A a comparison of the markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts

DOI10.1080/03610919108812948zbMath0850.62739OpenAlexW2033361390MaRDI QIDQ4019237

Charles W. Champ, Steven E. Rigdon

Publication date: 16 January 1993

Published in: Communications in Statistics - Simulation and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610919108812948

Mathematics Subject Classification ID

Applications of statistics in engineering and industry; control charts (62P30) Numerical methods for integral equations (65R20) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20)

Related Items (16)

On the average run lengths of quality control schemes using a Markov chain approach ⋮ The EWMA sign chart revisited: performance and alternatives without and with ties ⋮ Explicit analytical solutions for ARL of CUSUM chart for a long-memory SARFIMA model ⋮ Unnamed Item ⋮ Derivation of explicit formulae for performance measures of CUSUM control chart for SMA(Q)\(_s\) model with exponential white noise ⋮ Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts ⋮ Economic design of memory-type control charts: the fallacy of the formula proposed by Lorenzen and Vance (1986) ⋮ An Accurate Method for Determining the Pre-Change Run Length Distribution of the Generalized Shiryaev-Roberts Detection Procedure ⋮ Unnamed Item ⋮ Average run length of the long-memory autoregressive fractionally integrated moving average process of the exponential weighted moving average control chart ⋮ Necessary and sufficient conditions for non-interaction of a pair of one-sided EWMA schemes with reflecting boundaries ⋮ Evaluating properties of variable sampling interval control charts ⋮ Computation of the ARL for CUSUM-\(S^2\) schemes ⋮ The computation of average run length and average time to signal: an overview ⋮ Effect of Inspection Error on Out-of-Control Average Run Length of CUSUM Charts ⋮ Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL

Cites Work

• The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables
• Computational Methods for Integral Equations
• A Simple Method for Studying Run-Length Distributions of Exponentially Weighted Moving Average Charts
• The Performance of Control Charts and Cusums Under Linear Trend
• An approach to the probability distribution of cusum run length

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