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An adaptive EWMA control chart for monitoring the process mean in Bayesian theory under different loss functions
Author(s) -
NoorulAmin Muhammad,
Noor Surria
Publication year - 2021
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2764
Subject(s) - ewma chart , control chart , x bar chart , chart , statistics , shewhart individuals control chart , bayesian probability , computer science , standard deviation , control limits , statistical process control , mathematics , process (computing) , operating system
The Shewhart control chart is used for detecting the large shift and an exponentially weighted moving average (EWMA) control chart is used for detecting the small/moderate shift in the process mean. A scheme that combines both the Shewhart control chart and the EWMA control chart in a smooth way is called the adaptive EWMA (AEWMA) control chart. In this paper, we proposed a new AEWMA control chart for monitoring the process mean in Bayesian theory under different loss functions (LFs). We used informative (conjugate prior) under two different LFs: (1) squared error loss function and (2) linex loss function for posterior and posterior predictive distributions. We used the average run length and standard deviation of run length to measure the performance of the AEWMA control chart in the Bayesian theory. A comparative study is conducted for comparing the proposed AEWMA control chart in Bayesian theory with the existing Bayesian EWMA control chart. We conducted a Monte Carlo simulation study to evaluate the proposed AEWMA control chart. For the implementation purposes, we presented a real‐data example.