XploRe Help : spcewma1c

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:	spcewma1arl spcewma2c

Quantlet:		spcewma1c
Description:		Computes the critical value of a one-sided EWMA chart for a given in-control Average Run Length. 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:	`c = spcewma1c (ARL, lambda, zreflect, r)`
Input:
	`ARL`	scalar representing a user-defined in-control Average Run Length of a one-sided EWMA chart
	`lambda`	scalar representing the smoothing parameter
	`zreflect`	scalar representing a pre-defined border. It is usually less than zero.
	`r`	scalar, matrix dimension of the approximating one-dimensional Markov chain
Output:
	`c`	scalar, critical value of a one-sided EWMA chart with user-defined in-control ARL

Note:

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

Example:

; Compute the critical value c of a one-sided EWMA chart with ; in-control ARL = 100, smoothing parameter lambda = 0.5 ; and matrix dimension 50(of the approximating one-dimensional ; Markov chain): library("spc") c = spcewma1c(100, 0.5, -2, 50) c

Result:

Contents of c
[1,]   2.2594

Example:

library("spc") c = spcewma1c(100, 0.5, -3, 50) c

Result:

Contents of c
[1,]   2.2587

Example:

library("spc") c = spcewma1c(100, 0.5, -5, 50) c

Result:

Contents of c
[1,]   2.2586

Author: S. Knoth, 20011010 license MD*Tech