% I use this code to obtain the time of detecting the attacks against z3,
% using the nonparametric cusum algorithm
clear;
clc;
max_iter = 1000;
taoval = 1:3:400; %taoval means \tau, which is the threshold

iter1 = [];iter2 = [];iter3 = [];
for itao = 1:length(taoval)
    tao = taoval(itao);
    Si1 = 0;Si_1 = 0;
    for i = 1:max_iter-1
        Si1 = Si_1+0.01*abs(randn(1));
        if(i>100)
           Si1 = Si1+0.5*94.20; %94.20 is the \gamma?percentiles of z3, which is derived from historical data. 0.5 means the true value is changed by 50%
        end

        if(Si1>tao)
           iter_tmp1 = i;
           break;
        end
        Si_1 = Si1;
    end
    iter1 = [iter1,iter_tmp1-100];
    Si2=0; Si_1 = 0;
    for i = 1:max_iter-1
        Si2 = Si_1+0.01*abs(randn(1));

        if(i>100)
           Si2 = Si2+0.3*94.20; %0.3 means the true value is changed by 30%
        end
        if(Si2>tao)
           iter_tmp2 = i;
           break;
        end
        Si_1 = Si2;
    end
     iter2 = [iter2,iter_tmp2-100];
    Si3=0; Si_1 = 0;
    for i = 1:max_iter-1
        Si3 = Si_1+0.01*abs(randn(1));

        if(i>100)
           Si3 = Si3+0.1*94.20; %0.1 means the true value is changed by 10%
        end
        if(Si3>tao)
           iter_tmp3 = i;
           break;
        end
        Si_1 = Si3;
    end
     iter3 = [iter3,iter_tmp3-100];
end
figure(1);clf;
plot(taoval,iter1,'r--','linewidth',2);hold on;
plot(taoval,iter2,'g-.','linewidth',2);hold on;
plot(taoval,iter3,'b-','linewidth',2);hold off;
xlabel('\tau');ylabel('Average Detection Time(s)');
LEGEND('z_{a}=0.5*z','z_{a}=0.7*z','z_{a}=0.9*z','Location','northwest');
title('z_{3}')