| Library: | spc |
| See also: | spcewma2arl spcewma2c spcewma2pmfm spcewma1pmf |
| Quantlet: | spcewma2pmf | |
| Description: | Computes the probability mass function (PMF, P(L=i)) and the cumulative distribution function (CDF, P(L<=i)) of the two-sided EWMA chart run length for given i. The data are normally distributed with variance 1. |
| Usage: | pLi = spcewma2pmf (mu, lambda, c, Li, r) | |
| Input: | ||
| mu | scalar representing the expected value of the user-defined random variable | |
| lambda | scalar representing the smoothing parameter | |
| c | scalar, critical value | |
| Li | scalar, ARL of a SPC scheme starting in points Li | |
| r | scalar, matrix dimension of the approximated two-dimensional Markov chain. The larger r, the better is the approximation. | |
| Output: | ||
| pLi | n x 1 vector containing the values of the probability mass function and the corresponding cumulative distribution function at defined points Li. | |
; PMF and CDF of the two-sided EWMA run length with
; in-control ARL = 100, smoothing parameter lambda = 0.5 and
; matrix dimension 50(of the approximating two-dimensional
; Markov chain) for i in {1,10,20,30,40,50,75,100,150,200}:
library("spc")
Li = #(1,10,20,30,40,50,75,100,150,200)
c = spcewma2c(100, 0.5, 50)
pLi = spcewma2pmf(0,0.5,c,Li,50)
Li~pLi
Contents of _tmp [ 1,] 1 0.0034322 0.0034322 [ 2,] 10 0.0092852 0.088604 [ 3,] 20 0.0083902 0.17646 [ 4,] 30 0.0075814 0.25585 [ 5,] 40 0.0068506 0.32758 [ 6,] 50 0.0061902 0.3924 [ 7,] 75 0.0048045 0.52841 [ 8,] 100 0.003729 0.63398 [ 9,] 150 0.0022464 0.7795 [10,] 200 0.0013533 0.86717