Phase-I design structure of Bayesian variance chart

Aamir Saghir,Zudi Lu

doi:10.1080/23311835.2016.1172403

Aamir Saghir, Zudi Lu

Open Access

https://doi.org/10.1080/23311835.2016.1172403

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Abstract

AbstractThis article develops a new design structure for S2-Chart, namely Bayesian variance chart, in Phase-I analysis assuming the normality of the quality characteristic to incorporate the parameter uncertainty. Our approach consists of two stages: (i) construction of the control limits for S2-Chart and (ii) performance evaluation of the proposed control limits. The comparison of the proposed design structure with the frequentist design structure of S2-Chart is examined in terms of (i) width of control region and (ii) OC curves when the process variance goes out of control. It is observed that the proposed Phase-I S2-Chart is more efficient than the frequentist S2-Chart in discriminatory power of detecting a shift in the process dispersion. When the process variance is in-control (after implementation of Bayesian variance chart), then the control limits for X¯-Chart using in-control standard deviation are also given here for monitoring unknown mean under unknown standard deviation case.

Highlights

There is a large literature on the process variability control charts
Evaluation of control limits For the evaluation of the control limits obtained by frequentist and Bayesian methods, we use OC function under the hypothetical situation that the variance of the normal distribution does not remain at level σ2 following Sharma et al (2007), Saghir (2007), and Menzefricke (2010)
Let the sampling distribution for the sample mean be N(M, ) where M is the value of the in-control or out-of-control process mean and the n process standard deviation is in-control at σ =

Summary

Introduction

There is a large literature on the process variability control charts. To develop a variability control chart, a basic assumption is that the underlying distribution of the quality characteristics should be normal. Control limits based on Jeffrey’s prior In this subsection, we have proposed control limits for S2-Chart based on Jeffrey’s prior for unknown mean and variance of the normal distribution, so that we are relying primarily on the likelihood involved for our inference following the work of Box (1980), Chhikara and Guttman (1982), and Gelman (2006).

Results

Conclusion