mxk {mxcc}R Documentation

Determination of Probability Limit Coefficients for V and VSQ Charts for Maxwell-Distributed Quality Characteristics

Description

The function mxk calculates the coefficients for V and VSQ control charts used to monitor the scale parameter of Maxwell-distributed quality characteristics. It computes two coefficients based on the chosen chart type. For the V chart, the function returns L1 and L2, while for the VSQ chart, it returns P1,P2,P3 and P4.The coefficients P3 and P4 are used in case of estimated scale parameter value.These coefficients are utilized to construct a probability limits-based control chart.

Usage

mxk(n = 1, alpha = 0.0027, type = "V")

Arguments

n

Sample size. The number of observations in each subgroup (numeric). Defaults to 1.

alpha

Probability of false alarm (Type I error). Defaults to 0.0027 (numeric).

type

The type of chart. Accepts either "V" for the V chart or "VSQ" for the VSQ chart (character).

Details

The mxk function calculates the coefficients used in V and VSQ control charts for monitoring the scale parameter of Maxwell-distributed data. The user must specify the sample size n, the probability of a false alarm alpha, and the type of chart ("V" or "VSQ"). By default, n is set to 1, and alpha is set to 0.0027.

Value

Depending on the type of chart:

L1

Coefficient L1 for the V chart.

L2

Coefficient L2 for the V chart.

P1

Coefficient P1 for the VSQ chart.

P2

Coefficient P2 for the VSQ chart.

P3

Coefficient P3 for the VSQ chart.

P4

Coefficient P4 for the VSQ chart.

Author(s)

Zahid Khan

References

Hossain, M.P., Omar, M.H. and Riaz, M. (2017) "New V control chart for the Maxwell distribution". Journal of Statistical Computation and Simulation, 87(3), pp.594-606. <doi:10.1080/00949655.2016.1222391>

Shah, F., Khan, Z., Aslam, M. and Kadry, S. (2021) "Statistical Development of the VSQ‐Control Chart for Extreme Data with an Application to the Carbon Fiber Industry". Mathematical Problems in Engineering, 2021(1), p.9766986. <doi:10.1155/2021/9766986>

Examples

mxk(n = 4, alpha = 0.0027, type = "VSQ")

[Package mxcc version 0.0.3 Index]