XploRe Help : spcewma2arl

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:	spcewma2c spcewma1arl

Quantlet:		spcewma2arl
Description:		Computes the Average Run Lengths of a two-sided EWMA chart for a given critical value and for various expected values mu. The data is normally distributed with variance 1.

Reference(s):

Lucas, J.M. and Saccucci, M.S. (1990). Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements. Technometrics: 32. pp. 1-12. Roberts, S.W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics; 1. pp. 239-250.

Link:

Applied Quantitative Finance, see Chapter 12: "Statistical Process Control"

Usage:	`arl = spcewma2arl (mu, lambda, c, r)`
Input:
	`mu`	n x 1 vector representing the expected values of the user-defined random variable
	`lambda`	scalar representing the smoothing parameter
	`c`	scalar, critical value
	`r`	scalar, matrix dimension of the approximating two-dimensional Markov chain
Output:
	`arl`	n x 1 vector of scalars representing the Average Run Lengths of a two-sided EWMA chart

Note:

The algorithm is based on the Brook/Evans approach.

Example:

; ARLs of a two-sided EWMA chart for different expected values ; mu, smoothing parameters lambda = 0.5 and matrix dimension 50 ;(of the approximating two-dimensional Markov chain): library("spc") mu =(0:4)/4 c = spcewma2c(100,0.5,50) arl = spcewma2arl(mu,0.5,c,50) mu~arl

Result:

Contents of _tmp
[1,]        0   99.999
[2,]     0.25   63.156
[3,]      0.5    28.91
[4,]     0.75   14.664
[5,]        1   8.6018

Author: S. Knoth, 20011010 license MD*Tech