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

 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
(C) MD*TECH Method and Data Technologies, 05.02.2006