomial.ToString()+"/r/n";             textBox1.Text += "UpperLimit:"+UpperLimit.ToString("F2")+ "/r/n";             textBox1.Text += "LowerLimit:"+LowerLimit.ToString("F2") + "/r/n";             textBox1.Text += "Average:" + Avage(k).ToString("F3") + "/r/n";             textBox1.Text += "STD:" + StDev(k).ToString("F3") + "/r/n";             textBox1.Text += "Cp:" + Cp(UpperLimit, LowerLimit, StDev(k)).ToString("F3") + "/r/n";             textBox1.Text += "CpkU:" + CpkU(UpperLimit, Avage(k), StDev(k)).ToString("F3") + "/r/n";             textBox1.Text += "CpkL:" + CpkL(LowerLimit, Avage(k), StDev(k)).ToString("F3") + "/r/n";             textBox1.Text += "Cpk:" + Cpk(CpkU(UpperLimit, Avage(k), StDev(k)), CpkL(LowerLimit, Avage(k), StDev(k))).ToString("F3") + "/r/n";             textBox1.Text += "Min:" + Min(k).ToString("F3") + "/r/n";             textBox1.Text += "Max:" + Max(k).ToString("F3") + "/r/n";         }     } } 由于本人是做机器视觉的，对工厂制程管控并不是很了解，上面公式是根据网上资料而写，难免有些疏漏或勘误(比如有些资料还有Ca的参数,有些并不用到Ca)，如果有错，请与我联系。