A note on multivariate non-normal process capability analysis using "mvtnorm" library in R

In this note we examine using Genzbretz and Miwa algorithms to improve estimation of proposition of non-conformance in multivariate normal distributions. This estimation is required in the procedure outlined in Abbasi and Niaki (Int J Adv Manuf Technol 50(5-8):823-830, 2010) to determine process capability index of multivariate non-normal processes.

A transformation technique to estimate the process capability index for non-normal processes

Estimating the process capability index (PCI) for non-normal processes has been discussed by many researches. There are two basic approaches to estimating the PCI for non-normal processes. The first commonly used approach is to transform the non-normal data into normal data using transformation techniques and then use a conventional normal method to estimate the PCI for transformed data. This is a straightforward approach and is easy to deploy. The alternate approach is to use non-normal percentiles to calculate the PCI. The latter approach is not easy to implement and a deviation in estimating the distribution of the process may affect the efficacy of the estimated PCI. The aim of this paper is to estimate the PCI for non-normal processes using a transformation technique called root transformation. The efficacy of the proposed technique is assessed by conducting a simulation study using gamma, Weibull, and beta distributions. The root transformation technique is used to estimate the PCI for each set of simulated data. These results are then compared with the PCI obtained using exact percentiles and the Box-Cox method. Finally, a case study based on real-world data is presented.

Process capability analysis in non normal linear regression profiles

When the distribution of a process characterized by a profile is non normal, process capability analysis using normal assumption often leads to erroneous interpretations of the process performance. Profile monitoring is a relatively new set of techniques in quality control that is used in situations where the state of product or process is represented by a function of two or more quality characteristics. Such profiles can be modeled using linear or nonlinear regression models. In some applications, it is assumed that the quality characteristics follow a normal distribution; however, in certain applications this assumption may fail to hold and may yield misleading results. In this article, we consider process capability analysis of non normal linear profiles. We investigate and compare five methods to estimate non normal process capability index (PCI) in profiles. In three of the methods, an estimation of the cumulative distribution function (cdf) of the process is required to analyze process capability in profiles. In order to estimate cdf of the process, we use a Burr XII distribution as well as empirical distributions. However, the resulted PCI with estimating cdf of the process is sometimes far from its true value. So, here we apply artificial neural network with supervised learning which allows the estimation of PCIs in profiles without the need to estimate cdf of the process. Box-Cox transformation technique is also developed to deal with non normal situations. Finally, a comparison study is performed through the simulation of Gamma, Weibull, Lognormal, Beta and student-t data.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

Low-lying non-normal parity states in B-8 measured by proton elastic scattering on Be-7

A new measurement of proton resonance scattering on Be-7 was performed tip to the center-of-mass energy of 6.7 MeV using the low-energy RI beam facility CRIB (CNS Radioactive Ion Beam separator) at the Center for Nuclear Study of the University of Tokyo. The excitation function of Be-7 + p elastic scattering above 3.5 MeV was measured Successfully for the first time, providing important information about the resonance structure of the B-8 nucleus. The resonances are related to the reaction rate of Be-7(p.gamma)B-8. which is the key reaction in solar B-8 neutrino production. Evidence for the presence of two negative parity states is presented. One of them is a 2(-) state observed as a broad s-wave resonance, the existence of which had been questionable. Its possible effects on the determination of the astrophysical S-factor of Be-7(p.gamma)B-8 at solar energy are discussed. The other state had not been observed in previous measurements, and its spin and parity were determined as 1(-). (C) 2009 Elsevier B.V. All rights reserved.

The Conditional Phase-type distribution: Graphical Models for Continuous Non-Normal Data:The Conditional Phase-type (C-Ph) distribution:

Conditional Gaussian (CG) distributions allow the inclusion of both discrete and continuous variables in a model assuming that the continuous variable is normally distributed. However, the CG distributions have proved to be unsuitable for survival data which tends to be highly skewed. A new method of analysis is required to take into account continuous variables which are not normally distributed. The aim of this paper is to introduce the more appropriate conditional phase-type (C-Ph) distribution for representing a continuous non-normal variable while also incorporating the causal information in the form of a Bayesian network.

