| Library: | spc |
| See also: | spccusum1arl spccusum1c spccusum1pmf |
| Quantlet: | spccusum1pmfm | |
| Description: | Computes the probability mass function (PMF, P(L=i))and the cumulated distribution function (CDF, P(L<=i)) of the one-sided CUSUM chart run length up to a given i. The data are normally distributed with variance 1. |
| Usage: | pLi = spccusum1pmfm (mu, k, c, Li, r) | |
| Input: | ||
| mu | scalar, representing the expected value of the user-defined random variable. | |
| k | scalar, reference value. It must be positive and be expressed as a multiple of the standard error. | |
| c | scalar, critical value | |
| Li | scalar, ARL of a SPC scheme starting in point Li | |
| r | scalar, matrix dimension of the approximating one-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 up to a defined point Li. | |
; PMF and CDF of the one-sided CUSUM run length with
; in-control ARL = 100, reference value k = 0.5 and
; matrix dimension 50(of the approximating one-dimensional
; Markov chain) for i=1 to i=10:
library("spc")
c = spccusum1c(100, 0.5, 50)
pLi = spccusum1pmfm(0,0.5,c,10,50)
pLi
Contents of pLi [ 1,] 0.00040461 0.00040461 [ 2,] 0.0033207 0.0037253 [ 3,] 0.0063068 0.010032 [ 4,] 0.0081035 0.018136 [ 5,] 0.0090188 0.027155 [ 6,] 0.0094405 0.036595 [ 7,] 0.0096052 0.0462 [ 8,] 0.0096392 0.055839 [ 9,] 0.0096075 0.065447 [10,] 0.0095429 0.07499