A New Statistical High‐Quality Process Monitoring Method: The Counted Number Between Omega‐Event Control Charts

Control chart techniques for high‐quality process have attracted great attention in modern precision manufacturing. Traditional control charts are no longer applicable because of high false alarm rate. To solve this problem, in this article a new statistical process monitoring method, the counted number between omega‐event statistical process control charts, abbreviated as CBΩ charts, is proposed. The phrase omega event denotes that one observation falls into some certain interval and the CBΩ chart is to monitor the number of consecutive parts between successive r omega events. On the basis of CBΩ charts, a dual‐CBΩ monitoring scheme is developed. This scheme sets up two CBΩ charts with symmetrical omega events, (μ + ?σ, + ∞) and (? ∞, μ ? ?σ), respectively. The performance of CBΩ charts and dual‐CBΩ monitoring is investigated. Dual‐CBΩ monitoring has shown its capability in detecting both mean and variance shift and convenience in implementation compared with other traditional charts. Dual‐CBΩ monitoring can reduce false alarm rate greatly without introducing an unacceptable loss of sensitivity in detecting out‐of‐control signals in high‐quality process control. Copyright © 2011 John Wiley & Sons, Ltd.     

Phase‐I Risk‐Adjusted Geometric Control Charts to Monitor Health‐care Systems

Because of the importance of health‐care processes to people life, researchers attempted to reduce death rates using risk‐adjusted control charts. In this paper, the number of patients survived at least 30 days after a surgery is monitored using a novel risk‐adjusted geometric control chart. In this chart, the patient risk is modeled using a logistic regression. The new scheme is proposed to be used in Phase‐I where a likelihood ratio test derived from a change‐point model is employed. The application of the proposed chart is demonstrated in a case study. Furthermore, through simulation studies, it is shown that the proposed control chart is more effective in terms of power than the chart with a binary random variable. Copyright © 2014 John Wiley & Sons, Ltd.     

Monitoring Two Dependent Process Steps Using Special Variable Sample Sizes and Sampling Intervals Cause‐Selecting Control Charts

Cause‐selecting control charts are effective statistical process control tools for monitoring multistage processes. In this article, an adaptive statistical process control scheme to monitor a process with two dependent steps is proposed. Two different policies based on a combination of two different sample sizes and sampling intervals are utilized. Adjusted average time to signal measure, calculated through Markov chain approach, is applied to evaluate performance of the proposed control scheme. Numerical results indicate that the proposed scheme has improved performance over the fixed sample sizes at fixed sampling intervals scheme. Finally, the optimal parameters of the proposed scheme with two different policies are recommended, and comparisons between the minimum adjusted average time to signal of the proposed charts and variable sample sizes and sampling intervals cause‐selecting control charts with three different sample sizes and sampling intervals are performed. It is shown that performance of the proposed scheme with four variable parameters is similar and even somewhat better than that of the scheme with six variable parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Algorithmic Statistical Process Control: Concepts and an Application

The goal of algorithmic statistical process control is to reduce predictable quality variations using feedback and feedforward techniques and then monitor the complete system to detect and remove unexpected root causes of variation. This methodology seeks to exploit the strengths of both automatic control and statistical process control (SPC), two fields that have developed in relative isolation from one another. Recent experience with the control and monitoring of intrinsic viscosity from a particular General Electric polymerization process has led to a better understanding of how SPC and feedback control can be united into a single system. Building on past work by MacGregor, Box, Astrom, and others, the article covers the application from statistical identification and modeling to implementing feedback control and final SPC monitoring. Operational and technical issues that arose are examined, and a general approach is outlined.     

Latent Structures-Based Multivariate Statistical Process Control: A Paradigm Shift

ABSTRACT

The basic fundamentals of statistical process control (SPC) were proposed by Walter Shewhart for data-starved production environments typical in the 1920s and 1930s. In the 21st century, the traditional scarcity of data has given way to a data-rich environment typical of highly automated and computerized modern processes. These data often exhibit high correlation, rank deficiency, low signal-to-noise ratio, multistage and multiway structures, and missing values. Conventional univariate and multivariate SPC techniques are not suitable in these environments. This article discusses the paradigm shift to which those working in the quality improvement field should pay keen attention. We advocate the use of latent structure–based multivariate statistical process control methods as efficient quality improvement tools in these massive data contexts. This is a strategic issue for industrial success in the tremendously competitive global market.     

