A process variability control chart

In this study a Shewhart type control chart namely the V _t chart, is proposed for improved monitoring of the process variability of a quality characteristic of interest Y. The proposed control chart is based on the ratio type estimator of the variance using a single auxiliary variable X. It is assumed that (Y, X) follows a bivariate normal distribution. The design structure of the V _t chart is developed for Phase-I quality control and its comparison is made with those of the S ² chart (a well-known Shewhart control chart) and the V _r chart (a Shewhart type control chart proposed by Riaz (Comput Stat, 2008a) used for the same purpose. It is observed that the proposed V _t chart outperforms the S ² and V _r charts, in terms of discriminatory power, for detecting moderate to large shifts in the process variability. It is observed that the performance of the V _t chart keeps improving with an increase in |ρ _yx | , where ρ _yx is the correlation between Y and X.     

An explicit procedure for discretizing continuous,optimal control problems

An explicit procedure for obtaining discrete approximations to general, nonlinear, fixed-time, continuous, optimal control problems with no intermediate trajectory constraints is presented. It is proved that, if the associated system of differential equations is linear in the control variable, then the optimal solutions of these approximationsconverge to extremals of the original continuous problem.     

An interactive decision support system for on-line process control

We develop a technique for operational decision making at a starch refinery. The dynamic set of input control decisions required at process stages is computed based on overall production objectives. This technique, implemented as an interactive decision support system for on-line process control, has already contributed to significantly reducing the duration of transients, which, in turn, has directly increased daily refinery production by more than 18%.     

Engineering students designing a statistical procedure for quantifying variability

The study examined first-year engineering students’ responses to a statistics task that asked them to generate a procedure for quantifying variability in a data set from an engineering context. Teams used technological tools to perform computations, and their final product was a ranking procedure. The students could use any statistical measures, and they needed to explain their ranking procedure in detail. The responses were first categorized by the statistical measures used. The responses were categorized using a cyclic model development perspective moving from primitive to more sophisticated responses. The modeling cycle framework provided a developmental view of students’ responses and use of statistics. The study raised questions related to the measurement of variability, the application of statistics, and the process teams go through when designing an analysis procedure.     

An on-line procedure in discounted infinite-horizon stochastic optimal control

We consider the discrete-time, infinite-horizon optimal control problem with discounted cost. We propose a test to detect forecast/planning horizons, and derive an on-line procedure for solving the original problem.     

An algorithm for a selection procedure

When we have a selection problem that involves qualitative information, we can use the qualitative programming method and find the optimal choice by using integer programming. However, in practice after formulation of the problem we have a large scale model. In this note we introduce a very effective method for solving a qualitative programming problem. The only operations used in this method are scalar and matrix addition, and hence for problems of reasonable size, the method does not need high speed computers, and can be supplemented using hand calculators.     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.     

An analysis of Taguchi's on‐line quality monitoring procedure for attributes with diagnosis errors

The on‐line quality monitoring procedure for attributes proposed by Taguchi, Elsayed and Hsiang for processes in which the fraction defective shifts from 0 at some point are examined under the assumption of diagnosis errors. The renewal reward (economic) approach of Nayebpour and Woodall is used to develop a mathematical expression for the long‐run expected cost per item produced and assessment of the optimum inspection interval is discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

An integrated systems approach to process control and maintenance

Organizational leaders increasingly recognize process management as an essential element in organizational performance. Two key tools for process management––Statistical Process Control and Maintenance Management––can create profound economic benefits, particularly when they are coordinated. This paper demonstrates the value of integrating Statistical Process Control and maintenance by jointly optimizing their policies to minimize the total costs associated with quality, maintenance, and inspection. While maintenance is often scheduled periodically, this analysis encourages “adaptive” maintenance where the maintenance schedule accelerates when the process becomes unstable. This paper presents a number of models to demonstrate the economic behavior and value of coordinating process control and maintenance. Finally, a sensitivity analysis is conducted to develop insights into the economic and process variables that influence the integration efforts.     

