XploRe Help : spcewma1arl

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:	spcewma1c spcewma2arl spcewma1ad

Quantlet:		spcewma1arl
Description:		Computes the Average Run Lengths of a one-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.

Usage:	`arl = spcewma2arl (mu, lambda, c, zreflect, r)`
Input:
	`mu`	n x 1 vector representing the expected values of the user-defined random variable
	`lambda`	scalar, containing the smoothing parameter
	`c`	scalar, critical value
	`zreflect`	scalar, representing a pre-defined border. It is usually less than zero. If zreflect is small enough ARL and AD of the bounded scheme are the same as of the unbounded one.
	`r`	scalar, matrix dimension of the approximating one-dimensional Markov chain
Output:
	`arl`	n x 1 vector of scalars representing the Average Run Lengths of a one-sided EWMA chart

Note:

The algorithm is based on the Brook/Evans approach. At zreflect<=0 the EWMA statistic is reflected, i.e., the continuation region (-infinity,c] is truncated into (zreflect,c].

Example:

; ARLs of a one-sided EWMA chart for different expected ; values mu, smoothing parameters lambda = 0.5 and matrix ; dimension 50(of the approximating one-dimensional Markov ; chain): library("spc") mu =(0:4)/4 c = spcewma1c(100,0.5,-4,50) arl = spcewma1arl(mu,0.5,c,-4,50) mu~arl

Result:

Contents of _tmp
[1,]        0   99.999
[2,]     0.25   38.909
[3,]      0.5   18.238
[4,]     0.75   10.071
[5,]        1   6.3579

Author: S. Knoth, 20011010 license MD*Tech