A univariate procedure for monitoring location and dispersion with ordered categorical data

ABSTRACT The quality characteristic is usually measured by ordered attribute levels, such as good, general, and poor, which describe different magnitudes of the characteristic. The ordinal levels are determined by a continuous latent variable, the shifts of which are reflected by the observed counts in each level. This article devises a control procedure based on the discrepancy between observed average cumulative counts and their expected ones. Simulation results are shown to demonstrate its superior sensitivity in simultaneously detecting location and dispersion shifts of the latent variable. Flexibility in assigning the weight for each level can allow the chart to be more powerful.

[1]  Fugee Tsung,et al.  A simple categorical chart for detecting location shifts with ordinal information , 2014 .

[2]  G. Geoffrey Vining,et al.  CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes , 2014 .

[3]  Ful-Chiang Wu,et al.  A comparative study on optimization methods for experiments with ordered categorical data , 2006, Comput. Ind. Eng..

[4]  Fugee Tsung,et al.  Directional control schemes for processes with mixed-type data , 2016 .

[5]  Majid Jafari Khaledi,et al.  Estimation in Truncated GLG Model for Ordered Categorical Spatial Data Using the SAEM Algorithm , 2014, Commun. Stat. Simul. Comput..

[6]  Philippe Girard,et al.  Bayesian Analysis of Autocorrelated Ordered Categorical Data for Industrial Quality Monitoring , 2001, Technometrics.

[7]  Stefan H. Steiner,et al.  Control charts based on grouped observations , 1994 .

[8]  Vijayan N. Nair,et al.  Testing in industrial experiments with ordered categorical data , 1986 .

[9]  Chi-Jui Huang.  A New GWMA Control Chart for Monitoring Process Mean and Variability , 2015 .

[10]  A. K. McCracken,et al.  Control Charts for Joint Monitoring of Mean and Variance: An Overview , 2013 .

[11]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[12]  Fugee Tsung,et al.  Multivariate binomial/multinomial control chart , 2014 .

[13]  Fugee Tsung,et al.  A spatial rank‐based multivariate EWMA control chart , 2012 .

[14]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[15]  Christian H. Weiß,et al.  Continuously Monitoring Categorical Processes , 2012 .

[16]  Stelios Psarakis,et al.  Review of multinomial and multiattribute quality control charts , 2009, Qual. Reliab. Eng. Int..

[17]  Fugee Tsung,et al.  Rank-based process control for mixed-type data , 2016 .

[18]  Jennifer Brown,et al.  New Synthetic Control Charts for Monitoring Process Mean and Process Dispersion , 2015, Qual. Reliab. Eng. Int..

[19]  Yuehjen E. Shao,et al.  A Combined MLE and Generalized P Chart Approach to Estimate the Change Point of a Multinomial Process , 2013 .

[20]  Hülya Bayrak,et al.  Permutation approach for ordinal preference data , 2017, Commun. Stat. Simul. Comput..

[21]  Ing Rj Ser.  Approximation Theorems of Mathematical Statistics , 1980 .

[22]  Luigi Salmaso,et al.  Permutation Anderson–Darling Type and Moment-Based Test Statistics for Univariate Ordered Categorical Data , 2007, Commun. Stat. Simul. Comput..

[23]  William H. Woodall,et al.  Control Charts Based on Attribute Data: Bibliography and Review , 1997 .

[24]  Aamir Saghir,et al.  Control Charts for Dispersed Count Data: An Overview , 2015, Qual. Reliab. Eng. Int..

[25]  Tongdan Jin,et al.  An improved self-starting cumulative count of conforming chart for monitoring high-quality processes under group inspection , 2012 .

[26]  Stefan H. Steiner,et al.  Grouped data exponentially weighted moving average control charts , 2008 .

[27]  P. McCullagh.  Analysis of Ordinal Categorical Data , 1985 .

[28]  Kwok-Leung Tsui,et al.  A Control Chart Method for Ordinal Data , 2002 .

[29]  William H. Woodall,et al.  Methods for Monitoring Multiple Proportions When Inspecting Continuously , 2011 .

[30]  Thong Ngee Goh,et al.  CONTROL CHART FOR MULTIVARIATE ATTRIBUTE PROCESSES , 1998 .

[31]  M. Marcucci.  MONITORING MULTINOMIAL PROCESSES , 1985 .

[32]  Susan L. Albin,et al.  Monitoring and accurately interpreting service processes with transactions that are classified in multiple categories , 2009 .

[33]  Shin-Ming Guo,et al.  Quality improvement for RC06 chip resistor , 1996 .