mxm: Determination of K-sigma limit Coefficients for V and VSQ...

In mxcc: Maxwell Control Charts

Determination of K-sigma limit Coefficients for V and VSQ Charts for Maxwell-Distributed Quality Characteristics

Description

This function calculates the K-sigma multiplier (L) for control chart based on the specified type: V chart or VSQ chart. The calculation is based on the sample size and the false alarm probability.This multiplier can further be used in the construction of coefficients W1and W2 for the V chart and coefficients W1,W2,W3 and W4 for the VSQ chart.

Usage

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

Arguments

n	Sample size used in the chart. Default is 1.
alpha	False alarm probability. Default is 0.0027.
type	The type of control chart. Can be "V" for V chart or "VSQ" for VSQ chart. Default is "V".

Details

The function computes the K-sigma multiplier for either V chart or VSQ chart based on the specified type. If the type is "V", it uses the gamma distribution with the specified parameters. If the type is "VSQ", it uses the ch distribution. The output is the L value that represent multiplier in the K-sigma control limits for the respective chart.

Value

Returns the K-sigma multiplier (L) as a numeric value

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

mxm(n = 5, alpha = 0.005, type = "V")

mxcc documentation built on April 10, 2026, 5:06 p.m.