A Semiparametric Mixed Model Approach to Phase I Profile Monitoring

Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric (P) modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. More recently, in the absence of an obvious P model, nonparametric (NP) methods have been employed in the profile monitoring context. For situations where a P model is adequate over part of the data but inadequate of other parts, we propose a semiparametric procedure that combines both P and NP profile fits. We refer to our semiparametric procedure as mixed model robust profile monitoring (MMRPM). These three methods (P, NP and MMRPM) can account for the autocorrelation within profiles and treat the collection of profiles as a random sample from a common population. For each approach, we propose a version of Hotelling's T² statistic for use in Phase I analysis to determine unusual profiles based on the estimated random effects and obtain the corresponding control limits. Simulation results show that our MMRPM method performs well in making decisions regarding outlying profiles when compared to methods based on a misspecified P model or based on NP regression. In addition, however, the MMRPM method is robust to model misspecification because it also performs well when compared to a correctly specified P model. The proposed chart is able to detect changes in Phase I data and has easily calculated control limits. We apply all three methods to the automobile engine data of Amiri et al.⁵ and find that the NP and the MMRPM methods indicate signals that did not occur in a P approach. Copyright © 2012 John Wiley & Sons, Ltd.     

A Modeling Approach to Maintenance Decisions Using Statistical Quality Control and Optimization

Maintenance concerns impact systems in every industry and effective maintenance policies are important tools. We present a methodology for maintenance decision making for deteriorating systems under conditions of uncertainty that integrates statistical quality control (SQC) and partially observable Markov decision processes (POMDPs). We use simulation to develop realistic maintenance policies for real‐world environments. Specifically, we use SQC techniques to sample and represent real‐world systems. These techniques help define the observation distributions and structure for a POMDP. We propose a simulation methodology for integrating SQC and POMDPs in order to develop and valuate optimal maintenance policies as a function of process characteristics, system operating and maintenance costs. A two‐state machine replacement problem is used as an example of how the method can be applied. A simulation program developed using Visual Basic for Excel yields results on the optimal probability threshold and on the accuracy of the decisions as a function of the initial belief about the condition of the machine. This work lays a foundation for future research that will help bring maintenance decision models into practice. Copyright © 2005 John Wiley & Sons, Ltd.     

On the Performance of Phase I Dispersion Control Charts for Process Monitoring

Control charts are usually implemented in two phases: the retrospective phase (phase I) and the monitoring phase (phase II). The performance of any phase II control chart structure depends on the preciseness of the control limits obtained from the phase I analysis. In statistical process control, the performance of phase I dispersion charts has mainly been investigated for normal or contaminated normal distributions of the quality characteristic of interest. Little work has been carried out to investigate the performance of a wide range of possible phase I dispersion charts for processes following non‐normal distributions. The current study deals with the proper choice of a control chart for the evaluation of process dispersion in phase I. We have analyzed the performance of a wide range of dispersion control charts, including two distribution‐free structures. The performance of the control charts is evaluated in terms of probability to signal, under normal and non‐normal process setups. These results will be useful for quality control practitioners in their selection of a phase I control chart. Copyright © 2014 John Wiley & Sons, Ltd.     

A Statistical Investigation and Optimization of an Industrial Radiography Inspection Process for Aero‐engine Components

Obtaining a high‐quality radiographic image is imperative in a radiography inspection process as it improves the identification of flaws in aero‐engine parts, which in turn enhances the reliability and safety of aircrafts. Existing methods to improve the radiographic inspection process are ad hoc and rely heavily on the experiences of radiographers. The radiographic images obtained from X‐rays have dual conflicting quality features, contrast sensitivity and spatial resolution, and have to satisfy a density reading constraint. This paper investigates an industrial radiography inspection process using statistical design of experiments (DOE) and analysis to determine optimal design settings for the process. The investigation adapts from the standard response surface methodology (RSM) and provides a promising alternative to the current methods. It has several key features such as the sequential DOE to first determine the feasible region imposed by the film density constraint, a sliding‐level system design to handle the irregular region, and an optimization formulation to optimize the dual image quality responses simultaneously. It provides a systematic approach to analyzing processes with secondary response constraints, and provides a quantitative basis for selecting optimum process settings. To evaluate the effectiveness of the statistical models obtained for industrial radiography, the probability of detection methodology is used to compare the optimum process settings recommended. Copyright © 2005 John Wiley & Sons, Ltd.     

