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Industrial processes are often monitored via data sampled at a high frequency and hence are likely to be autocorrelated time series that may or may not be stationary. To determine if a time series is stationary or not the standard approach is to check whether sample autocorrelation function fades out relatively quickly. An alternative and somewhat sounder approach is to use the variogram. In this article we review the basic properties of the variogram and then derive a general expression for asymptotic confidence intervals for variogram based on the Delta method. We illustrate the computations with an industrial process example.

This paper studies design schemes for the control chart under non-normality. Different estimators of the standard deviation are considered and the effect of the estimator on the performance of the control chart under non-normality is investigated. Two situations are distinguished. In the first situation, the effect of non-normality on the control chart is investigated by using the control limits based on normality. In the second situation we incorporate the knowledge of non-normality to correct the limits of the control chart. The schemes are evaluated by studying the characteristics of the in-control and the out-of-control run length distributions. The results indicate that when the control limits based on normality are applied the best estimator is the pooled sample standard deviation both under normality and under non-normality. When the control limits are corrected for non-normality, the estimator based on Gini's mean sample differences is the best choice.

This paper argues that currently available methods for the assessment of the repeatability and reproducibility of ordinal classifications are not satisfactory. The paper aims to study whether we can modify a class of models from Item Response Theory, well established for the study of the reliability of categorical measurements in psychometrics and education, for use in business and industry, and whether the resulting approaches offer a satisfactory solution. The fitted models can be presented graphically, but also allow the calculation of probabilities of correct ordering and consistent classification. In addition, the modelbased approach allows refined diagnostics, giving the user insight into the workings of a classification procedure, which is vital information for a user willing to improve a poor classification procedure. The approach is illustrated from a real-life example, and the proposed analysis is contrasted to two popular alternative analyses, based on Goodman and Kruskal's gamma and Kendall's coefficient of concordance. The datasets and mathematical proofs are available as online supplemental materials. © 2010 American Statistical Association and the American Society for Quality.

In the practice of process improvement, tools such as the flowchart, the value-stream map (VSM), and a variety of ad hoc variants of such diagrams are commonly used. The purpose of this paper is to present a clear, precise, and consistent framework for the use of such flow diagrams in process improvement projects. The paper finds that traditional diagrams, such as the flowchart, the VSM, and OR-type of diagrams, have severe limitations, miss certain elements, or are based on implicit but consequential premises. These limitations restrict the applicability of traditional diagrams in non-manufacturing areas such as service and healthcare processes.We show that a rational reconstruction for the use of diagrams in various disciplines regarding process flow boils down to a generic framework of elements, definitions of generic process metrics, and three classes of applications, namely the ‘as-is’, ‘could-be’, and ‘should-be’ analysis.The goal is not to replace all currently used diagrams, but merely to discuss the role of diagram usage in process flow modeling. This paper provides an explicit framework that is unambiguous and flexible, and has the potential to serve as a guideline for the practitioner, in manufacturing as well as in service and healthcare. Besides, it may serve as a starting point to develop an ontology of business processes.

When measurements are nonreplicable, assessing the measurement system is a difficult task and cannot be done using the conventional gauge repeatability and reproducibility methods. This is due to the fact that the object measured is affected by the measurement and/or changes with time. This article describes an alternative method that can be used to study the repeatability and reproducibility of a measurement system in case the measured quantity varies over time. The essence of the method is that each part is measured simultaneously by multiple gauges.

When using x̄-R charts it is a crucial assumption that the observations within samples are independent and have common variance. However, this assumption is almost never checked. We propose to use the samples gathered during the phase I study and the test for distributional sphericity, to check this assumption. We supply a graph of the exact percentage points for the distribution of the test statistics. The test statistics can be computed with standard statistical software. Together with the graph of the exact percentage points, the test can easily be performed during a phase I study. We illustrate the method with examples.

Nonclinical healthcare processes are sometimes created on an ad hoc basis and hence over time may grow unnecessarily complex and difficult to assess, teach, improve, or transfer. Intentionally designing processes are more likely to yield an efficient and effective process. Originally developed in industry, Design for Six Sigma (DFSS) is a method for planning new processes applicable to healthcare. Benefits from using DFSS include well-defined process steps and documentation that makes processes easier to teach, monitor, control, and transfer to other units. We describe the DFSS process and provide an example of its application to an employee influenza vaccination program at a New England hospital.

A Shewhart-type control chart is proposed for monitoring changes in the process variability of a bivariate process. The chart is based on the generalized Gini mean differences. The design structure of the proposed chart is developed assuming bivariate n..

