Control Chart for Heavy Tailed Distributions

ABSTRACT Standard control charts with control limits determined by the mean and standard error of the mean are constructed based on the assumption that the distribution of the quality characteristic being monitored follows a normal distribution. However, this assumption is not always valid. It is proposed to use a chart based on computing the control limits using the process mean and the standard error of the least absolute deviation for the case where the process quality characteristics follow a heavy tailed t distribution. Such a control chart is more effective than the normal distribution based chart since it has a low out-of-control average run length for both small and large values of process shift. OPSOMMING 'n Kontrolekaart wat gebruik maak van kontrolelimiete gebaseer op die standaardafwyking van die geringste absolute limiet word ontwerp vir 'n t-verdeling met 'n betekenisvolle stert. Simulasietoetse vir vergelyking van die voorgestelde kontrolekaart met normaalverdeelde kontrolekaarte toon dat korter gemiddelde looplengtes voor diagnose van beheerverlies uitgewys word, bereik word. 10

Estimation of Longevity using Survival Functions

Estimation of life expectancy and longevity are frequently used in several fields basically on convectional model. The study considers Longevity estimation models and variances as alternative to conventional model incorporating non-parametric, semi-parametric and parametric with relevant survival functions to formulate longevity models that will accommodate expected variables in the estimation of life expectancy. These models can be used to analyze both grouped and individual data. We consider Kaplan Meier model as nonparametric methods, Cox proportional model as semi parametric methods. The parametric methods considered are exponential, weibull and gompertz proportional models which are commonly used for analyzing discrete data. The derived variances of KM and Cox proportional longevity estimator models are equivalent this confirm the result of major work done in this field. The other derived longevity models have difference variances due to their peculiarities. We shall consider these models empirically in another paper

Max-EWMA chart for autocorrelated processes (MEWMAP chart)

This paper proposes an exponentially weighted moving average (EWMA) control chart that is capable of detecting changes in both process mean and standard deviation for autocorrelated data (referred to as the Maximum Exponentially Weighted Moving Average Chart for Autocorrelated Process, or MEWMAP chart). This chart is based on fitting a time series model to the data, and then calculating the residuals. The observations are represented as a first-order autoregressive process plus a random error term. The Average Run Lengths (ARLs) for fixed decision intervals and reference values (h, k) are calculated. The proposed chart is compared with the Max-CUSUM chart for autocorrelated data proposed by Thaga (2003). Comparisons are based on the out-of-control ARLs. The MEWMAP chart detects moderate to large shifts in the mean and/or standard deviation at both low and high levels of autocorrelations more quickly than the Max-CUSUM chart for autocorrelated processes.Die navorsing stel voor dat 'n eksponensiaal geweegde bewegende gemiddelde kontrolekaart gebruik word om verandering van prosesgemiddelde en –standaardafwyking van outogekorreleerde data te bepaal. Die kontrolekaart word gedryf deur passing van 'n tydreeks as datamodel met bepaling van residuwaardes. Met hierdie gegewens as vertrekpunt word gemiddelde looplengtes vir vaste besluitintervalle en verwysingwaardes (h, k) bereken. Die kontrolekaart bepaal matige en groot verskuiwings van waardes vir hoë en lae outokorrelasiewaardes heel snel.nf2010 (Author correction

Linear Cholesky decomposition of covariance matrices in mixed models with correlated random effects

Modelling the covariance matrix in linear mixed models provides an additional advantage in making inference about subject-specific effects, particularly in the analysis of repeated measurement data, where time-ordering of the responses induces significant correlation. Some difficulties encountered in these modelling procedures include high dimensionality and statistical interpretability of parameters, positive definiteness constraint and violation of model assumptions. One key assumption in linear mixed models is that random errors and random effects are independent, and its violation leads to biased and inefficient parameter estimates. To minimize these drawbacks, we developed a procedure that accounts for correlations induced by violation of this key assumption. In recent literature, variants of Cholesky decomposition were employed to circumvent the positive definiteness constraint, with parsimony achieved by joint modelling of mean and covariance parameters using covariates. In this article, we developed a linear Cholesky decomposition of the random effects covariance matrix, providing a framework for inference that accounts for correlations induced by covariate(s) shared by both fixed and random effects design matrices, a circumstance leading to lack of independence between random errors and random effects. The proposed decomposition is particularly useful in parameter estimation using the maximum likelihood and restricted/residual maximum likelihood procedures

SYSTEMS WITH EXTENDED AVAILABILITY AND SWITCHOVER DELAYS

<p>ENGLISH ABSTRACT: A system with extended availability and switchover delays with a single repair facility is considered, with a random extended available period having a switching delay from online failure to the repair of the facility. Identifying suitable regeneration points, several operating characteristics, such as the moment generating function of the total uptime, mean, and mean square number of various events, are obtained, apart from reliability and availability functions.</p><p>AFRIKAANSE OPSOMMING: 'n Stelsel met verlengde beskikbaarheid, oorskakelvertraging met 'n enkele herstelfasiliteit en 'n toevalverlengde beskikbaarheidsperiode met oorskakeling vanaf intydse mislukking tot herstel, word behandel. Deur geskikte regenerasiepunte te identifiseer, kan verskeie bedryfseienskappe (benewens betroubaarheid en beskikbaarheid) soos 'n momentgenerende funksie vir totale beskikbare tyd, gemiddelde en gemiddelde kwadraatwaardes vir verskeie gebeurtenisse, bepaal word.</p&gt

Increasing sport participation and physical well-being in the general population : the case of Botswana

Enquête par questionnaire (1422 réponses) auprès d'étudiants, jeunes sortis de l'école, personnes handicapées, femmes, administrateurs et dirigeants politiques et sportifs afin de comprendre les raisons d'un faible développement de la pratique sportive depuis l'indépendanc

Increasing sport participation and physical well-being in the general population : the case of Botswana

Enquête par questionnaire (1422 réponses) auprès d'étudiants, jeunes sortis de l'école, personnes handicapées, femmes, administrateurs et dirigeants politiques et sportifs afin de comprendre les raisons d'un faible développement de la pratique sportive depuis l'indépendanc

Systems with extended availability and switchover delays

A system with extended availability and switchover delays with a single repair facility is considered, with a random extended available period having a switching delay from online failure to the repair of the facility. Identifying suitable regeneration points, several operating characteristics, such as the moment generating function of the total uptime, mean, and mean square number of various events, are obtained, apart from reliability and availability functions.'n Stelsel met verlengde beskikbaarheid, oorskakelvertraging met 'n enkele herstelfasiliteit en 'n toevalverlengde beskikbaarheidsperiode met oorskakeling vanaf intydse mislukking tot herstel, word behandel. Deur geskikte regenerasiepunte te identifiseer, kan verskeie bedryfseienskappe (benewens betroubaarheid en beskikbaarheid) soos 'n momentgenerende funksie vir totale beskikbare tyd, gemiddelde en gemiddelde kwadraatwaardes vir verskeie gebeurtenisse, bepaal word