function arlv = ARL_Fcn(L)

       % generate 5000 observations based on "mu" and "covarince"   
                          
p     = 2    ;                        % no of multivariate measurements
lamda = .2   ;
omega   = .2 ; 

Mu  = [0 0];
cov_matrix = [1 0; 0 1];

x = zeros(5000,2); 

simulate = mvnrnd(Mu,cov_matrix,5000);		% generate multivariate data

    for j=1:2                               % data transformation
            x(:,j) = (simulate(:,j)-Mu(:,j))./sqrt(cov_matrix(j,j)) ;           
    end


    for t = 1:5000
        
        Identity = eye (t);              % creat an t*t identity matrix
        
        M = zeros(t,t);                 
        
        for i = 1:t                     % compute matrix M
            for j = 1:t
                if (j==i)
                    M(j,i) = lamda ;
                elseif (j>=i)
                    M(j,i) = lamda*(1-lamda)^(j-i);
                end
            end
        end
        
        I_M = Identity - M ;            % Compute I-M
        
        ci      = zeros(t,t);           
        
        for i = 1:t                      % Computation of Ci matrix
            if (i==1)
                ci(i,i) = (1-omega)^(t-1);
            else
                ci(i,i) = omega*(1-omega)^(t-i);
            end
        end
                
        Q = I_M'*ci*I_M    ;                 % compute Q
        
        Vt = x(1:t,:)'*Q*x(1:t,:) ;         % compute Vt
        
        LCL_MV   = p*trace(Q) - L*sqrt(2*p*(sum(Q(:).^2))) ;           % limits varies depending on number of variables
        
        UCL_MV   = p*trace(Q) + L*sqrt(2*p*(sum(Q(:).^2)));
        
        if ((trace(Vt)>= UCL_MV) || (trace(Vt) <= LCL_MV))      % the value will return depend on this condition            
            arlv =  t ;
            break;
        end
    end

end