問題描述：
有一組裝件由七個零件組成，這七個零件引數服從正態分佈
x1～n(0.1,(0.005/3) ^2)；
x2～n(0.3，0.0052^2)；
x3～n(0.1,(0.005/3)^2)；
x4～n(0.1,0.0052^2)；
x5～n(1.5,(0.225/3)^2);
x6～n(16,(0.8/3)^2)；
x7～n(0.75,(0.0375/3)^2)；
該組裝件的效能函式：
目標值是y0 = 1.5，偏離±0.1時，產品為次品，損失1000元；偏離±0.3時為廢品，損失9000元。
（1）計算生產一件該產品的損失期望值；
（2）以各零件引數的均值u為變數，波動範圍為20%，方差為固定值，試確定各零件的均值來優化產品效能。
1*第一問求解：
用normrnd建立七個服從正態分佈的隨機變數，對y進行大量實驗，統計其落在某區間的概率，以求得損失期望值。
syms k j n m
k=0;
n=0;
m=0;
for i=1:1000
x1 = normrnd(0.1,(0.005/3));
x2 = normrnd(0.3,0.005);
x3 = normrnd(0.1,(0.005/3));
x4 = normrnd(0.1,0.005);
x5 = normrnd(1.5,(0.225/3));
x6 = normrnd(16,(0.8/3));
x7 = normrnd(0.75,(0.0375/3));
y = 174.42*(x1/x5)*(x3/(x2-x1))^0.85*sqrt((1-2.62*(1-0.36*(x4/x2)^(-0.56))^(3/2)*(x4/x2)^1.16)/(x6*x7));
if(1.41.8||y==1.8||y<1.2||y==1.2)
m=m+1; %統計廢品個數
endendknm
j = (n*1000+m*9000)/1000 %損失
分別用fmincon和ga遺傳演算法求解，二者均可以設定所求變數的上下限和其滿足的約束函式；二者均需另外建立方法的**檔案，再在另一**檔案中呼叫；前者要給出變數初值，後者不用。
用fmincon求解
#fun.m#**檔案
function y0 = fun(x)
y1 = 'abs(174.42*(normrnd(x(1),(0.005/3))/normrnd(x(5),(0.225/3)))*(normrnd(x(3),(0.005/3))/(normrnd(x(2),0.005)-normrnd(x(1),(0.005/3))))^0.85*sqrt((1-2.62*(1-0.36*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^(-0.56))^(3/2)*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^1.16)/(normrnd(x(6),(0.8/3))*normrnd(x(7),(0.0375/3))))-1.5)';
y2 = '+abs(174.42*(normrnd(x(1),(0.005/3))/normrnd(x(5),(0.225/3)))*(normrnd(x(3),(0.005/3))/(normrnd(x(2),0.005)-normrnd(x(1),(0.005/3))))^0.85*sqrt((1-2.62*(1-0.36*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^(-0.56))^(3/2)*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^1.16)/(normrnd(x(6),(0.8/3))*normrnd(x(7),(0.0375/3))))-1.5)';
for i = 1:100
y1 = strcat(y1,y2); %前面y1，y2定義為字串，用strcat將y1,y2拼接起來，目的是使其求出的解更接近最優解
endy0 = eval(y1); %eval將字串轉化為命令
end
syms k j n m
k=0;
n=0;
m=0;
x0 = [0.1;0.3;0.1;0.1;1.5;16;0.75]; %初值
lb = [0.08;0.24;0.08;0.08;1.2;12.8;0.6]; %變數下限
ub = [0.12;0.36;0.12;0.12;1.8;19.2;0.9]; %變數上限
fval = 150;
while (fval>100)
[x,fval] = fmincon(@fun,x0,,,,,lb,ub); %其中四個表示等式約束和不等式約束均為空，x是所求變數的數列，fval是#fun.m#中所求函式的「最優值」（可能只是區域性最優，甚至因為變數本身有隨機性而產生的錯誤結果）
endx
fval
for i=1:1000
x1 = normrnd(x(1),0.005/3);
x2 = normrnd(x(2),0.005);
x3 = normrnd(x(3),0.005/3);
x4 = normrnd(x(4),0.005);
x5 = normrnd(x(5),0.225/3);
x6 = normrnd(x(6),0.8/3);
x7 = normrnd(x(7),0.0375/3);
y = 174.42*(x1/x5)*(x3/(x2-x1))^0.85*sqrt((1-2.62*(1-0.36*(x4/x2)^(-0.56))^(3/2)*(x4/x2)^1.16)/(x6*x7));
if(1.41.8|y==1.8|y<1.2|y==1.2)
m=m+1; %統計廢品個數
endendknm
j = (n*1000+m*9000)/1000 %損失
function f = ga_fun(x)
y1 = 'abs(174.42*(normrnd(x(1),(0.005/3))/normrnd(x(5),(0.225/3)))*(normrnd(x(3),(0.005/3))/(normrnd(x(2),0.005)-normrnd(x(1),(0.005/3))))^0.85*sqrt((1-2.62*(1-0.36*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^(-0.56))^(3/2)*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^1.16)/(normrnd(x(6),(0.8/3))*normrnd(x(7),(0.0375/3))))-1.5)';
y2 = '+abs(174.42*(normrnd(x(1),(0.005/3))/normrnd(x(5),(0.225/3)))*(normrnd(x(3),(0.005/3))/(normrnd(x(2),0.005)-normrnd(x(1),(0.005/3))))^0.85*sqrt((1-2.62*(1-0.36*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^(-0.56))^(3/2)*(normrnd(x(4),0.005)/normrnd(x(2),0.005))^1.16)/(normrnd(x(6),(0.8/3))*normrnd(x(7),(0.0375/3))))-1.5)';
for i = 1:13
y1 = strcat(y1,y2);
endf = eval(y1);
end
syms k j n m
k=0;
n=0;
m=0;
lb = [0.08;0.24;0.08;0.08;1.2;12.8;0.6];
ub = [0.12;0.36;0.12;0.12;1.8;19.2;0.9];
[x,fval,exitflag] = ga(@ga_fun,7,,,,,lb,ub); %7表示有七個變數
x fval
for i=1:1000
x1 = normrnd(x(1),0.005/3);
x2 = normrnd(x(2),0.005);
x3 = normrnd(x(3),0.005/3);
x4 = normrnd(x(4),0.005);
x5 = normrnd(x(5),0.225/3);
x6 = normrnd(x(6),0.8/3);
x7 = normrnd(x(7),0.0375/3);
y = 174.42*(x1/x5)*(x3/(x2-x1))^0.85*sqrt((1-2.62*(1-0.36*(x4/x2)^(-0.56))^(3/2)*(x4/x2)^1.16)/(x6*x7));
if(1.41.8|y==1.8|y<1.2|y==1.2)
m=m+1; %統計廢品個數
endendknm
j = (n*1000+m*9000)/1000 %損失
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