Variable parameter and double sampling (X)over-bar charts in the presence of correlation: The Markov chain approach

The general assumption under which the (X) over bar chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the (X) over bar chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the (X) over bar chart. The performance of the chat (X) over bar with variable parameters and the (X) over bar with double sampling are compared. (C) 2011 Elsevier B.V. All rights reserved.

(X)OVER-BAR CHARTS WITH VARIABLE SAMPLE-SIZE

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours This article considers the properties of the XBAR chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) XBAR chart are obtained using Markov chains. The VSS XBAR chart is substantially quicker than the traditional XBAR chart in detecting moderate shifts in the process.

X̄ charts with variable sample size

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours. This article considers the properties of the X̄ chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) X̄ chart are obtained using Markov chains. The VSS X̄ chart is substantially quicker than the traditional X̄ chart in detecting moderate shifts in the process.

X̄ chart with variable sample size and sampling intervals

Recent theoretical studies have shown that the X̄ chart with variable sampling intervals (VSI) and the X̄ chart with variable sample size (VSS) are quicker than the traditional X̄ chart in detecting shifts in the process. This article considers the X̄ chart with variable sample size and sampling intervals (VSSI). It is assumed that the amount of time the process remains in control has exponential distribution. The properties of the VSSI X̄ chart are obtained using Markov chains. The VSSI X̄ chart is even quicker than the VSI or VSS X̄ charts in detecting moderate shifts in the process.

Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Structural modelling of Eu3+-based siloxane-poly( oxyethylene) nanohybrids

The modelling of the local structure of sol-gel derived Eu3+-based organic/inorganic hybrids is reported, based on Small-Angle X-ray Scattering (SAXS), photoluminescence and mid-infrared spectroscopy. The hybrid matrix of these organically modified silicates, classed as di-ureasils and termed U(2000) and U(600), is formed by poly( oxyethylene) (POE) chains of variable length grafted to siloxane domains by means of urea cross-linkages. Europium triflate, Eu(CF3SO3)(3), was incorporated in the two di-ureasil matrices with compositions 400 greater than or equal ton greater than or equal to 10, n is the molar ratio of ether oxygens per Eu3+. The SAXS data for undoped hybrids (n=infinity) show the presence of a well-defined peak attributed to the existence of a liquid-like spatial correlation of siloxane rich domains embedded in the polymer matrix and located at the ends of the organic segments. The obtained siloxane particle gyration radius Rg(1) is around 5 Angstrom (error within 10%), whereas the interparticle distance d is 25 +/-2 Angstrom and 40 +/-2 Angstrom, for U(600) and U(2000), respectively. For the Eu3+-based nanocomposites the formation of a two-level hierarchical local structure is discerned. The primary level is constituted by strongly spatially correlated siloxane particles of gyration radius Rg(1) (4-6 and 3-8 Angstrom, errors within 5%, for U(600())n Eu(CF3SO3)(3), 200 greater than or equal ton greater than or equal to 40, and U(2000)(n)Eu(CF3SO3)(3), 400 greater than or equal ton greater than or equal to 40, respectively) forming large clusters of gyration radius Rg(2) (approximate to 75 +/- 10 Angstrom). The local coordination of Eu3+ in both di-ureasil series is described combining the SAXS, photoluminescence and mid-infrared results. In the di-ureasils containing long polymer chains, U(2000)(n)Eu(CF3SO3)(3), the cations interact exclusively with the carbonyl oxygens atoms of the urea bridges at the siloxane-POE interface. In the hybrids containing shorter chains, U(600)(n)Eu(CF3SO3)(3) with n ranging from 200 to 60, the Eu3+ ions interact solely with the ether-type oxygens of the polymer chains. Nevertheless, in this latter family of hybrids a distinct Eu3+ local site environment involving the urea cross-linkages is detected when the europium content is increased up to n=40.

Structure of magnetic poly(oxyethylene)-siloxane nanohybrids doped with Fe-II and Fe-III

Hybrid organic - inorganic nanocomposites doped with Fe-II and Fe-III ions and exhibiting interesting magnetic properties have been obtained by the sol - gel process. The hybrid matrix of these ormosils ( organically modified silicates), classed as di-ureasils and termed U( 2000), is composed of poly( oxyethylene) chains of variable length grafted to siloxane groups by means of urea crosslinkages. Iron perchlorate and iron nitrate were incorporated in the diureasil matrices, leading to compositions within the range 80 greater than or equal to n greater than or equal to 10, n being the molar ratio of ether-type O atoms per cation. The structure of the doped diureasils was investigated by small-angle X-ray scattering (SAXS). For Fe-II-doped samples, SAXS results suggest the existence of a two-level hierarchical structure. The primary level is composed of spatially correlated siloxane clusters embedded in the polymeric matrix and the secondary, coarser level consists of domains where the siloxane clusters are segregated. The structure of Fe-III-doped hybrids is different, revealing the existence of iron oxide based nanoclusters, identified as ferrihydrite by wide-angle X-ray diffraction, dispersed in the hybrid matrix. The magnetic susceptibility of these materials was determined by zero-field-cooling and field-cooling procedures as functions of both temperature and field. The different magnetic features between Fe-II- and Fe-III-doped samples are consistent with the structural differences revealed by SAXS. While Fe-II-doped composites exhibit a paramagnetic Curie-type behaviour, hybrids containing Fe-III ions show thermal and field irreversibilities.