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are commonly used for monitoring the process mean. In this paper, a new hybrid EWMA (HEWMA) control chart is proposed by mixing two EWMA control charts. An interesting feature of the proposed control chart is that the traditional Shewhart and EWMA control charts are its special cases. Average run lengths are used to evaluate the performances of each of the control charts. It is worth mentioning that the proposed HEWMA control chart detects smaller shifts substantially quicker than the classical CUSUM, classical EWMA and mixed EWMA–CUSUM control charts. Copyright © 2012 John Wiley & Sons, Ltd.     

A New Rank‐based Multivariate CUSUM Approach for Monitoring the Process Mean

In many cases, data do not follow a specific probability distribution in practice. As a result, a variety of distribution‐free control charts have been developed to monitor changes in the processes. An existing rank‐based multivariate cumulative sum (CUSUM) procedure based on the antirank vector does not quickly detect the large shift levels of the process mean. In this paper, we explore and develop an improved version of the existing rank‐based multivariate CUSUM procedure in order to overcome the difficulty. The numerical experiments show that the proposed approach dramatically outperforms the existing rank‐based multivariate CUSUM procedure in terms of the out‐of‐control average run length. In addition, the proposed approach particularly resolves the critical problem of the original approach, which occurs in the simultaneous shifts whose components are all the same but not 0. We believe that the proposed approach can be utilized for monitoring real data. Copyright © 2015 John Wiley & Sons, Ltd.     

A Statistical Control Chart for Monitoring High‐dimensional Poisson Data Streams

Multivariate count data are popular in the quality monitoring of manufacturing and service industries. However, seldom effort has been paid on high‐dimensional Poisson data and two‐sided mean shift situation. In this article, a hybrid control chart for independent multivariate Poisson data is proposed. The new chart was constructed based on the test of goodness of fit, and the monitoring procedure of the chart was shown. The performance of the proposed chart was evaluated using Monte Carlo simulation. Numerical experiments show that the new chart is very powerful and sensitive at detecting both positive and negative mean shifts. Meanwhile, it is more robust than other existing multiple Poisson charts for both independent and correlated variables. Besides, a new standardization method for Poisson data was developed in this article. A real example was also shown to illustrate the detailed steps of the new chart. Copyright © 2016 John Wiley & Sons, Ltd.     

Applying Real-Time Statistical Process Control to Manufacturing Processes Exhibiting Between and Within Part Size Variability in the Wood Products Industry

In this paper, we develop a control charting procedure to monitor average part size, as well as between and within part size variation for sawn lumber in an automated lumbermill. We present a review of the sawing process followed by a discussion of sampling methods for a real-time noncontact laser measuring device. A statistical model based on the components of variation analysis of variance model is proposed both for the analysis of the data and the construction of control charts that can be used to monitor the process. The details of the resulting statistical process control system are developed and an example from the lumber industry is provided and compared to other possible approaches. The resulting techniques may have applicability in many other industries where within and between variation in processes occurs.     

An Overview of Control Charts for High‐quality Processes

Major difficulties in the study of high‐quality processes with traditional process monitoring techniques are a high false alarm rate and a negative lower control limit. The purpose of time‐between‐events control charts is to overcome existing problems in the high‐quality process monitoring setup. Time‐between‐events charts detect an out‐of‐control situation without great loss of sensitivity as compared with existing charts. High‐quality control charts gained much attention over the last decade because of the technological revolution. This article is dedicated to providing an overview of recent research and presenting it in a unifying framework. To summarize results and draw a precise conclusion from the statistical point of view, cross‐tabulations are also given in this article. Copyright © 2016 John Wiley & Sons, Ltd.     

