function y = variance_func(lam1,lam2,al)

%function returns the variance of the number of components failing each
%month with the given parameters
basics_f
s_r(1:(m)) = lam2+lam1*exp(-al*(0:m-1));    %the failure rate with the given parameters
pfail(1:m) = 1-exp(-s_r(1:m));              %probability of a component prduced in month i is pfail(i)

for i=1:m   %for each month of production i, calculate the expected number of components that were produced in that month, that fail in each month j
    pf = pfail(i); %each month of production has a different failure rate.
    for j=(i+1):(m+m2)
            %s_varKs(i,j) = (n*pf*((1-pf)^(j-i)))-(n*(pf^2)*((1-pf)^(2*(j-i-1)))) +(n*(pf^2)*((1-pf)^(j-i-1)));
            temp1 = log(n) + log(pf) + (j-i)*(-s_r(i));
            temp2 = log(n) + 2*log(pf) + 2*(j-i-1)*(-s_r(i));
            temp3 = log(n) + 2*log(pf) + (j-i-1)*(-s_r(i));
            maxt = max([temp1 temp2 temp3]);
            temp = maxt + log(exp(temp1-maxt) - exp(temp2-maxt) + exp(temp3-maxt));
            varKs(i,j) = exp(temp);
    end
end
varK(1:m+m2) = sum(varKs);
y=varK;
clear i j varKs pf