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.

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.

Process capability estimation for leukocyte filtering process in blood service: a comparison study

This article considers a comparison study between different non-normal process capability estimation methods and utilizing themin the leukocyte filtering process in blood service sectors. Since the amount of leukocyte in a unit of the blood is a critical issue inthe blood transfusion process and patient safety, estimating and monitoring the capability of the leukocyte filtering process to meetthe target window is very important for blood service sectors. However, observed data from the leukocyte filtering process showthat the leukocyte levels after filtering demonstrate a right skewed distribution and applying conventional methods with a normalityassumption fails to provide trustful results. Hence, we first conduct a simulation study to compare different methods in estimating theprocess capability index of non-normal processes and then we apply these techniques to obtain the process capability of the leukocytefiltering process. The study reveals that the Box-Cox transformation method provides reliable estimation of the process capability ofthe leukocyte filtering process.

Univariate and multivariate process yield indices based on location-scale family of distributions

Several measures of process yield, defined on univariate and multivariate normal process characteristics, have been introduced and studied by several authors. These measures supplement several well-known Process Capacity Indices (PCI) used widely in assessing the quality of products before being released into the marketplace. In this paper, we generalise these yield indices to the location-scale family of distributions which includes the normal distribution as one of its member. One of the key contributions of this paper is to demonstrate that under appropriate conditions, these indices converge in distribution to a normal distribution. Several numerical examples will be used to illustrate our procedures and show how they can be applied to perform statistical inferences on process capability.

Normative life satisfaction: measurement issues and a homeostatic model

Previous studies have established that, when life satisfaction is measured over a range from 0 to 100 the mean scores of Western populations average 75 ± 2.5. The consistency of these data has given rise to the idea that life satisfaction may be held under homeostatic control. This paper further investigates this hypothesis by examining the distribution of data within populations. It also examines these data with a view to elucidating various methodological issues regarding life satisfaction measurement. In terms of the methodological issues it is concluded that measurement is best achieved using bi-directional Likert scales with at least 11 choice points. It is also determined that the life satisfaction of Western populations did not change over the decade 1980–1990, and that data derived from college students cannot be validly employed as proxy general population data. In terms of data distribution, it is calculated that the normal range of life satisfaction within Western populations lies within the range 40 to 100. The consistency of this non-normal distribution is argued to be further evidence that life satisfaction is held under homestatic control, and a descriptive model is proposed.

Neutrosophic information fusion applied to the options market

In this paper we basically make two propositions - firstly a non-linear process that is primarily fuelled by mass cognitive dissonance could generate systematic deviations between the theoretical and market prices of long-term options, and secondly such deviations are best reconciled in terms of neutrosophic rather than ruled-based reasoning, especially in the context of the users of automated trading systems designed to generate trading signals based on analysis of information  from conflicting sources.

Testing for the random walk hypothesis in the case of visitor arrivals : evidence from Indian tourism

Testing for the random walk hypothesis, which asserts that a series is a non-stationary process or a unit root process, in the case of visitor arrivals has important implications for policy. If, for instance, visitor arrivals are characterized by a unit root, then it implies that shocks to visitor arrivals are permanent. However, if visitor arrivals are without a unit root, this implies that shocks to visitor arrivals are temporary. This study provides evidence on the random walk hypothesis for visitor arrivals to India using the recently developed Im et al. (2003) and Maddala and Wu (1999) panel unit root tests. Both tests allow one to reject the random walk hypothesis, implying that shocks to visitor arrivals to India from the 10 major source markets have a temporary effect on visitor arrivals.

Many-sample location and scale tests with quantile-function error distributions /by Azmeri Khan

This thesis, using a computer simulation, studies the effect of the normal distribution assumption on the power of several many-sample location and scale test procedures. It also suggests an almost robust parametric test, namely numerical likelihood ratio test (NLRT) for non-normal situations. The NLRT is found better than all of the tests considered. Some real life data sets were used as examples.

