Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi`s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is nonconforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure. (C) 2009 Elsevier B. V. All rights reserved.

Effects of the preventive and corrective adjustments in economical designs for online process control for attributes with misclassification errors

The procedure for online process control by attributes consists of inspecting a single item at every m produced items. It is decided on the basis of the inspection result whether the process is in-control (the conforming fraction is stable) or out-of-control (the conforming fraction is decreased, for example). Most articles about online process control have cited the stoppage of the production process for an adjustment when the inspected item is non-conforming (then the production is restarted in-control, here denominated as corrective adjustment). Moreover, the articles related to this subject do not present semi-economical designs (which may yield high quantities of non-conforming items), as they do not include a policy of preventive adjustments (in such case no item is inspected), which can be more economical, mainly if the inspected item can be misclassified. In this article, the possibility of preventive or corrective adjustments in the process is decided at every m produced item. If a preventive adjustment is decided upon, then no item is inspected. On the contrary, the m-th item is inspected; if it conforms, the production goes on, otherwise, an adjustment takes place and the process restarts in-control. This approach is economically feasible for some practical situations and the parameters of the proposed procedure are determined minimizing an average cost function subject to some statistical restrictions (for example, to assure a minimal levelfixed in advanceof conforming items in the production process). Numerical examples illustrate the proposal.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Economic design of an X chart for short-run production

The aim of this paper is to present an economical design of an X chart for a short-run production. The process mean starts equal to mu(0) (in-control, State I) and in a random time it shifts to mu(1) > mu(0) (out-of-control, State II). The monitoring procedure consists of inspecting a single item at every m produced ones. If the measurement of the quality characteristic does not meet the control limits, the process is stopped, adjusted, and additional (r - 1) items are inspected retrospectively. The probabilistic model was developed considering only shifts in the process mean. A direct search technique is applied to find the optimum parameters which minimizes the expected cost function. Numerical examples illustrate the proposed procedure. (C) 2009 Elsevier B.V. All rights reserved.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Evaluation of algorithms used to order markers on genetic maps

When building genetic maps, it is necessary to choose from several marker ordering algorithms and criteria, and the choice is not always simple. In this study, we evaluate the efficiency of algorithms try (TRY), seriation (SER), rapid chain delineation (RCD), recombination counting and ordering (RECORD) and unidirectional growth (UG), as well as the criteria PARF (product of adjacent recombination fractions), SARF (sum of adjacent recombination fractions), SALOD (sum of adjacent LOD scores) and LHMC (likelihood through hidden Markov chains), used with the RIPPLE algorithm for error verification, in the construction of genetic linkage maps. A linkage map of a hypothetical diploid and monoecious plant species was simulated containing one linkage group and 21 markers with fixed distance of 3 cM between them. In all, 700 F(2) populations were randomly simulated with and 400 individuals with different combinations of dominant and co-dominant markers, as well as 10 and 20% of missing data. The simulations showed that, in the presence of co-dominant markers only, any combination of algorithm and criteria may be used, even for a reduced population size. In the case of a smaller proportion of dominant markers, any of the algorithms and criteria (except SALOD) investigated may be used. In the presence of high proportions of dominant markers and smaller samples (around 100), the probability of repulsion linkage increases between them and, in this case, use of the algorithms TRY and SER associated to RIPPLE with criterion LHMC would provide better results. Heredity (2009) 103, 494-502; doi:10.1038/hdy.2009.96; published online 29 July 2009

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

Asymmetry and duration dependence in Australian GDP and unemployment

The per iodic structure of business cycles suggests that significant asymmetries are present over different phases of the cycle. This paper uses markov regime-switching models with fixed and duration dependent transition probabilities to directly model expansions, contractions and durations in Australian GDP growth and unemployment growth. Evidence is found of significant asymmetry in growth rates across expansions and contractions for both series. GDP contractions exhibit duration dependence implying that as output recessions age the likelihood of switching into an expansion phase increases. Unemployment growth does not exhibit duration dependence in either phase. Evidence is also presented that non-linearities in unemployment growth are well explained by the asymmetries in the GDP growth cycle. The analysis suggests that recessions are periods of rapid and intense job destruction, that Australian unemployment tends to ratchet up in recessionary periods and, in contrast to US and UK studies, that shocks to Australian unemployment growth are more persistent in recessions than expansions. [E37 C5 C41].

Absorptive quantum measurements via coherently coupled quantum dots

We propose an absorptive measurement scheme via coupled quantum dots based on studies of the quantum dynamics of coherently coupled dots. The system is described through a Markov master equation that is related to a measurable quantity, the current. We analyse the measurement configuration and calculate the correlations and noise spectra beyond the adiabatic approximation.

Prediction of promiscuous peptides that bind HLA class I molecules

Promiscuous T-cell epitopes make ideal targets for vaccine development. We report here a computational system, multipred, for the prediction of peptide binding to the HLA-A2 supertype. It combines a novel representation of peptide/MHC interactions with a hidden Markov model as the prediction algorithm. multipred is both sensitive and specific, and demonstrates high accuracy of peptide-binding predictions for HLA-A*0201, *0204, and *0205 alleles, good accuracy for *0206 allele, and marginal accuracy for *0203 allele. multipred replaces earlier requirements for individual prediction models for each HLA allelic variant and simplifies computational aspects of peptide-binding prediction. Preliminary testing indicates that multipred can predict peptide binding to HLA-A2 supertype molecules with high accuracy, including those allelic variants for which no experimental binding data are currently available.

Methods for prediction of peptide binding to MHC molecules: A comparative study

Background: A variety of methods for prediction of peptide binding to major histocompatibility complex (MHC) have been proposed. These methods are based on binding motifs, binding matrices, hidden Markov models (HMM), or artificial neural networks (ANN). There has been little prior work on the comparative analysis of these methods. Materials and Methods: We performed a comparison of the performance of six methods applied to the prediction of two human MHC class I molecules, including binding matrices and motifs, ANNs, and HMMs. Results: The selection of the optimal prediction method depends on the amount of available data (the number of peptides of known binding affinity to the MHC molecule of interest), the biases in the data set and the intended purpose of the prediction (screening of a single protein versus mass screening). When little or no peptide data are available, binding motifs are the most useful alternative to random guessing or use of a complete overlapping set of peptides for selection of candidate binders. As the number of known peptide binders increases, binding matrices and HMM become more useful predictors. ANN and HMM are the predictive methods of choice for MHC alleles with more than 100 known binding peptides. Conclusion: The ability of bioinformatic methods to reliably predict MHC binding peptides, and thereby potential T-cell epitopes, has major implications for clinical immunology, particularly in the area of vaccine design.

Computational methods for prediction of T-cell epitopes - a framework for modelling, testing, and applications

Computational models complement laboratory experimentation for efficient identification of MHC-binding peptides and T-cell epitopes. Methods for prediction of MHC-binding peptides include binding motifs, quantitative matrices, artificial neural networks, hidden Markov models, and molecular modelling. Models derived by these methods have been successfully used for prediction of T-cell epitopes in cancer, autoimmunity, infectious disease, and allergy. For maximum benefit, the use of computer models must be treated as experiments analogous to standard laboratory procedures and performed according to strict standards. This requires careful selection of data for model building, and adequate testing and validation. A range of web-based databases and MHC-binding prediction programs are available. Although some available prediction programs for particular MHC alleles have reasonable accuracy, there is no guarantee that all models produce good quality predictions. In this article, we present and discuss a framework for modelling, testing, and applications of computational methods used in predictions of T-cell epitopes. (C) 2004 Elsevier Inc. All rights reserved.