An integrated model of statistical process control and condition-based maintenance for deteriorating systems

This paper proposes an integrated model of statistical process control and condition-based maintenance for a deteriorating system. We study a system that will not be as good as new after a preventive maintenance and can only survive a certain number of preventive maintenances. The system is modeled as a geometric process and monitored by an \(\bar{X}\) control chart. By analyzing the evolution of the system in different scenarios, we establish a mathematical model to minimize the expected cost during the expected cycle time that can be used to make an optimal replacement policy in applications. A computational scheme is presented and illustrated through a numerical example. A sensitivity analysis is performed to investigate the effect of statistical constraint, mean shift, and the parameters of the system.     

An automatic procedure for Box-Jenkins model building

CAPRI is a fully automatic procedure which quickly builds Box-Jenkins model and satisfactory forecasts. Its main peculiarity relies on the selection of the most recent values of the series for which all the statistical assumptions are checked.The fitted model can also be controlled and updated when new data are available.     

Statistical quality control for ternary ordinal quality data

The paper considers various aspects of statistical quality control by means of sample data received on a ternary ordinal scale. A new method for evaluating quality level and dispersion, free of any latent numerical scale assumptions, is proposed. The emphasis is on working with large samples, which enable the statistical analysis, estimation and control by the use of approximate analytical expressions of these measures to be considerably simplified. Two complementary studies demonstrate the usage of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Monitoring process variability using auxiliary information

In this study a Shewhart type control chart namely V _r chart is proposed for improved monitoring of process variability (targeting large shifts) of a quality characteristic of interest Y. The proposed control chart is based on regression type estimator of variance using a single auxiliary variable X. It is assumed that (Y, X) follow a bivariate normal distribution. The design structure of V _r chart is developed and its comparison is made with the well-known Shewhart control chart namely S ² chart used for the same purpose. Using power curves as a performance measure it is observed that V _r chart outperforms the S ² chart for detecting moderate to large shifts, which is main target of Shewhart type control charts, in process variability under certain conditions on ρ _yx . These efficiency conditions on ρ _yx are also obtained for V _r chart in this study.     

An advanced quality function deployment model using fuzzy analytic network process

Quality function deployment (QFD) is a customer-oriented design tool used to ensure that the voice of customers is employed throughout the product planning and design stages. QFD uses the house of quality (HOQ), which is a matrix that provides a conceptual map for inter-functional planning and communication. In this paper, an advanced QFD model, based on fuzzy analytic network process (ANP) approach, is proposed to systematically take into account the interrelationship between and within the QFD components. The proposed method is aimed at expanding the current research scope from the product planning phase to the part deployment phase to provide product developers with more valuable information (ex. the importance and bottleneck level of part characteristics). Both customer requirements and the company’s production demands will be used as the inputs for the QFD process to enhance the completeness and accuracy of the QFD analysis results. A case study is presented to illustrate the application of the proposed method.     

Information theoretic framework for process control

This paper proposes a general framework for constructing control charts based on information theory. The potential applications include developing information charts, for monitoring moments and distributions of a process variable and process attributes. In information theoretic process control (ITPC), process moments are mapped to process distributions at in-control and monitoring states, and then to a control function via constrained maximization of entropy and minimization of Kullback–Leibler function (cross-entropy). Variants of information charts can be developed without using distributional assumptions and based on a single criterion function, the information discrepancy between two distributions. An example of an information chart, Information mean-variance chart, IMV-chart, for monitoring process mean and variance is developed. The IMV-chart combines the standard x̄-chart and s²-chart, and provides an information theoretic explication of the traditional procedures. Based on a run-length study, it is found that the IMV-chart singly possesses certain advantages over the standard two-chart implementation of x̄-chart and s²-chart. Multivariate extension, monitoring counts and proportions, and monitoring distributional changes are briefly discussed.