% I use this code to obtain the false positive rate of the nonparametric cusum algorithm
max_iter = 1000;
taoval = 1:0.5:200;            %taoval means \tau, which is the threshold
false_pos = zeros(size(taoval));
for itao = 1:length(taoval)
    tao = taoval(itao);
    num = 0;
    for is = 1:100 % the number of the normal data are 100
        flag = 0;
        Si_1 = 0;
        Si1 = 0;
    for i = 1:max_iter
        Si1 = Si_1+0.1*abs(randn(1)); %Si1 is the the nonparametric cusum algorithm statistics, 0.1 decides the power of the attack

        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)
            flag = 1;
            break;
        end
        Si_1 = Si1;
    end
    if(flag)
       num = num+1;
    end
    end
    false_pos(itao) = num/100; %false_pos(i) is the false positive rate

end

figure;
plot(taoval,false_pos,'b-','linewidth',4);
xlabel('\tau');
ylabel('False Positive Rate');
title('z_{4}')