A process variability control chart
type: Item
instance of: scholarly article
title: A process variability control chart
zbMATH Open document ID: 1236.62163
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Computational Statistics
publication date: 2011-07-18T00:00:00Z
review text: Construction of a Shewhart-type control chart is considered for the variance (deviation) of a monitored process \(Y\) in the case when some information on an auxiliary characteristic X is available. The chart utilizes a ratio type estimator for the variance \(V_t\) of \(Y\) at the moment \(t\), i.e., \(\hat V_t=s^2_Y(\sigma^2_x/s^2_x)^{\rho^2_{xy}}\), where \(s_y^2\), \(s^2_x\) are the sample variances of \(Y\) and \(X\), \(\sigma_x^2\) is the true variance of \(X\) (known) and \(\rho^2_{xY}\) is the known true correlation between \(X\) and \(Y\). The authors construct the center line, and lower and upper control limits for their control chart, basing on Monte Carlo approximations for the corresponding constants. The performance of the constructed \(V_t\) chart is compared to the performance of the classical Shewhart \(S^2\)-chart and some other charts by simulated data.
Mathematics Subject Classification ID: 62P30
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 5925222
zbMATH Keywords: Shewhart control chart
zbMATH Keywords: variance
zbMATH Keywords: auxiliary information
zbMATH Keywords: ratio estimator
MaRDI profile type: Publication
full work available at URL: s00180-008-0122-z
OpenAlex ID: W2161423277
cites work: Self-adapting control charts
cites work: Repeated substitution method: The ratio estimator for the population variance
cites work: Semi-economic design of \(\overline{X}\)-control charts assuming gamma distribution
cites work: Design of R control Chart Assuming a Gamma Distribution
cites work: Joint statistical design of double sampling \(\bar X\) and \(s\) charts
cites work: Variance Estimation Using Auxiliary Information
cites work: Fast initial response features for EWMA control charts
cites work: Estimation of the mean of a univariate normal distribution with known variance
cites work: Probability Weighted Moments Approach to Quality Control Charts
cites work: Statistical quality control based on ranked set sampling
cites work: A general class of estimators for estimating population mean using auxiliary information
cites work: MULTIVARIATE RATIO ESTIMATION FOR FINITE POPULATIONS
cites work: ON THE PROBABILITY THAT TWO INDEPENDENT DISTRIBUTIONS OF FREQUENCY ARE REALLY SAMPLES FROM THE SAME PARENT POPULATION
cites work: Shewhart control charts for the scale parameter of a Weibull control variable with fixed and variable sampling intervals
cites work: Monitoring process variability using auxiliary information
cites work: Q4211224
cites work: Regression Estimator in Ranked Set Sampling
DOI: 10.1007/S00180-008-0122-Z
description: scientific article; zbMATH DE number 5925222