Strain gradient plasticity modelling of high-pressure torsion

Gradient plasticity modelling combining a micro-structure-related constitutive description of the local material behaviour with a particular gradient plasticity frame is presented. The constitutive formulation is based on a phase mixture model in which the dislocation cell walls and the cell interiors are considered as separate 'phases', the respective dislocation densities entering as internal variables. Two distinct physical mechanisms, which give rise to gradient plasticity, are considered. The first one is associated with the occurrence of geometrically necessary dislocations leading to first-order strain gradients; the second one is associated with the reaction stresses due to plastic strain incompatibilities between neighbouring grains, which lead to second-order strain gradients. These two separate variants of gradient plasticity were applied to the case of high-pressure torsion: a process known to result in a fairly uniform, ultrafine grained structure of metals. It is shown that the two complementary variants of gradient plasticity can both account for the experimental results, thus resolving a controversial issue of the occurrence of a uniform micro-structure as a result of an inherently non-uniform process. © 2007 Elsevier Ltd. All rights reserved.

FEA simulation of contact and wear between non-metallic materials for accelerated new product development

The conventional approach ie laboratory life testing to examine the reliability of products takes long time and involves tremendous cost as samples are tested till failures. The accelerated life test (ALT) has recently been used as an alternative method. Although ALT reduces the cost of reliability testing through applying more severe environmental conditions than the normal ones, it is no longer sufficient as it does not describe the process of products’ failure explicitly and it is still highly dependent on physical testing. Consequently, novel practices need to be developed for better understanding of the products’ reliability. A novel Finite Element Analysis (FEA) model incorporating mathematical wear equations is developed in the current work and applied to polymer materials. Wear rate, a key parameter, is calculated by using a combinatorial formula that combines a conventional linear equation with a recently published exponential equation. The local wear is firstly calculated and then integrated over the sliding distance. The FEA simulation works in a loop and performs a series of simulation with updated surface geometries. The simulation is in good agreement with the physical testing result.

Tensile behaviour of non-uniform fibres and fibrous composites

This work investigates the tensile behaviour of non-uniform fibres and fibrous composites. Wool fibres are used as an example of non-uniform fibres because they're physical, morphological and geometrical properties vary greatly not only between fibres but also within a fibre. The focus of this work is on the effect of both between-fibre and within-fibre diameter variations on fibre tensile behaviour. In addition, fit to the Weibull distribution by the non-brittle and non-uniform visco-elastic wool fibres is examined, and the Weibull model is developed further for non-uniform fibres with diameter variation along the fibre length. A novel model fibre composite is introduced to facilitate the investigation into the tensile behaviour of fibre-reinforced composites. This work first confirms that for processed wool, its coefficient of variation in break force can be predicted from that of minimum fibre diameters, and the prediction is better for longer fibres. This implies that even for processed wool, fibre breakage is closely associated with the occurrence of thin sections along a fibre, and damage to fibres during processing is not the main cause of fibre breakage. The effect of along-fibre diameter variation on fibre tensile behaviour of scoured wool and mohair is examined next. Only wet wool samples were examined in the past. The extensions of individual segments of single non-uniform fibres are measured at different strain levels. An important finding is the maximum extension (%) (Normally at the thinnest section) equals the average fibre extension (%) plus the diameter variation (CV %) among the fibre segments. This relationship has not been reported before. During a tensile test, it is only the average fibre extension that is measured. The third part of this work is on the applicability of Weibull distribution to the strength of non-uniform visco-elastic wool fibres. Little work has been done for wool fibres in this area, even though the Weibull model has been widely applied to many brittle fibres. An improved Weibull model incorporating within-fibre diameter variations has been developed for non-uniform fibres. This model predicts the gauge length effect more accurately than the conventional Weibull model. In studies of fibre-reinforced composites, ideal composite specimens are usually prepared and used in the experiments. Sample preparation has been a tedious process. A novel fibre reinforced composite is developed and used in this work to investigate the tensile behaviour of fibre-reinforced composites. The results obtained from the novel composite specimen are consistent with that obtained from the normal specimens.

Degradation of VOCs using non-film titania in a hybrid process

This study reports the preparation and characterization of titanium dioxide (TiO2)-based non-film catalysts, reactor design and their utilization in a hybrid dynamic degradation of acetone and toluene. The behaviours of deactivation and regeneration of catalysts are explored as well. The regression equations of conversion rate in differing operating modes are concluded.