EATME (version 0.1.0)

cont_to_disc_M: Convert data to M statistic

Description

Convert continuous random variables in in-control process into discrete random variables with M statistic, where M statistic is the total number of samples satisfying \(X_{ij}>\mu\) at time \(i\), where \(X_{ij}\) is the observation for the \(i^{th}\) sampling period and the \(j^{th}\) sample in the in-control data, \(n\) is the number of the sample size and \(m\) is the number of the sampling periods. \(\mu\) is the population mean of continuous in-control data. If \(\mu\) is unknown, it can be estimated by \(\hat{\mu}=\overline{\overline{x}}=\frac{\sum^m_{i = 1}\sum^n_{j=1} X_{ij}}{n\times m}\).

Usage

cont_to_disc_M(ICdata, OCdata, mu.p = mean(ICdata))

Arguments

ICdata

The in-control data.

OCdata

The out-of-control data.

mu.p

Mean of the random variable in the in-control data.

Value

M0\(\hspace{2cm}\) The M statistic for in-control data.

M1\(\hspace{2cm}\) The M statistic for out-of-control data.

p0\(\hspace{2cm}\) The process proportion for in-control data.

p1\(\hspace{2cm}\) The process proportion for out-of-control data.

n\(\hspace{2.2cm}\) The number of the sample size.

References

Yang, S. F., Lin, J. S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert Systems with Applications, 38(5), 6239-6243.

Yang, S. F. & Arnold, B. C. (2014). A simple approach for monitoring business service time variation.The Scientific World Journal, 2014:16.

Yang, S. F. (2016). An improved distribution-free EWMA mean chart. Communications in Statistics-Simulation and Computation, 45(4), 1410-1427.

Examples

# NOT RUN {
IC = matrix(rnorm(100,0,1),ncol = 10,byrow = TRUE)
OC = matrix(rnorm(100,2,1),ncol = 10,byrow = TRUE)
cont_to_disc_M(IC,OC)
# }