arlCusum            package:surveillance            R Documentation

_C_a_l_c_u_l_a_t_i_o_n _o_f _A_v_e_r_a_g_e _R_u_n _L_e_n_g_t_h _f_o_r _d_i_s_c_r_e_t_e _C_U_S_U_M _s_c_h_e_m_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     Calculates the average run length (ARL) for an upward CUSUM scheme
     for discrete distributions (i.e. Poisson and binomial) using the
     Markov chain approach.

_U_s_a_g_e:

     arlCusum(h=10, k=3, theta=2.4, distr=c("poisson","binomial"),
              W=NULL, digits=1, ...)

_A_r_g_u_m_e_n_t_s:

       h: decision interval

       k: reference value

   theta: distribution parameter for the cumulative distribution
          function (cdf) F, i.e. rate lambda for Poisson variates or
          probability p for binomial variates

   distr: '"poisson"' or '"binomial"' 

       W: Winsorizing value 'W' for a robust CUSUM, to get a nonrobust
          CUSUM set  'W' > 'k'+'h'. If 'NULL', a nonrobust CUSUM is
          used.

  digits: 'k' and 'h' are rounded to 'digits' decimal places 

     ...: further arguments for the distribution function, i.e. number
          of trials 'n' for binomial cdf 

_V_a_l_u_e:

     Returns a list with the ARL of the regular (zero-start) and the
     fast initial response (FIR) CUSUM scheme with reference value 'k',
     decision interval 'h' for X sim F(theta), where F is the Poisson
     or binomial cdf 

     ARL: one-sided ARL of the regular (zero-start) CUSUM scheme

 FIR.ARL: one-sided ARL of the FIR CUSUM scheme with head start
          frac{'h'}{2} 

_S_o_u_r_c_e:

     Based on the FORTRAN code of

     Hawkins, D. M. (1992). Evaluation of Average Run Lengths of
     Cumulative Sum Charts for an Arbitrary Data Distribution.
     Communications in Statistics - Simulation and Computation, 21(4),
     p. 1001-1020.