Economic and Economic‐Statistical Designs of Phase II Profile Monitoring

In economic design of profiles, parameters of a profile are determined such that the total implementation cost is minimized. These parameters consist of the number of set points, n, the interval between two successive sampling, h, and the parameters of a control chart used for monitoring. In this paper, the Lorenzen–Vance cost function is extended to model the costs associated with implementing profiles. The in‐control and the out‐of‐control average run lengths, ARL₀ and ARL₁, respectively, are used as two statistical measures to evaluate the statistical performances of the proposed model. A genetic algorithm (GA) is developed for solving both the economic and the economic‐statistical models, where response surface methodology is employed to tune the GA parameters. Results indicate satisfactory statistical performance without much increase in the cost of implementation. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to bar and S2 Charts

Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, a statistical criterion, an economic criterion, or a joint economic statistical criterion. Each method has its strengths and weaknesses. One weakness of the methods of design listed is their lack of flexibility and adaptability, a primary objective of practical mathematical models. In this article, we explore multiobjective models as an alternative for the methods listed. These provide a set of optimal solutions rather than a single optimal solution and thus allow the user to tailor their solution to the temporal imperative of a specific industrial situation. We present a solution to a well‐known industrial problem and compare optimal multiobjective designs with economic designs, statistical designs, economic statistical designs, and heuristic designs. Copyright © 2012 John Wiley & Sons, Ltd.     

Statistical Process Control‐Based Intrusion Detection and Monitoring

Intrusion detection systems have a vital role in protecting computer networks and information systems. In this article, we applied a statistical process control (SPC)–monitoring concept to a certain type of traffic data to detect a network intrusion. We proposed an SPC‐based intrusion detection process and described it and the source and the preparation of data used in this article. We extracted sample data sets that represent various situations, calculated event intensities for each situation, and stored these sample data sets in the data repository for use in future research. This article applies SPC charting methods for intrusion detection. In particular, it uses the basic security module host audit data from the MIT Lincoln Laboratory and applies the Shewhart chart, the cumulative sum chart, and the exponential weighted moving average chart to detect a denial of service intrusion attack. The case study shows that these SPC techniques are useful for detecting and monitoring intrusions. Copyright © 2013 John Wiley & Sons, Ltd.     

A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors

Abstract

Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and relate them via a multiresponse cross-covariance matrix. We introduce a substantially different approach that maps each qualitative factor to underlying numerical latent variables (LVs), with the mapped values estimated similarly to the other correlation parameters, and then uses any standard GP covariance function for numerical variables. This provides a parsimonious GP parameterization that treats qualitative factors the same as numerical variables and views them as affecting the response via similar physical mechanisms. This has strong physical justification, as the effects of a qualitative factor in any physics-based simulation model must always be due to some underlying numerical variables. Even when the underlying variables are many, sufficient dimension reduction arguments imply that their effects can be represented by a low-dimensional LV. This conjecture is supported by the superior predictive performance observed across a variety of examples. Moreover, the mapped LVs provide substantial insight into the nature and effects of the qualitative factors. Supplementary materials for the article are available online.     

A one‐sided MEWMA chart for health surveillance

It is often important to rapidly detect an increase in the incidence rate of a given disease or other medical condition. It has been shown that when disease counts are sequentially available from a single region, a univariate control chart designed to detect rate increases, such as a one‐sided cumulative sum chart, is very effective. When disease counts are available from several regions at corresponding times, the most efficient monitoring method is not readily apparent. Multivariate monitoring methods have been suggested for dealing with this detection problem. Some of these approaches have shortcomings that have been recently demonstrated in the quality control literature. We discuss these limitations and suggest an alternative multivariate exponentially weighted moving average chart. We compare the average run‐length performance of this chart with that of competing methods. We also evaluate the statistical performance of these charts when the actual increase in the disease count rate is different from the one that the chart was optimized to detect quickly. Copyright © 2008 John Wiley & Sons, Ltd.     

Improved Phase I Control Charts for Monitoring Times Between Events

In many situations, the times between certain events are observed and monitored instead of the number of events particularly when the events occur rarely. In this case, it is common to assume that the times between events follow an exponential distribution. Control charts are one of the main tools of statistical process control and monitoring. Control charts are used in phase I to assist operating personnel in bringing the process into a state of statistical control. In this paper, phase I control charts are considered for the observations from an exponential distribution with an unknown mean. A simulation study is carried out to compare the in‐control robustness and out‐of‐control performance of the proposed chart. It is seen that the proposed charts are considerably more in‐control robust than two competing charts and have comparable out‐of‐control properties. Copyright © 2014 John Wiley & Sons, Ltd.