Self-Structuring of Lamellar Bridged Silsesquioxanes with Long Side Spacers

Diurea cross-linked bridged silsesquioxanes (BSs) C(10)C(11)C(10) derived from organosilane precursors, including decylene chains as side spacers and alkylene chains with variable length as central spacers (EtO)(3)Si- (CH(2))(10)-Y(CH(2))(n)-Y-(CH(2))(10)-Si(OEt)(3) (n = 7, 9-12; Y = urea group and Et = ethyl), have been synthesized through the combination of self-directed assembly and an acid-catalyzed sol gel route involving the addition of dimethylsulfoxide (DMSO) and a large excess of water. This new family of hybrids has enabled us to conclude that the length of the side spacers plays a unique role in the structuring of alkylene-based BSs, although their morphology remains unaffected. All the samples adopt a lamellar structure. While the alkylene chains are totally disordered in the case of the C(10)C(7)C(10) sample, a variable proportion of all-trans and gauche conformers exists in the materials with longer central spacers. The highest degree of structuring occurs for n = 9. The inclusion of decylene instead of propylene chains as side spacers leads to the formation of a stronger hydrogen-bonded urea-urea array as evidenced by two dimensional correlation Fourier transform infrared spectroscopic analysis. The emission spectra and emission quantum yields of the C(10)C(n)C(10) Cm materials are similar to those reported for diurea cross-linked alkylene-based BSs incorporating propylene chains as side spacers and prepared under different experimental conditions. The emission of the C(10)C(n)C(10) hybrids is ascribed to the overlap of two distinct components that occur within the urea cross-linkages and within the siliceous nanodomains. Time-resolved photoluminescence spectroscopy has provided evidence that the average distance between the siliceous domains and the urea cross-links is similar in the C(10)C(n)C(10) BSs and in oxyethylene-based hybrid analogues incorporating propylene chains as side spacers (diureasils), an indication that the longer side chains in the former materials adopt gauche conformations. It has also allowed us to demonstrate for the first time that the emission features of the urea-related component of the emission of alkylene-based BSs depend critically on the length of the side spacers.

Aplicações das Cadeias de Markov para o Ensino Médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Técnicas de otimização em alinhamentos múltiplos de sequência via Cadeias de Markov

Pós-graduação em Ciência da Computação - IBILCE

O efeito da autocorrelação no planejamento das cartas de controle de x̄ e EWMA

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Analytical and Monte Carlo approaches to evaluate probability distributions of interruption duration

Regulatory authorities in many countries, in order to maintain an acceptable balance between appropriate customer service qualities and costs, are introducing a performance-based regulation. These regulations impose penalties-and, in some cases, rewards-that introduce a component of financial risk to an electric power utility due to the uncertainty associated with preserving a specific level of system reliability. In Brazil, for instance, one of the reliability indices receiving special attention by the utilities is the maximum continuous interruption duration (MCID) per customer.This parameter is responsible for the majority of penalties in many electric distribution utilities. This paper describes analytical and Monte Carlo simulation approaches to evaluate probability distributions of interruption duration indices. More emphasis will be given to the development of an analytical method to assess the probability distribution associated with the parameter MCID and the correspond ng penalties. Case studies on a simple distribution network and on a real Brazilian distribution system are presented and discussed.

Adaptive control charts: A Markovian approach for processes subject to independent disturbances

Recent studies have shown that adaptive X control charts are quicker than traditional X charts in detecting small to moderate shifts in a process. In this article, we propose a joint statistical design of adaptive X and R charts having all design parameters varying adaptively. The process is subjected to two independent assignable causes. One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. It is assumed that the quality characteristic is normally distributed and the time that the process remains in control has exponential distribution. Performance measures of these adaptive control charts are obtained through a Markov chain approach. (c) 2005 Elsevier B.V. All rights reserved.

MOTILIN-IMMUNOREACTIVE CELLS IN THE DUODENUM, PYLORIC STOMACH AND PANCREAS OF CAIMANS (CAIMAN-LATIROSTRIS AND CAIMAN-CROCODILUS, ALLIGATORINAE) - A FURTHER COMPARISON USING REGION-SPECIFIC MOTILIN ANTISERA

Motilin-immunoreactive cells in the duodenum, pyloric stomach and pancreas of Caiman latirostris and Caiman crocodilus were investigated using region specific antisera for porcine and canine motilin molecules. Motilin-immunoreactive cells were found in the duodenum, pyloric stomach and pancreas of both caiman species. These cells were primarily open-type endocrine ones in the epithelium of the duodenum and pyloric stomach. Motilin-immunoreactive cells were observed in both the exocrine and endocrine portions of the pancreas, and frequently exhibited one or more cytoplasmic processes of variable length. Since motilin-immunoreactive cells do not cross-react with serotonin or any of the other pancreatic and gut hormones, they are considered to be cell type independent from any of the other known pancreatic or gut endocrine cells. The molecular similarity between caiman motilin and porcine and canine motilins and the heterogeneity of the motilin molecule in the caiman digestive system is discussed.

Chronological Monte Carlo-based assessment of distribution system reliability

Regulatory authorities in many countries, in order to maintain an acceptable balance between appropriate customer service qualities and costs, are introducing a performance-based regulation. These regulations impose penalties, and in some cases rewards, which introduce a component of financial risk to an electric power utility due to the uncertainty associated with preserving a specific level of system reliability. In Brazil, for instance, one of the reliability indices receiving special attention by the utilities is the Maximum Continuous Interruption Duration per customer (MCID). This paper describes a chronological Monte Carlo simulation approach to evaluate probability distributions of reliability indices, including the MCID, and the corresponding penalties. In order to get the desired efficiency, modern computational techniques are used for modeling (UML -Unified Modeling Language) as well as for programming (Object- Oriented Programming). Case studies on a simple distribution network and on real Brazilian distribution systems are presented and discussed. © Copyright KTH 2006.