Optimal designs of the double sampling X¯ chart with estimated parameters
TL;DR: In this paper, the authors evaluate the performance of the DS X ¯ chart when process parameters are estimated by means of a new proposed theoretical method, and show that performances with estimated parameters are different from that with known parameters, and propose three optimal design procedures.
About: This article is published in International Journal of Production Economics.The article was published on 2013-07-01. It has received 36 citations till now. The article focuses on the topics: X-bar chart & \bar x and R chart.
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TL;DR: In this article, the need for a nonparametric approach to phase I analysis and the use of variable selection-based control charts in multivariate phase II monitoring is reviewed and discussed.
Abstract: This article reviews and discusses two particular topics of statistical process monitoring: the need for a nonparametric approach to Phase I analysis and the use of variable selection–based control charts in multivariate Phase II monitoring.
53 citations
TL;DR: The average time to signal (ATS) is used instead of the average run length to evaluate the performance of TBE charts, since the ATS involves both the number and the time of samples inspected until a signal occurs.
Abstract: Exponential charts based on time-between-events (TBE) data are widely investigated and applied in various fields. The average time to signal (ATS) is used instead of the average run length to evaluate the performance of TBE charts, since the ATS involves both the number and the time of samples inspected until a signal occurs. An ATS-unbiased exponential control chart is proposed when the in-control parameter is known. Considering the need in practice to start monitoring a production process as soon as possible, a sequential sampling scheme is adopted and the in-control parameter is estimated by an unbiased and consistent estimator. Some specific guidelines to stop updating control limits are obtained from the relationship between the phase I sample size and the actual false alarm rate. Finally, two real examples are given to illustrate the implementation and efficiency of the proposed method.
39 citations
TL;DR: For the phase I monitoring, a new ATS-unbiased design with unknown parameters is developed, and a sequential sampling scheme is adopted to start process monitoring as soon as possible.
Abstract: Gamma charts for time between events are very useful in the high-quality processes, which monitor the time until the rth event. The average time to signal (ATS) is adopted to evaluate the performance of Gamma charts, because it reflects both the number and the sampling interval of samples inspected until an out-of-control signal occurs. An ATS-unbiased design for Gamma charts with known parameters is proposed based on the hypothesis test of the scale parameter. For the phase I monitoring, a new ATS-unbiased design with unknown parameters is developed, and a sequential sampling scheme is adopted to start process monitoring as soon as possible. Some specific guidelines to stop updating the control limits are suggested from the convergence of the width between control limits with different phase I sample sizes. Finally, a real example is illustrated to demonstrate the implementation of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.
34 citations
TL;DR: In this article, the Markov chain approach for the variable sample size and sampling interval (VSSI) X ¯ chart with estimated parameters is developed to facilitate process monitoring in manufacturing and service industries.
30 citations
TL;DR: In this article, the performance of the SDS X chart with estimated process parameters was investigated in terms of the average run length (ARL), average number of observations to signal (ANOS), and standard deviation of the run length.
Abstract: The synthetic double sampling (SDS) X chart comprises the double sampling (DS) X and conforming run length (CRL) sub-charts. The SDS X chart has been studied under the assumption of known process parameters in the literature. Nevertheless, in practice, process parameters are usually unknown and are estimated from an in-control Phase I dataset. This paper investigates the performance of the SDS X chart with estimated process parameters, in terms of the average run length (ARL), average number of observations to signal (ANOS) and standard deviation of the run length (SDRL). The performance of the SDS X chart with estimated process parameters by minimizing the out-of-control ARL and the out-of-control ANOS is compared with the corresponding chart’s performance with known process parameters. In addition, the minimum number of Phase I samples required by the SDS X chart with estimated process parameters so that it has approximately the same in-control ARL and ANOS performances as the chart with k...
23 citations
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References
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TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.
27,271 citations
Journal Article•
TL;DR: The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done.
1,624 citations
TL;DR: In this article, the authors evaluate the properties of an exponentially weighted moving average (EWMA) control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value.
Abstract: Roberts (1959) first introduced the exponentially weighted moving average (EWMA) control scheme. Using simulation to evaluate its properties, he showed that the EWMA is useful for detecting small shifts in the mean of a process. The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done. In this article, we evaluate the properties of an EWMA control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value. A design procedure for EWMA control schemes is given. Parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process. In addition, several enhancements to EWMA control schemes are considered. These include a fast initial response feature that makes the EWMA control scheme more sensitive to start-up problems, a combined Shewhart EWMA that provides protection against both larg...
1,380 citations
Book•
19 Jan 1989TL;DR: This paper presents a meta-analysis of the design of Experiments of Genichi Taguchi and Alternative Approaches using Combinations of Quality Improvement Tools, as well as some of the techniques used in this book, on the basis of its results.
Abstract: FUNDAMENTAL QUALITY IMPROVEMENT AND STATISTICAL CONCEPTS. Basic Tools for Improving Quality. Basic Concepts in Statistics and Probability. CONTROL CHARTS AND PROCESS CAPABILITY. Control Charts for Measurements with Subgrouping (for One Variable). Control Charts for Measurements without Subgrouping (for One Variable). Control Charts for Attributes. Process Capability. Alternatives to Shewhart Charts. Multivariate Control Charts for Measurement Data. Miscellaneous Control Chart Topics. BEYOND CONTROL CHARTS: GRAPHICAL AND STATISTICAL METHODS. Other Graphical Methods. Linear Regression. Design of Experiments. Contributions of Genichi Taguchi and Alternative Approaches. Evolutionary Operation. Analysis of Means. Using Combinations of Quality Improvement Tools. Answers to Selected Exercises. Appendix. Indexes.
751 citations
TL;DR: In this article, the control chart limits are calculated using parameter estimates from an in-control Phase I reference sample, and statistics based on new samples are compared with the estimated control limits to monitor for departures from the in..
Abstract: Control chart limits are often calculated using parameter estimates from an in-control Phase I reference sample. In Phase II monitoring, statistics based on new samples are compared with the estimated control limits to monitor for departures from the in..
532 citations