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