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  • 1.
    Albing, Malin
    et al.
    Department of Mathematics, Luleå University of Technology.
    Vännman, Kerstin
    Department of Mathematics, Luleå University of Technology.
    Elliptical safety region plots for Cpk2011In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, no 6, p. 1169-1187Article in journal (Refereed)
    Abstract [en]

    The process capability index C pk is widely used when measuring the capability of a manufacturing process. A process is defined to be capable if the capability index exceeds a stated threshold value, e.g. C pk >4/3. This inequality can be expressed graphically using a process capability plot, which is a plot in the plane defined by the process mean and the process standard deviation, showing the region for a capable process. In the process capability plot, a safety region can be plotted to obtain a simple graphical decision rule to assess process capability at a given significance level. We consider safety regions to be used for the index C pk . Under the assumption of normality, we derive elliptical safety regions so that, using a random sample, conclusions about the process capability can be drawn at a given significance level. This simple graphical tool is helpful when trying to understand whether it is the variability, the deviation from target, or both that need to be reduced to improve the capability. Furthermore, using safety regions, several characteristics with different specification limits and different sample sizes can be monitored in the same plot. The proposed graphical decision rule is also investigated with respect to power.

  • 2.
    Andersson Tano, Ingrid
    et al.
    Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    A multivariate process capability index based on the first principal component only2013In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 29, no 7, p. 987-1003Article in journal (Refereed)
    Abstract [en]

    Often the quality of a process is determined by several correlated univariate variables. In such cases, the considered quality characteristic should be treated as a vector. Several different multivariate process capability indices (MPCIs) have been developed for such a situation, but confidence intervals or tests have been derived for only a handful of these. In practice, the conclusion about process capability needs to be drawn from a random sample, making confidence intervals or tests for the MPCIs important. Principal component analysis (PCA) is a well-known tool to use in multivariate situations. We present, under the assumption of multivariate normality, a new MPCI by applying PCA to a set of suitably transformed variables. We also propose a decision procedure, based on a test of this new index, to be used to decide whether a process can be claimed capable or not at a stated significance level. This new MPCI and its accompanying decision procedure avoid drawbacks found for previously published MPCIs with confidence intervals. By transforming the original variables, we need to consider the first principal component only. Hence, a multivariate situation can be converted into a familiar univariate process capability index. Furthermore, the proposed new MPCI has the property that if the index exceeds a given threshold value the probability of non-conformance is bounded by a known value. Properties, like significance level and power, of the proposed decision procedure is evaluated through a simulation study in the two-dimensional case. A comparative simulation study between our new MPCI and an MPCI previously suggested in the literature is also performed. These studies show that our proposed MPCI with accompanying decision procedure has desirable properties and is worth to study further.

  • 3.
    Andersson Tano, Ingrid
    et al.
    Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Comparing confidence intervals for multivariate process capability indices2012In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 28, no 4, p. 481-495Article in journal (Refereed)
    Abstract [en]

    Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index Cp. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way.

  • 4.
    Kvarnström, Björn
    et al.
    Luleå University of Technology, Luleå, Sweden.
    Bergquist, Bjarne
    Luleå University of Technology, Luleå, Sweden.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Department of Statistics.
    RFID to improve traceability in continuous granular flows: an experimental case study2011In: Quality Engineering, ISSN 0898-2112, E-ISSN 1532-4222, Vol. 23, no 4, p. 343-357Article in journal (Refereed)
    Abstract [en]

    Traceability is important for identifying the root causes of production-related quality problems. Traceability can often be reached by adding identification markers on products, but this is not a solution when the value of the individual product is much lower than the incurred cost of a marking system. This is the case for continuous production of granular media. The use of radio frequency identification (RFID) techniques to achieve traceability in continuous granular flows has been proposed in the literature. We study through experiments different methods to improve the performance of such an RFID system. For example, larger transponders and multiple readers are shown to improve the RFID system performance.

  • 5. Lundkvist, Peder
    et al.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Kulahci, Murat
    A comparison of decision methods for C-pk when data are autocorrelated2012In: Quality Engineering, ISSN 0898-2112, E-ISSN 1532-4222, Vol. 24, no 4, p. 460-472Article in journal (Refereed)
    Abstract [en]

    In many industrial applications, autocorrelated data are becoming increasingly common due to, for example, on-line data collection systems with high-frequency sampling. Therefore, the basic assumption of independent observations for process capability analysis is not valid. The purpose of this article is to compare decision methods using the process capability index C-pk when data are autocorrelated. This is done through a case study followed by a simulation study. In the simulation study the actual significance level and power of the decision methods are investigated. The outcome of the article is that two methods appeared to be better than the others.

  • 6.
    Vanhatalo, Erik
    et al.
    Quality Technology and Management, Luleå University of Technology, Luleå, Sweden.
    Bergquist, Bjarne
    Quality Technology and Management, Luleå University of Technology, Luleå, Sweden.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden and Department of Engineering Science, University West, Trollhättan, Sweden.
    Towards improved analysis methods for two-level factorial experiments with time series responses2013In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 29, no 5, p. 725-741Article in journal (Refereed)
    Abstract [en]

    Dynamic processes exhibit a time delay between the disturbances and the resulting process response. Therefore, one has to acknowledge process dynamics, such as transition times, when planning and analyzing experiments in dynamic processes. In this article, we explore, discuss, and compare different methods to estimate location effects for two-level factorial experiments where the responses are represented by time series. Particularly, we outline the use of intervention-noise modeling to estimate the effects and to compare this method by using the averages of the response observations in each run as the single response. The comparisons are made by simulated experiments using a dynamic continuous process model. The results show that the effect estimates for the different analysis methods are similar. Using the average of the response in each run, but removing the transition time, is found to be a competitive, robust, and straightforward method, whereas intervention-noise models are found to be more comprehensive, render slightly fewer spurious effects, find more of the active effects for unreplicated experiments and provide the possibility to model effect dynamics.

  • 7.
    Vanhatalo, Erik
    et al.
    Quality Technology, Luleå University of Technology, Luleå, Sweden.
    Kvarnström, Björn
    Quality Technology, Luleå University of Technology, Luleå, Sweden.
    Bergquist, Bjarne
    Quality Technology, Luleå University of Technology, Luleå, Sweden.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Department of Statistics.
    A method to determine transition time for experiments in dynamic processes2011In: Quality Engineering, ISSN 0898-2112, E-ISSN 1532-4222, Vol. 23, no 1, p. 30-45Article in journal (Refereed)
    Abstract [en]

    Process dynamics is an important consideration during the planning phase of designed experiments in dynamic processes. After changes of experimental factors, dynamic processes undergo a transition time before reaching a new steady state. To minimize experimental time and reduce costs and for experimental design and analysis, knowledge about this transition time is important. In this article, we propose a method to analyze process dynamics and estimate the transition time by combining principal component analysis and transfer function–noise modeling or intervention analysis. We illustrate the method by estimating transition times for a planned experiment in an experimental blast furnace.

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