Distribution-free (nonparametric)
control chart
Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1)
The hourly status is arranged on the graph, and the occurrence of abnormalit ...
s are one of the most important tools of
statistical process monitoring and control. Implementation techniques of distribution-free
control chart
Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1)
The hourly status is arranged on the graph, and the occurrence of abnormalit ...
s do not require any knowledge about the underlying
process distribution or its parameters. The main advantage of distribution-free
control chart
Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1)
The hourly status is arranged on the graph, and the occurrence of abnormalit ...
s is its in-control robustness, in the sense that, irrespective of the nature of the underlying process distributions, the properties of these control charts remain the same when the process is smoothly operating without presence of any
assignable cause.
Early research on nonparametric control charts may be found in 1981 when P.K. Bhattacharya and D. Frierson introduced a nonparametric control chart for detecting small disorders. However, major growth of nonparametric control charting schemes has taken place only in the recent years.
Popular distribution-free control charts
There are distribution-free control charts for both Phase-I analysis and Phase-II monitoring.
One of the most notable distribution-free control charts for Phase-I analysis is RS/P chart proposed by G. Capizzi and G. Masaratto. RS/P charts separately monitor location and scale parameters of a univariate process using two separate charts. In 2019, Chenglong Li, Amitava Mukherjee and Qin Su proposed a single distribution-free control chart for Phase-I analysis using multisample Lepage statistic.
Some popular Phase-II distribution-free control charts for
univariate
In mathematics, a univariate object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one variable are multivariate. In some cases the distinction between the univariate and multivariat ...
continuous processes includes:
* Sign charts based on the
sign statistic - used to monitor location parameter of a process
*Wilcoxon rank-sum charts based on the
Wilcoxon rank-sum Wilcoxon is a surname, and may refer to:
* Charles Wilcoxon, drum educator
* Henry Wilcoxon, an actor
* Frank Wilcoxon, chemist and statistician, inventor of two non-parametric tests for statistical significance:
** The Wilcoxon signed-rank test
...
test - used to monitor location parameter of a process
*Control charts based on precedence or excedance statistic
* Shewhart-Lepage chart based on the
Lepage test - used to monitor both location and scale parameters of a process simultaneously in a single chart
* Shewhart-Cucconi chart based on the
Cucconi test - used to monitor both location and scale parameters of a process simultaneously in a single chart
References
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Statistical charts and diagrams
Quality control tools