XploRe Help : spccusum1c

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	spc
See also:	spccusum1arl spccusum2c spccusumCc

Quantlet:		spccusum1c
Description:		Computes the critical value of a one-sided CUSUM chart for a given in-control Average Run Length. The data is normally distributed with variance 1.

Reference(s):

Page, E.S. (1954). Continuous inspection schemes. Biometrika 41: pp. 100-115. Brook, D. and Evans, D. A. (1972). An approach to the probability distribution of CUSUM run length. Biometrika: 59. pp. 539-549.

Usage:	`c = spccusum1c (ARL, k, r)`
Input:
	`ARL`	scalar, representing a user-defined in-control Average Run Length of a one-sided CUSUM chart
	`k`	scalar, reference value. It must be positive and be expressed as a multiple of the standard error.
	`r`	scalar, matrix dimension of the approximating one-dimensional Markov chain
Output:
	`c`	scalar, critical value of a one-sided CUSUM chart with user-defined in-control ARL

Note:

The algorithm is based on the Brook/Evans approach and on the regula falsi.

Example:

; Computation of the critical value c of a one-sided CUSUM ; chart with in-control ARL = 100, reference value k = 0.5 ; and matrix dimension 50(of the approximating ; one-dimensional Markov chain): library("spc") c = spccusum1c(100, 0.5, 50) c

Result:

Contents of c
[1,]   2.8496

Example:

library("spc") c = spccusum1c(100, 0.25, 50) c

Result:

Contents of c
[1,]   4.4192

Author: S. Knoth, 20011010 license MD*Tech