The Variable Sample Size Chart with Estimated Parameters

Philippe Castagliola · Ying Zhang · Antonio Samuel Da Silva Costa · Petros E. Maravelakis

57 citations0/0 files storedQuality and Reliability Engineering International

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

The VSS chart, dedicated to the detection of small to moderate mean shifts in the process, has been investigated by several researchers under the assumption of known process parameters. In practice, the process parameters are rarely known and are usually estimated from an in‐control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS chart when the process parameters are estimated, we compare them in the case where the process parameters are assumed known and we propose specific optimal control chart parameters taking the number of Phase I samples into account.

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References

1999Introduction to Matrix Analytic Methods in Stochastic Modeling 2006Effects of Parameter Estimation on Control Chart Properties: A Literature Review 1993The Effect of Sample Size on Estimated Limits forXandXControl Charts 2001The Performance of Exponentially Weighted Moving Average Charts With Estimated Parameters 1994XCharts with Variable Sample Size 1991SPCQCharts for Start-Up Processes and Short or Long Runs 1998A Survey of Recent Developments in the Design of Adaptive Control Charts 1993X¯ chart with adaptive sample sizes

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2016Optimal Designs of the Variable Sample Size Chart Based on Median Run Length and Expected Median Run Length 2013Optimal designs of the double sampling X¯ chart with estimated parameters 2015The Performance of Variable Sample Size Chart with Measurement Errors 2015A direct procedure for monitoring the coefficient of variation using a variable sample size scheme 2018Hotelling's T2 control charts with fixed and variable sample sizes for monitoring short production runs

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