Distribution-free Lepage Type Circular-grid Charts for Joint Monitoring of Location and Scale Parameters of a Process

2016 ◽  
Vol 33 (2) ◽  
pp. 241-274 ◽  
Author(s):  
Amitava Mukherjee ◽  
Marco Marozzi
Keyword(s):  
Distribution Free ◽  
Scale Parameters ◽  
Joint Monitoring ◽  
Circular Grid

Performance comparisons of distribution-free Shewhart-type Lepage and Cucconi schemes in monitoring complex process distributions

2020 ◽  
Vol 42 (14) ◽  
pp. 2787-2811 ◽  
Author(s):  
Zhi Lin Chong ◽  
Shuo Huang ◽  
Amitava Mukherjee ◽  
Jun Yang
Keyword(s):  
Additional Parameter ◽  
Control Performance ◽  
Monitoring And Control ◽  
Performance Study ◽  
Time To Event ◽  
Distribution Free ◽  
Scale Parameters ◽  
Scale Family ◽  
Joint Monitoring ◽  
And Control

In recent years, researchers introduced several distribution-free schemes for simultaneously monitoring the location and scale parameters of distribution in the literature related to process monitoring and control. To this end, the Shewhart-Lepage (SL) and Shewhart-Cucconi (SC) schemes are two fundamental distribution-free schemes. These schemes are primarily designed to monitor the location-scale family of densities. In practice, apart from the location and scale parameters, we often encounter the presence of a shape (or skewness) parameter. In this article, we investigate the performance of the SL and SC schemes in monitoring such models. We consider some skewed distributions in the location-scale family with one or two additional parameters, some three-parameter time-to-event processes, such as three-parameter Weibull and Gamma, which are very common in various measurement and control literature. First, we present the in-control performance of the two competing schemes and then carry out a comprehensive out-of-control performance study by considering different combinations of shifts. Several recent investigations showed that the SC scheme performs just as well or better than the SL scheme in joint monitoring of the location and scale parameters for a large number of process distributions. The current study shows that in the presence of an additional parameter, especially when the shift in the shape parameter is substantial, the SL scheme is better; for a small change in shape, the SC scheme is more competitive. In general, the SL scheme performs better in monitoring the three-parameter distributions for time-to-event processes. Finally, a real application and some concluding remarks are presented.

scholarly journals Distribution-free Phase II CUSUM Control Chart for Joint Monitoring of Location and Scale

2014 ◽  
Vol 31 (1) ◽  
pp. 135-151 ◽  
Author(s):  
Shovan Chowdhury ◽  
Amitava Mukherjee ◽  
Subhabrata Chakraborti
Keyword(s):  
Control Chart ◽  
Phase Ii ◽  
Distribution Free ◽  
Cusum Control Chart ◽  
Joint Monitoring

scholarly journals A Nonparametric Test For Homogeneity Of Variances: Application To GPAs Of Students Across Academic Majors

2010 ◽  
Vol 3 (3) ◽  
pp. 47-54 ◽  
Author(s):  
Saad T. Bakir
Keyword(s):  
Nonparametric Test ◽  
Grade Point Averages ◽  
Academic Majors ◽  
Distribution Free ◽  
Grade Point ◽  
Population Means ◽  
Scale Parameters ◽  
Analysis Of Means ◽  
Homogeneity Of Variances ◽  
Graph Paper

We propose a nonparametric (or distribution-free) procedure for testing the equality of several population variances (or scale parameters). The proposed test is a modification of Bakir’s (1989, Commun. Statist., Simul-Comp., 18, 757-775) analysis of means by ranks (ANOMR) procedure for testing the equality of several population means. A proof is given to establish the distribution-free property of the modified procedure. The proposed procedure is then applied to test whether or not the variability in the grade point averages (GPAs) of students differs across five business academic majors. We collect the GPAs (observations) of a random sample of students from each major under study. The absolute deviations of the observations from the overall median of the combined sample are then calculated and ranked from least to largest. The average ranks and two decision lines are then plotted on a graph paper to detect not only the existence of significant differences among variances, but also to pinpoint which variances are causing those differences.

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