EWMA_p_two {EATME}

The two-sided control limits of an EWMA-p chart

Description

This function is used to calculate the two-sided control limit for EWMA-p charts with the correction of measurement error effects. If two truly classified probabilities pi1 and pi2 are given by 1, then the corresponding control limit is free of measurement error.

Usage

EWMA_p_two(p, lambda, n, pi1 = 1, pi2 = pi1, ARL0 = 200, M = 500, error = 10)

Arguments

p

The proportion of defectives in the in-control process.

lambda

An EWMA smooth constant, which is a scalar in [0,1].

n

A sample size in the data.

pi1

The proportion that the observed defectives are the same as unobserved ones.

pi2

The proportion that the observed non-defectives are the same as unobserved ones.

ARL0

A prespecified average run length (ARL) of a control chart in the in-control process.

M

The number of simulation times for the Monte Carlo method

error

The tolerant for the absolute different between an itevated ARL calue and prespecified ARL0.

Value

L1\hspace{2.2cm} The coefficient of the upper control limit.

L2\hspace{2.2cm} The coefficient of the lower control limit.

hat_ARL0\hspace{1.1cm} The estimated in-control average run length based on given L1 and L2.

hat_MRL0\hspace{1.1cm} The estimated in-control median of run length based on given L1 and L2.

hat_SDRL0\hspace{0.9cm} The estimated in-control standard deviation of run length based on given L1 and L2.

UCL\hspace{2cm} The limiting value of the upper control limit with L1.

LCL\hspace{2cm} The limiting value of the lower control limit with L2.

References

Chen, L. P., & Yang, S. F. (2022). A New p-Control Chart with Measurement Error Correction. arXiv preprint arXiv:2203.03384.

Examples

set.seed(2)
EWMA_p_two(0.2,0.05,5,1,1,200,100,20)