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Run Length (run + length)

Distribution by Scientific Domains

Mathematics and Statistics	20%

Kinds of Run Length

average run length

Selected Abstracts

Global analysis of runs of annual precipitation and runoff equal to or below the median: run length

INTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 7 2004
Murray C. Peel
Abstract The investigation of fluctuations of wet and dry years has a long history in the climatology and hydrology literature. In this, the first of two papers investigating runs of consecutive dry years, the lengths (persistence) of dry runs are investigated. In the second paper the magnitude/intensity and severity (length × magnitude) of dry runs will be investigated. Consecutive dry years are associated with drought, which is a significant physical and economic phenomenon that imposes great stress on ecosystems and societies. Run lengths of consecutive years equal to or below the median were analysed for 3863 precipitation and 1236 runoff stations from around the world. Run lengths were found to be similar across all continents and Köppen climate zones, expect for tropical and arid North Africa (Sahel), which showed a distinct bias toward longer run lengths than any other region of the world. Generally, the run length observed in annual runoff was found to be similar to that observed in annual precipitation for the same location. Both annual precipitation and runoff data were found to be well described by the lag-one autoregressive (AR(1)) model or by white noise. The influence of the El Niño,southern oscillation on run lengths was not observed to be significant. The presence of decadal and multi-decadal oscillations was weakly observed in the results of the precipitation runs analysis. The faintness of the decadal and multi-decadal oscillation signal may be due to the sample sizes not being long enough and/or the runs analysis not being sensitive enough to detect their presence. Copyright © 2004 Royal Meteorological Society [source]

Global analysis of runs of annual precipitation and runoff equal to or below the median: run magnitude and severity

INTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 5 2005
Murray C. Peel
Abstract Fluctuations of wet and dry years have long been investigated in the climatology and hydrology literature. In this, the second of two papers investigating runs of consecutive dry years, the magnitude, also known as the intensity, and severity (length × magnitude) of dry runs are investigated. In the first paper the length of dry runs was investigated. Periods of consecutive dry years are associated with drought and the attendant physical and economic stresses that are placed on society. Run magnitudes of consecutive years equal to or below the median were analysed for 3863 precipitation and 1236 runoff stations from around the world. For both annual precipitation and runoff, run magnitude was found to be predominately related to interannual variability and to a lesser extent skewness. Run magnitude of annual runoff was observed to be greater than that for annual precipitation, due to annual runoff having a higher coefficient of variation than annual precipitation. Continental differences in run magnitude of annual runoff were observed and were consistent with continental differences in interannual variability reported previously. Annual run severity was also investigated and found to be independent of run length and strongly related to run magnitude. These findings differ from previously published work; this difference is primarily due to the methodology of comparing run metrics between stations (used in this paper) rather than at a station (previous research). The relationships between run magnitude, severity and interannual variability highlight the importance of adequately reproducing interannual variability within global climate models for future modelling of drought scenarios, as well as having economic implications for drought relief and management policy-making. Copyright © 2005 Royal Meteorological Society. [source]

Global analysis of runs of annual precipitation and runoff equal to or below the median: run length

On the exponentially weighted moving variance

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2009
Longcheen Huwang
Abstract MacGregor and Harris (J Quality Technol 25 (1993) 106,118) proposed the exponentially weighted mean squared deviation (EWMS) and the exponentially weighted moving variance (EWMV) charts as ways of monitoring process variability. These two charts are particularly useful for individual observations where no estimate of variability is available from replicates. However, the control charts derived by using the approximate distributions of the EWMS and EWMV statistics are difficult to interpret in terms of the average run length (ARL). Furthermore, both control charting schemes are biased procedures. In this article, we propose two new control charts by applying a normal approximation to the distributions of the logarithms of the weighted sum of chi squared random variables, which are respectively functions of the EWMS and EWMV statistics. These new control charts are easy to interpret in terms of the ARL. On the basis of the simulation studies, we demonstrate that the proposed charts are superior to the EWMS and EWMV charts and they both are nearly unbiased for the commonly used smoothing constants. We also compare the performance of the proposed charts with that of the change point (CP) CUSUM chart of Acosta-Mejia (1995). The design of the proposed control charts is discussed. An example is also given to illustrate the applicability of the proposed control charts. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source]

Optimal production and maintenance policy for imperfect production systems

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2006
Chih-Hsiung Wang
Abstract A joint optimization of the production run length and preventive maintenance (PM) policy is studied for a deteriorating production system where the in-control period follows a general probability distribution with non-decreasing failure rate. In the literature, the sufficient conditions for the optimality of the equal-interval PM schedule is explored to derive an optimal production run length and an optimal number of PM actions. Nevertheless, an exhaustive search may arise. In this study, based on the assumption that the conditions for the optimality of the equal-interval PM schedule hold, we derive some structural properties for the optimal production/PM policy, which increases the efficiency of the solution procedure. These analyses have implications for the practical application of the production/PM model to be more available in practice. A numerical example of gamma shift distribution with non-decreasing failure rates is used to illustrate the solution procedure, leading to some insight into the management process. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source]

Double sampling hotelling's T2 charts

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 2 2008
Charles W. Champ
Abstract Two double sampling T2 charts are discussed. They only differ in how the second sample is used to suggest to the practitioner the state of the process. An optimal method using a genetic algorithm is given for designing these charts based on the average run length (ARL). An analytical method is used to determine run length performance of the chart. Comparisons are made with various other control charting procedures. Some recommendations are given. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Process monitoring for correlated gamma-distributed data using generalized-linear-model-based control charts

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 6 2003
Duangporn Jearkpaporn
Abstract A model-based scheme is proposed for monitoring multiple gamma-distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Global analysis of runs of annual precipitation and runoff equal to or below the median: run length

Recipe determination and scheduling of gasoline blending operations

AICHE JOURNAL, Issue 2 2010
Jie Li
Abstract Gasoline is a major contributor to the profit of a refinery. Scheduling gasoline-blending operations is a critical and complex routine task involving tank allocation, component mixing, blending, product storage, and order delivery. Optimized schedules can maximize profit by avoiding ship demurrage, improving order delivery, minimizing quality give-aways, avoiding costly transitions and slop generation, and reducing inventory costs. However, the blending recipe and scheduling decisions make this problem a nonconvex mixed-integer nonlinear program (MINLP). In this article, we develop a slot-based MILP formulation for an integrated treatment of recipe, specifications, blending, and storage and incorporate many real-life features such as multipurpose product tanks, parallel nonidentical blenders, minimum run lengths, changeovers, piecewise constant profiles for blend component qualities and feed rates, etc. To ensure constant blending rates during a run, we develop a novel and efficient procedure that solves successive MILPs instead of a nonconvex MINLP. We use 14 examples with varying sizes and features to illustrate the superiority and effectiveness of our formulation and solution approach. The results show that our solution approach is superior to commercial solvers (BARON and DICOPT). © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

Group inspection of dependent binary processes

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 2 2009
Christian H. Weiß
Abstract We consider serially dependent binary processes, how they occur in several fields of practice. If such a process cannot be monitored continuously, because of process speed for instance, then one can analyze connected segments instead, where two successive segments have a sufficiently large time-lag. Nevertheless, the serial dependence has to be considered at least within the segments, i.e. the distribution of the segment sums is not binomial anymore. We propose the Markov binomial distribution to approximate the true distribution of the segment sums. Based on this distribution, we develop a Markov np chart and a Markov exponentially weighted moving average (EWMA) chart. We show how average run lengths (ARLs) can be computed exactly for both types of chart. Based on such ARL computations, we derive recommendations for chart design and investigate the out-of-control performance. A real-data example illustrates the application of these charts in practice. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A Bootstrap Control Chart for Weibull Percentiles

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 2 2006
Michele D. Nichols
Abstract The problem of detecting a shift of a percentile of a Weibull population in a process monitoring situation is considered. The parametric bootstrap method is used to establish lower and upper control limits for monitoring percentiles when process measurements have a Weibull distribution. Small percentiles are of importance when observing tensile strength and it is desirable to detect their downward shift. The performance of the proposed bootstrap percentile charts is considered based on computer simulations, and some comparisons are made with an existing Weibull percentile chart. The new bootstrap chart indicates a shift in the process percentile substantially quicker than the previously existing chart, while maintaining comparable average run lengths when the process is in control. An illustrative example concerning the tensile strength of carbon fibers is presented. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Designing Accurate Control Charts Based on the Geometric and Negative Binomial Distributions

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 8 2005
Neil C. Schwertman
Abstract Attribute control charts are used effectively to monitor for process change. Their accuracy can be improved by judiciously selecting the sample size. The required sample sizes to achieve accuracy can be quite restrictive, especially when the nominal proportions of non-conforming units are quite small. The usual attribute control chart has a set sample size and the number of non-conforming units in the sample is plotted. If, instead of setting a specific sample size the number of non-conforming units is set, an alternative monitoring process is possible. Specifically, the cumulative count of conforming (CCC- r) control chart is a plot of the number of units that must be tested to find the rth non-conforming unit. These charts, based on the geometric and negative binomial distributions, are often suggested for monitoring very high quality processes. However, they can also be used very efficiently to monitor processes of lesser quality. This procedure has the potential to find process deterioration more quickly and efficiently. Xie et al. (Journal of Quality and Reliability Management 1999; 16(2):148,157) provided tables of control limits for CCC- r charts for but focused mainly on high-quality processes and the tables do not include any assessments of the risk of a false alarm or the reliability of detecting process change. In this paper, these tables are expanded for processes of lesser quality and include such assessments using the number of expected monitoring periods (average run lengths (ARLs)) to detect process change. Also included is an assessment of the risk of a false alarm, that is, a false indication of process deterioration. Such assessments were not included by Xie et al. but are essential for the quality engineer to make sound decisions. Furthermore, a hybrid of the control charts based on the binomial, geometric and negative binomial distributions is proposed to monitor for process change. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Controlling jumps in correlated processes of Poisson counts

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009
Christian H. WeißArticle first published online: 3 DEC 200
Abstract Processes of autocorrelated Poisson counts can often be modelled by a Poisson INAR(1) model, which proved to apply well to typical tasks of SPC. Statistical properties of this model are briefly reviewed. Based on these properties, we propose a new control chart: the combined jumps chart. It monitors the counts and jumps of a Poisson INAR(1) process simultaneously. As the bivariate process of counts and jumps is a homogeneous Markov chain, average run lengths (ARLs) can be computed exactly with the well-known Markov chain approach. Based on an investigation of such ARLs, we derive design recommendations and show that a properly designed chart can be applied nearly universally. This is also demonstrated by a real-data example from the insurance field. Copyright © 2008 John Wiley & Sons, Ltd. [source]