Economic, environmental and mixed objective functions in non-linear process optimization using simulated annealing and tabu search

Screening of topologies developed by hierarchical heuristic procedures can be carried out by comparing their optimal performance. In this work we will be exploiting mono-objective process optimization using two algorithms, simulated annealing and tabu search, and four different objective functions: two of the net present value type, one of them including environmental costs and two of the global potential impact type. The hydrodealkylation of toluene to produce benzene was used as case study, considering five topologies with different complexities mainly obtained by including or not liquid recycling and heat integration. The performance of the algorithms together with the objective functions was observed, analyzed and discussed from various perspectives: average deviation of results for each algorithm, capacity for producing high purity product, screening of topologies, objective functions robustness in screening of topologies, trade-offs between economic and environmental type objective functions and variability of optimum solutions.

Non-normal real estate return distributions by property type in the UK

Investment risk models with infinite variance provide a better description of distributions of individual property returns in the IPD UK database over the period 1981 to 2003 than normally distributed risk models. This finding mirrors results in the US and Australia using identical methodology. Real estate investment risk is heteroskedastic, but the characteristic exponent of the investment risk function is constant across time – yet it may vary by property type. Asset diversification is far less effective at reducing the impact of non‐systematic investment risk on real estate portfolios than in the case of assets with normally distributed investment risk. The results, therefore, indicate that multi‐risk factor portfolio allocation models based on measures of investment codependence from finite‐variance statistics are ineffective in the real estate context

Non-normal real estate return distributions by property type in the U.K.

Investment risk models with infinite variance provide a better description of distributions of individual property returns in the IPD database over the period 1981 to 2003 than Normally distributed risk models, which mirrors results in the U.S. and Australia using identical methodology. Real estate investment risk is heteroscedastic, but the Characteristic Exponent of the investment risk function is constant across time yet may vary by property type. Asset diversification is far less effective at reducing the impact of non-systematic investment risk on real estate portfolios than in the case of assets with Normally distributed investment risk. Multi-risk factor portfolio allocation models based on measures of investment codependence from finite-variance statistics are ineffectual in the real estate context.

Production and purification of xylooligosaccharides from oil palm empty fruit bunch fibre by a non-isothermal process

Oil palm empty fruit bunches (OPEFB) fibre, a by-product generated from non-woody, tropical perennial oil palm crop was evaluated for xylooligosaccharides (XOS) production. Samples of OPEFB fibre were subjected to non-isothermal autohydrolysis treatment using a temperature range from 150 to 220 °C. The highest XOS concentration, 17.6 g/L which relayed from solubilisation of 63 g/100 g xylan was achieved at 210 °C and there was a minimum amount of xylose and furfural being produced. The chromatographic purification which was undertaken to purify the oligosaccharide-rich liquor resulted in a product with 74–78% purity, of which 83–85% was XOS with degree of polymerisation (DP) between 5 and 40.

A non-normal topology generated by a two-point selection

We construct a two-point selection f : [P](2) -> P, where P is the set of the irrational numbers, such that the space (P, tau(f)) is not normal and it is not collectionwise Hausdorff either. Here, tau(f) denotes the topology generated by the two-point selection f. This example answers a question posed by V. Gutev and T. Nogura. We also show that if f :[X](2) -> X is a two-point selection such that the topology tau(f) has countable pseudocharacter, then tau(f) is a Tychonoff topology. (C) 2008 Elsevier B.V. All rights reserved.

Simultaneous crystallization and decomposition of PVA/MMT composites during non-isothermal process

Decomposition of poly(vinyl alcohol)/montmorillonite clay (PVA/MMT) composites during melting-crystallization was experimentally confirmed by morphology and molecular structure changes. In particular, FTIR spectra show the shift of O-H stretching band as well as enhanced intensities of C-O stretching and CH2 rocking vibrational modes. Furthermore, Raman deconvolution indicates that C-H wagging, CH2-CH wagging, CH-CO bending and CH2 wagging modes in amorphous domains were all decreased greatly. Moreover, this decomposition leads to decreased melting enthalpy, melting point, crystallization enthalpy and crystallization temperature. Crystallization analysis shows that the MMT incorporated slows down the crystallization process in the PVA matrix regardless of the nucleation capability of MMT. Despite the severe decomposition, the crystallization kinetics still corroborated well with common classical models. As a result, molecular structure changes and crystallization retardation observed in this study clearly indicate the strong effects of the thermal degradation on the non-isothermal crystallization of PVA/MMT composites.