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 |
alpha |
Probability of false alarm (Type I error). Defaults to |
type |
The type of chart. Accepts either |
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")