Application of Bernoulli Process-based Charts to Electronic Assembly

The application of protective gel, which is a subprocess of the electronic assembly of the exhaust gas recirculation sensor, is a highly capable process with the fraction of nonconforming units as low as 200 ppm. Every unit is inspected immediately after gel application. The conventional Shewhart chart is of no use here, and the approach based on the Bernoulli process is therefore considered. The number of conforming items in a row until the occurrence of first or the r-th nonconforming is determined and CCC-r, CCC-r EWMA, and CCC CUSUM charts are applied. The aim of the control is to detect the process deterioration, and so the one-sided charts are used. So that the charts based on the geometric or negative binomial distribution can be compared, their performance is assessed through the average number of inspected units until a signal (ANOS). Our study confirmed that CCC-r EWMA and CCC CUSUM are able to detect the process shift more quickly than the CCC-r chart. Of the two charts, the first is easier to construct

Parametric, Nonparametric, and Semiparametric Linear Regression in Classical and Bayesian Statistical Quality Control

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a practitioner’s guide to provide a stepby- step application for parametric, nonparametric, and semiparametric methods in profile monitoring, creating an in-depth guideline for novice practitioners. We then consider the commonly used cumulative sum (CUSUM), multivariate CUSUM (mCUSUM), exponentially weighted moving average (EWMA), multivariate EWMA (mEWMA) charts under a Bayesian framework for monitoring respiratory disease related hospitalizations and global suicide rates with parametric, nonparametric, and semiparametric linear models

A Binary Control Chart to Detect Small Jumps

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is su- perior in terms of out-of-control average run length, when one is interest in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives which explains that unexpected and interesting behavior. Since real observations are often not independent, the question arises whether these re- sults still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, firstly, to a large class time series models, and, secondly, to locally dependent image data, as we demonstrate by an example

Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Design and Application of Risk Adjusted Cumulative Sum (RACUSUM) for Online Strength Monitoring of Ready Mixed Concrete

The Cumulative Sum (CUSUM) procedure is an effective statistical process control tool that can be used to monitor quality of ready mixed concrete (RMC) during its production process. Online quality monitoring refers to monitoring of the concrete quality at the RMC plant during its production process. In this paper, we attempt to design and apply a new CUSUM procedure for RMC industry which takes care of the risks involved and associated with the production of RMC. This new procedure can be termed as Risk Adjusted CUSUM (RACUSUM). The 28 days characteristic cube compressive strengths of the various grades of concrete and detailed information regarding the production process and the risks associated with the production of RMC were collected from the operational RMC plants in and around Ahmedabad and Delhi (India). The risks are quantified using a likelihood based scoring method. Finally a Risk Adjusted CUSUM model is developed by imposing the weighted score of the estimated risks on the conventional CUSUM plot. This model is a more effective and realistic tool for monitoring the strength of RMC.

Exponentially Weighted Moving Averages of Counting Processes When the Time between Events Is Weibull Distributed

There are control charts for Poisson counts, zero-inflated Poisson counts, and over dispersed Poisson counts (negative binomial counts) but nothing on counting processes when the time between events (TBEs) is Weibull distributed. In our experience the in-control distribution for time between events is often Weibull distributed in applications. Counting processes are not Poisson distributed or negative binomial distributed when the time between events is Weibull distributed. This is a gap in the literature meaning that there is no help for practitioners when this is the case. This book chapter is designed to close this gap and provide an approach that could be helpful to those applying control charts in such cases