Recursive parameter estimation for categorical process control

Abstract

Statistical process adjustment (SPA) is utilised prevalently in novel manufacturing scenarios. When quality characteristics rather than internal process variables are inspected for the purpose of quality control, data with different resolutions may be collected. This paper proposes a Bayesian framework for parameter estimation when only categorical observations are available. The proposed method incorporates categorical information recursively and updates parameter estimates in real time. Simulation results show that the framework is effective in utilising low-resolution information in parameter estimation, model building and process control.

A run-to-run control algorithm based on timely and delayed mixed-resolution information

“…In many R2R processes, linear models can be used to characterise processes with continuous inputs and outputs (see, e.g., Del Castillo and Hurwitz 1997;Tsung 2007, 2008;Shang, Wang, and Tsung 2009;Wang and Tsung 2010). Othman et al (2006) showed that a linear model between the removal rate and the controller factors is adequate for the lapping process.…”

“…Shang, Wang, and Tsung (2009) improved this controller by considering misclassification errors in which misclassification possibilities were used to compensate for process adjustment bias. Wang and Tsung (2010) studied recursive parameter estimation with categorical observations that were available and proposed a Bayesian Categorical Controller. The authors assumed that all of the cut-points were known and only studied the estimation of a linear process model.…”

Change-Point Detection in Multivariate Categorical Processes With Variable Selection

“…where u (0) indicates the overall mean; u (1) , u (2) and u (3) represent the main effects; u (1,2) , u (1,3) and u (2,3) represent the two-factor interaction effects; u (1,2,3) is the three-factor interaction effect.…”

“…The associate editor coordinating the review of this manuscript and approving it for publication was Md Asaduzzaman. the etching profiles into negative, normal and positive than measuring their angles of sidewalls accurately [2].…”

Latent change‐point detection in ordinal categorical data

“…Such phase I analysis is important since it sets a base for estimating IC parameters and further for phase II online surveillance. In practice, it often encounters the case that timely and accurate numerical measurements are not available because of the high cost or categorical nature of the characteristic . For example, in a welding process for electronic toothbrushes, it is hard to measure the length of flash caused by excessive material leakage on the brush head, and quality inspectors classify the head flash of each brush into four levels, slight, small, medium, and large, before further treatments .…”