Posterior Distribution Charts: A Bayesian Approach for Graphically Exploring a Process Mean

@article{Apley2012PosteriorDC,
  title={Posterior Distribution Charts: A Bayesian Approach for Graphically Exploring a Process Mean},
  author={Daniel W. Apley},
  journal={Technometrics},
  year={2012},
  volume={54},
  pages={279 - 293}
}
  • D. Apley
  • Published 23 May 2012
  • Mathematics
  • Technometrics
We develop a Bayesian approach for monitoring and graphically exploring a process mean and informing decisions related to process adjustment. We assume a rather general model, in which the observations are represented as a process mean plus a random error term. In contrast to previous work on Bayesian methods for monitoring a mean, we allow any Markov model for the mean. This includes a mean that wanders slowly, that is constant over periods of time with occasional random jumps or combinations… 

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References

SHOWING 1-10 OF 33 REFERENCES

A Bayesian Sequential Look at u-Control Charts

TLDR
It is argued that the sequential, full Bayesian uCC is a powerful and versatile tool for process monitoring.

On sequential Monte Carlo sampling methods for Bayesian filtering

TLDR
An overview of methods for sequential simulation from posterior distributions for discrete time dynamic models that are typically nonlinear and non-Gaussian, and how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature are shown.

Feedback quality adjustment with Bayesian state-space models

TLDR
A Bayesian procedure for feedback adjustment and control of a single process that replaces the usual exponentially weighted moving average predictor by a predictor of a local level model and gives the posterior and predictive distributions for both the process and the NVR.

Comparing the Effectiveness of Various Bayesian X Control Charts

TLDR
The results from the comparative numerical study indicate that the chart parameter having the most positive impact on the economic performance by being adaptive is the sampling interval, so it is sufficient in most cases to use control charts with adaptive sampling intervals rather than other types of partially adaptive charts or the more complicated fully adaptive control charts.

Feedback quality adjustment with Bayesian state-space models: Research Articles

TLDR
A Bayesian procedure for feedback adjustment and control of a single process that replaces the usual exponentially weighted moving average predictor by a predictor of a local level model and gives the posterior and predictive distributions for both the process and the NVR.

Bayesian process control for attributes

We consider a process control procedure with fixed sample sizes and sampling intervals, where the fraction defective is the quality variable of interest, a standard attributes control chart

A Bayesian Scheme to Detect Changes in the Mean of a Short-Run Process

TLDR
A Bayesian formulation suitable for statistical process control in short production runs is proposed, leading to a mixture of normal distributions, and issues of decisions about whether the process is within specification and forecasting are addressed.

ESTIMATING THE CURRENT MEAN OF A NORMAL DISTRIBUTION WHICH IS SUBJECTED TO CHANGES IN TIME

Abstract : A tracking problem is considered. Observations are taken on the successive positions of an object traveling on a path, and it is desired to estimate its current position. The objective is

Bayesian Process Monitoring, Control and Optimization

TLDR
This book discusses Bayesian Inference in Process Monitoring, Control, and Optimization, and Bayesian Approaches to Process Monitoring and Process Adjustment, as well as applications to Sequential Empirical Optimization.

Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series

TLDR
The analysis of random mean- shift models to random variance-shift models is extended and a method for predicting when a shift is about to occur is considered, which involves adding to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables.