Monitoring the covariance matrix with the VMAX chart

In this article, we propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample vat-lances of the two quality characteristics, shortly VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar are faster detection of process changes and better diagnostic feature, that is, with the VMAX statistic It is easier to identify the out-of-control variable.

A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

An adaptive chart for monitoring the process mean and variance

Traditionally, an (X) over bar chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive ($) over bar and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint (X) over bar and R charts with fixed or adaptive parameters, they are not reliable in identifing the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non-central chi-square statistic chart. This new chart is more effective than the adaptive (X) over bar and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects. Copyright (c) 2006 John Wiley & Sons, Ltd.

Synthetic control chart for monitoring the pprocess mean and variance

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control the process mean and variance. During the first stage, one item of the sample is inspected; if its value X, is close to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the statistic T = Sigma [x(i) - mu(0) + xi sigma(0)](2) is computed taking into account all items of the sample. The design parameter is function of X-1. When the statistic T is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on Conforming Run Length (CRL). The CRL is the number of samples taken from the process since the previous nonconforming sample until the occurrence of the next nonconforming sample. If the CRL is sufficiently small, then a signal is generated. A comparative study shows that the SyTS chart and the joint X and S charts with double sampling are very similar in performance. However, from the practical viewpoint, the SyTS chart is more convenient to administer than the joint charts.

Monitoring the process mean and variance using a synthetic control chart with two-stage testing

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

Mixed venous oxygen saturation monitoring revisited : thoughts for critical care nursing practice

Background Less invasive methods of determining cardiac output are now readily available. Using indicator dilution technique, for example has made it easier to continuously measure cardiac output because it uses the existing intra-arterial line. Therefore gone is the need for a pulmonary artery floatation catheter and with it the ability to measure left atrial and left ventricular work indices as well the ability to monitor and measure a mixed venous saturation (SvO2). Purpose The aim of this paper is to put forward the notion that SvO2 provides valuable information about oxygen consumption and venous reserve; important measures in the critically ill to ensure oxygen supply meets cellular demand. In an attempt to portray this, a simplified example of the septic patient is offered to highlight the changing pathophysiological sequelae of the inflammatory process and its importance for monitoring SvO2. Relevance to clinical practice SvO2 monitoring, it could be argued, provides the gold standard for assessing arterial and venous oxygen indices in the critically ill. For the bedside ICU nurse the plethora of information inherent in SvO2 monitoring could provide them with important data that will assist in averting potential problems with oxygen delivery and consumption. However, it has been suggested that central venous saturation (ScvO2) might be an attractive alternative to SvO2 because of its less invasiveness and ease of obtaining a sample for analysis. There are problems with this approach and these are to do with where the catheter tip is sited and the nature of the venous admixture at this site. Studies have shown that ScvO2 is less accurate than SvO2 and should not be used as a sole guiding variable for decision-making. These studies have demonstrated that there is an unacceptably wide range in variance between ScvO2 and SvO2 and this is dependent on the presenting disease, in some cases SvO2 will be significantly lower than ScvO2. Conclusion Whilst newer technologies have been developed to continuously measure cardiac output, SvO2 monitoring is still an important adjunct to clinical decision-making in the ICU. Given the information that it provides, seeking alternatives such as ScvO2 or blood samples obtained from femorally placed central venous lines, can unnecessarily lead to inappropriate treatment being given or withheld. Instead when using ScvO2, trending of this variable should provide clinical determinates that are useable for the bedside ICU nurse, remembering that in most conditions SvO2 will be approximately 16% lower.

Evaluating and validating abundance monitoring methods in the absence of populations of known size: review and application to a passive tracking index

Rarely is it possible to obtain absolute numbers in free-ranging populations and although various direct and indirect methods are used to estimate abundance, few are validated against populations of known size. In this paper, we apply grounding, calibration and verification methods, used to validate mathematical models, to methods of estimating relative abundance. To illustrate how this might be done, we consider and evaluate the widely applied passive tracking index (PTI) methodology. Using published data, we examine the rationality of PTI methodology, how conceptually animal activity and abundance are related and how alternative methods are subject to similar biases or produce similar abundance estimates and trends. We then attune the method against populations representing a range of densities likely to be encountered in the field. Finally, we compare PTI trends against a prediction that adjacent populations of the same species will have similar abundance values and trends in activity. We show that while PTI abundance estimates are subject to environmental and behavioural stochasticity peculiar to each species, the PTI method and associated variance estimate showed high probability of detection, high precision of abundance values and, generally, low variability between surveys, and suggest that the PTI method applied using this procedure and for these species provides a sensitive and credible index of abundance. This same or similar validation approach can and should be applied to alternative relative abundance methods in order to demonstrate their credibility and justify their use.

Monitoring of seasonal snow cover in Bhutan using remote sensing technique

All major rivers in Bhutan depend on snowmelt for discharge. Therefore, changes in snow cover due to climate change can influence distribution and availability of water. However, information about distribution of seasonal snow cover in Bhutan is not available. The MODIS snow product was used to study snow cover status and trends in Bhutan. Average snow cover area (SCA) of Bhutan estimated for the period 2002 to 2010 was 9030 sq. km, about 25.5% of the total land area. SCA trend of Bhutan for the period 2002-2010 was found to decrease (-3.27 +/- 1.28%). The average SCA for winter was 14,485 sq. km (37.7%), for spring 7411 sq. km (19.3%), for summer 4326 sq. km (11.2%), and for autumn 7788 sq. km (20.2%), mostly distributed in the elevation range 2500-6000 m amsl. Interannual and seasonal SCA trend both showed a decline, although it was not statistically significant for all sub-basins. Pho Chu sub-basin with 19.5% of the total average SCA had the highest average SCA. The rate of increase of SCA for every 100 m elevation was the highest (2.5%) in the Pa Chu sub-basin. The coefficient of variance of 1.27 indicates high variability of SCA in winter.

Use of aerial survey and aerophotogrammetry methods in monitoring manatee populations

We evaluated the use of strip-transect survey methods for manatees through a series of replicate aerial surveys in the Banana River, Brevard County, Florida, during summer 1993 and summer 1994. Transect methods sample a representative portion of the total study area, thus allowing for statistical extrapolation to the total area. Other advantages of transect methods are less flight time and less cost than total coverage, ease of navigation, and reduced likelihood of double-counting. Our objectives were: (1) to identify visibility biases associated with the transect survey method and to adjust the counts accordingly; (2) to derive a population estimate with known variance for the Banana River during summer; and (3) to evaluate the potential value of this survey method for monitoring trends in manatee population size over time. (51 page document)

Survey of plankton blooms and red tides and their interaction with environmental factors through monitoring satellite images

One of the most important marine ecological phenomena is red tide which is created by increasing of phytoplankton population, influenced by different factors such as climate condition changes, utrification hydrological factors and can leave sever and undesired ecological and economical effects behind itself in the case of durability. Coast line of Hormozgan is about 900km from east to west, within the range of geographical coordinates of 56 16 23.8, 26 58 8.8 to 54 34 5.33 and 26 34 32 eastern longitude and northern latitude, seven sampling stations were considered and sampled for a period of one year from October 2008 to October 2009. after the analysis of Satellite images, monthly, during the best time. In several stages, samplings were performed. In each station, three samples were collected for identification and determination of Bloom- creating species abundance. Cochlodinium polykrikoides was the species responsible for the discoloration which occurred at October 2008 in Hormozgan marine water. Environmental parameters such as sea surface temperature, pH, salinity, Dissolved Oxygen concentration, Total Dissolved Solids (T.D.S.), conductivity, nitrate, nitrite and phosphate and also chlorophyll a were measured and calculated. Kruscal Wallis test was used to compare the densities between different months, seasons and the studied stations. Mann-whitney test from Nonparametric Tests was used for couple comparison. Pearson correlation coefficient was used to determine the relationship between physical and chemical data set and the abundance of Cochlodinium polykrikoides. Multivariate Regression and analysis of variance (ANOVA) also were used to obtain the models and equations of red tide occurrence relationship, environmental parameters and nutrient data. The highest density was 26 million cells per liter in Qeshm station. A meaningful difference was observed between sampling months and seasons but there was no between sampling stations which indicates that in favorable conditions, the occurrence of this phenomenon by the studied species is probable. Regarding to β coefficients of nitrate, temperature, phosphate, Total Dissolvable Solutions (T.D.S) and pH these parameters are effective on the abundance of this species and red tide occurrence. Increase in these factors can represent the effects and outcomes of human activities and increase in marine pollution.

Bridge-vehicle interaction for structural health monitoring: potentials, applications, and limitations

Structural Health Monitoring (SHM) is an integral part of infrastructure maintenance and management systems due to socio-economic, safety and security reasons. The behaviour of a structure under vibration depends on structure characteristics. The change of structure characteristics may suggest the change in system behaviour due to the presence of damage(s) within. Therefore the consistent, output signal guided, and system dependable markers would be convenient tool for the online monitoring, the maintenance, rehabilitation strategies, and optimized decision making policies as required by the engineers, owners, managers, and the users from both safety and serviceability aspects. SHM has a very significant advantage over traditional investigations where tangible and intangible costs of a very high degree are often incurred due to the disruption of service. Additionally, SHM through bridge-vehicle interaction opens up opportunities for continuous tracking of the condition of the structure. Research in this area is still in initial stage and is extremely promising. This PhD focuses on using bridge-vehicle interaction response for SHM of damaged or deteriorating bridges to monitor or assess them under operating conditions. In the present study, a number of damage detection markers have been investigated and proposed in order to identify the existence, location, and the extent of an open crack in the structure. The theoretical and experimental investigation has been conducted on Single Degree of Freedom linear system, simply supported beams. The novel Delay Vector Variance (DVV) methodology has been employed for characterization of structural behaviour by time-domain response analysis. Also, the analysis of responses of actual bridges using DVV method has been for the first time employed for this kind of investigation.

Marine biodiversity and ecosystem function relationships:the potential for practical monitoring applications

There is an increasing demand for environmental assessments of the marine environment to include ecosystem function. However, existing schemes are predominantly based on taxonomic (i.e. structural) measures of biodiversity. Biodiversity and Ecosystem Function (BEF) relationships are suggested to provide a mechanism for converting taxonomic information into surrogates of ecosystem function. This review assesses the evidence for marine BEF relationships and their potential to be used in practical monitoring applications (i.e. operationalized). Five key requirements were identified for the practical application of BEF relationships: (1) a complete understanding of strength, direction and prevalence of marine BEF relationships, (2) an understanding of which biological components are influential within specific BEF relationships, (3) the biodiversity of the selected biological components can be measured easily, (4) the ecological mechanisms that are the most important for generating marine BEF relationships, i.e. identity effects or complementarity, are known and (5) the proportion of the overall functional variance is explained by biodiversity, and hence BEF relationships, has been established. Numerous positive and some negative BEF relationships were found within the literature, although many reproduced poorly the natural species richness, trophic structures or multiple functions of real ecosystems (requirement 1). Null relationships were also reported. The consistency of the positive and negative relationships was often low that compromised the ability to generalize BEF relationships and confident application of BEF within marine monitoring. Equally, some biological components and functions have received little or no investigation. Expert judgement was used to attribute biological components using spatial extent, presence and functional rate criteria (requirement 2). This approach highlighted the main biological components contributing the most to specific ecosystem functions, and that many of the particularly influential components were found to have received the least amount of research attention. The need for biodiversity to be measureable (requirement 3) is possible for most biological components although difficult within the functionally important microbes. Identity effects underpinned most marine BEF relationships (requirement 4). As such, processes that translated structural biodiversity measures into functional diversity were found to generate better BEF relationships. The analysis of the contribution made by biodiversity, over abiotic influences, to the total expression of a particular ecosystem function was rarely measured or considered (requirement 5). Hence it is not possible to determine the overall importance of BEF relationships within the total ecosystem functioning observed. In the few studies where abiotic factors had been considered, it was clear that these modified BEF relationships and have their own direct influence on functional rate. Based on the five requirements, the information required for immediate ‘operationalization’ of BEF relationships within marine functional monitoring is lacking. However, the concept of BEF inclusion within practical monitoring applications, supported by ecological modelling, shows promise for providing surrogate indicators of functioning.

Process monitoring approach using fast moving window PCA

This paper introduces a fast algorithm for moving window principal component analysis (MWPCA) which will adapt a principal component model. This incorporates the concept of recursive adaptation within a moving window to (i) adapt the mean and variance of the process variables, (ii) adapt the correlation matrix, and (iii) adjust the PCA model by recomputing the decomposition. This paper shows that the new algorithm is computationally faster than conventional moving window techniques, if the window size exceeds 3 times the number of variables, and is not affected by the window size. A further contribution is the introduction of an N-step-ahead horizon into the process monitoring. This implies that the PCA model, identified N-steps earlier, is used to analyze the current observation. For monitoring complex chemical systems, this work shows that the use of the horizon improves the ability to detect slowly developing drifts.