This paper discusses the investments needed for the introduction of hydrogen as a transport fuel. Using option theory, we develop a model to calculate the value and optimal timing of a first commercial rollout of hydrogen vehicles in a larger area, taking Japan as a specific example. We find that the project is best viewed as an out-of-the-money call option with a small but positive option value. We estimate this value at approximately 1.5 billion euros, without tax advantages. An important finding is that the moment of investment is first and foremost determined by the maturing of the technology. By contrast, the investment timing is not as much affected by deployment strategy as is frequently thought: in particular, whether or not the hydrogen retail infrastructure is introduced smoothly does not sensitively influence the investment timing. Fairly independent of parameter assumptions, the project value at the moment of deployment is negative for the retailer and positive for the car manufacturer. This implies the need for a negotiated partnership. Finally, we assess various forms of government support, e.g. subsidies or tax cuts. Looking at the effectiveness of this support spending in relation to the advancement of hydrogen deployment, we find, again because investment timing is primarily determined by technology maturation, that tax incentives are relatively ineffective. We are lead to believe that government subsidy for technology development is a more effective means to achieve earlier investment, as faster production cost reductions for hydrogen and fuel cell vehicles lead to accelerated investment. Keywords: Hydrogen; Infrastructure; Investment; Option theory

We begin by thanking the authors for an inspiring paper. They have made athoughtful contribution in the discussion about our profession’s future.There is a certain paralysis in the field. The sense of urgency is there, wethink, but yet there is not enough momentum to get the profession moving.The majority of statisticians in the field have had their training and experi-ence mainly in the old paradigm, and we imagine that many of them feelinsecure about the challenges of the new paradigm. We imagine a persontrained in mathematics, who has never been taught anything about engin-eering or management, who is suddenly challenged by the new paradigmto ‘‘provide leadership to the organization.’’ Empathy is not our strongesttrait, but we can imagine that this person will at best react passively butprobably will resist.The angle we take in our reply is that our profession is best helpedforward by providing a path for us and our colleagues, which providespractical steps a statistician can take for moving himself from the old para-digm to the new one—to help those shivering on the brink to go into thewater step-by-step. We do not pretend to provide such a path in this replybut at least wish to provide a few first ideas.

Background: The University Medical Center Groningen is a level I trauma center in the northern part of the Netherlands. Sixty-three percent of all the patients admitted at the Trauma Nursing Department (TND) are acute patients who are admitted directly after trauma. In 2006 and 2007, the University Medical Center Groningen was not always capable of admitting all trauma patients to the TND due to the relatively high-bed occupation. Therefore, the reduction of the average length of stay (LOS) formed the objective of the project described in this study. Methods: We used the process-focused method of Lean Six Sigma to reduce hospital stay by improving the discharge procedure of patients in the care processes and eliminating waste and waiting time. We used the "Dutch Appropriateness Evaluation Protocol" to identify the possible causes of inappropriate hospital stay. The average LOS of trauma patients at the TND at the beginning of the project was 10.4 days. Results: Thirty percent of the LOS was unnecessary. The main causes of the inappropriate hospital stay were delays in several areas. The implementation of the improvement plan reduced almost 50% of the inappropriate hospital stay, enabling the trauma center to admit almost all trauma patients to the TND. After the implementation of the improvements, the average LOS was 8.5 days. Conclusion: Our study shows that Lean Six Sigma is an effective method to reduce inappropriate hospital stay, thereby improving the quality and financial efficiency of trauma care.

Problem: Health care today is facing serious problems: quality of care does not meet patients’ needs and costs are exploding. Inefficient utilization of expensive operating rooms is one of the major problems in many hospitals worldwide. A benchmark study of 13 hospitals in the Netherlands and Belgium showed that, for a variety of reasons, surgery consistently started too late. Approach: For a short and a somewhat longer period, two selected hospitals from the benchmark study agreed to record the start times of the first operation each day for each of their operating rooms. In addition to start times, the improvement team also recorded potential influence factors (covariates, or X’s). Statistical techniques used during the project were statistical graphics, Pareto charts, histograms, box plots, time-series plots, Box-Cox transformations, and ANOVA to determine possible influential factors. Results: It is shown that anesthesia technique and specialty are influence factors. However, the poor planning and scheduling process turned out to be the most important factor in the delay of start times. After introducing a new planning process, the hospitals involved were able to gain substantial cost savings, increased efficiency, and substantial reductions of the delay in start times for surgery. Key Words: ANOVA; Box-Cox transformation; Health Care Quality; Lean Six Sigma; Pareto Charts.

The standard method to assess a measurement system’s precision is a gauge repeatability and reproducibility (gauge R&R) study. It exploits replications to estimate variance components that are interpreted as measurement spread. For nonrepeatable measurements, it is not feasible to obtain replications because objects are destroyed when they are measured or because the object changes over time. Possible solutions are to replace replications with measurements of multiple objects or with the measurement of one object at multiple times. Subsequently, these measurements are modeled by a fixed pattern (over time or over positions). We show that the experimental design used in this type of nonrepeatable gauge R&R studies is best constructed in a way that is similar to a Latin square design. These designs have a great flexibility, can be applied in many situations encountered in practice, and have nice mathematical properties as well. We consider several examples in which this approach is applied and worked out. For the examples given, we provide the analysis and the results following the worked-out approach. Analysis of the envisaged experimental set-up is done with linear and nonlinear mixed models in which variance components are estimated by restricted maximum-likelihood estimators.

This account considers a parallel queue, which is two-queue network, where any arrival generates a job at both queues. It is noted that earlier work has revealed that this class of models is notoriously hard to analyze. We first evaluate a number of bounds developed in the literature, and observe that under fairly broad circumstances these can be rather inaccurate. For the 'homogeneous' case we present a number of approximations, which are extensively tested by simulation, and turn out to perform remarkably well.

Data used for monitoring and control of industrial processes are often best modeled as a time series. An important issue is to determine whether such time series are stationary. In this article we discuss the variogram—a graphical tool for assessing stationarity. We build on previous work and provide further details and more general results including analytical structures of variogram for various non-stationary processes, and illustrate with a number of examples of variograms using standard data sets from the literature and simulated data sets.

Some of the issues involved in selecting adequate models for time series data are discussed using an example concerning the number of users of an Internet server. The process of selecting an appropriate model is subjective and requires experience and ju..

De vraag "Wat komt er na Lean Six Sigma?" is actueel. In dit artikel beargumenteren we dat, los van het specifieke stempel wat je kunt gebruiken, kwaliteit ook in de toekomst bestaansrecht heeft. Maar kwaliteitsmanagement zal zich verder moeten aanpassen en moeten evolueren. Strategisch is het verstandig om de kerncompetentie van deze discipline systematische innovatie te noemen. Om te kunnen concurreren moeten organisaties innoveren en aan verbetering van hun producten, processen en diensten werken. Nu meer dan ooit. De rol van de kwaliteitsprofessional in de moderne kenniseconomie zou er een moeten zijn van een vakspecialist met de nodige onderzoeksvaardigheden en de juiste kennis van systematische innovatie. De huidige situatie is voor deze beroepsgroep een kans om de sleutel te vormen van de kenniseconomie.

Zorgaanbieders moeten steeds meer met elkaar concurreren. De wetten van de markteconomie worden daarom meer en meer van toepassing in de zorgsector die dat tot voor kort helemaal niet gewend was. Dat vergt veranderingen, zowel in het besturen van deze organisaties, als in de omgang met patiënten en medewerkers. Daarbij kan gebruik worden gemaakt van methoden die hun waarde in andere sectoren hebben bewezen. Om processen efficiënter te maken, wordt in de industrie tegenwoordig ‘Lean’ gebruikt, of ‘Six Sigma’, of een combinatie van beide. Ook in de zorg vindt de methode steeds meer weerklank. In dit artikel beschrijven we de ervaringen van het Universitair Medisch Centrum Groningen met ‘Lean Six Sigma’.

This paper studies several issues regarding the design of the X control chart under normality. Different estimators of the standard deviation are considered and the effect of the estimator on the performance of the control chart is investigated. Furthermore, the choice of the factor used to get accurate control limits for moderate sample sizes is addressed. The paper gives an overview on the performance of the charts by studying different characteristics of the run length distribution, both in the in-control and in the out-of-control situation.

Lean Six Sigma is an advanced process improvement methodology. Initially, Six Sigma focused on the reduction of the number of defects in manufacturing. It was introduced at Motorola in 1986, and it incorporates previous methodologies, such as Statistical Process Control, Total Quality Management, and Zero Defects. The assimilation of Lean Thinking tools led to the popular Lean Six Sigma program. Nowadays, the program is deployed at companies such as General Electric, Honeywell International, and Citibank.

We would like to thank the editor for organizing this discussion of our paper, and we appreciate the points brought forward by the discussants. Professor Vining's example of the chemical company il...