Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

Accelerating solutions of perfect fluid hydrodynamics for initial energy density and life-time measurements in heavy ion collisions

A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density and life-time of high energy heavy ion collisions. Accelerating solutions are also given for spherical expansions in arbitrary number of spatial dimensions.

On Queueinginventory Models – product form solution; reservation, Cancellation and common life time

Queueing theory is the mathematical study of ‘queue’ or ‘waiting lines’ where an item from inventory is provided to the customer on completion of service. A typical queueing system consists of a queue and a server. Customers arrive in the system from outside and join the queue in a certain way. The server picks up customers and serves them according to certain service discipline. Customers leave the system immediately after their service is completed. For queueing systems, queue length, waiting time and busy period are of primary interest to applications. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, mean queue length, traffic intensity, the expected number waiting or receiving service, mean busy period, distribution of queue length, and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.

Residence time distribution in holding tubes using generalized convection model and numerical convolution for non-ideal tracer detection

A procedure is proposed for the determination of the residence time distribution (RTD) of curved tubes taking into account the non-ideal detection of the tracer. The procedure was applied to two holding tubes used for milk pasteurization in laboratory scale. Experimental data was obtained using an ionic tracer. The signal distortion caused by the detection system was considerable because of the short residence time. Four RTD models, namely axial dispersion, extended tanks in series, generalized convection and PER + CSTR association, were adjusted after convolution with the E-curve of the detection system. The generalized convection model provided the best fit because it could better represent the tail on the tracer concentration curve that is Caused by the laminar velocity profile and the recirculation regions. Adjusted model parameters were well cot-related with the now rate. (C) 2010 Elsevier Ltd. All rights reserved.

Investigation of the residence time distribution in a plate heat exchanger with series and parallel arrangements using a non-ideal tracer detection technique

The objective was to study the flow pattern in a plate heat exchanger (PHE) through residence time distribution (RTD) experiments. The tested PHE had flat plates and it was part of a laboratory scale pasteurization unit. Series flow and parallel flow configurations were tested with a variable number of passes and channels per pass. Owing to the small scale of the equipment and the short residence times, it was necessary to take into account the influence of the tracer detection unit on the RID data. Four theoretical RID models were adjusted: combined, series combined, generalized convection and axial dispersion. The combined model provided the best fit and it was useful to quantify the active and dead space volumes of the PHE and their dependence on its configuration. Results suggest that the axial dispersion model would present good results for a larger number of passes because of the turbulence associated with the changes of pass. This type of study can be useful to compare the hydraulic performance of different plates or to provide data for the evaluation of heat-induced changes that occur in the processing of heat-sensitive products. (C) 2011 Elsevier Ltd. All rights reserved.

Life-time redistribution effects of the Spanish public pension system

The paper analyses the inter and intragenerational redistribution effects ofthe public pensions system in Spain. This is achieved by first comparing the expected present value of life-time income transfers (PVT) and internalrates of return (IRR) of different population cohorts. Secondly, we study the intragenerational aspects of the Spanish public pensions by calculating PVTs the IRRs for workers of different categories, grouped by earnings, gender and marital status.The results obtained show the nature of the important intergenerational effects of the Social Security System in Spain. The oldest 1935 cohort clearlybenefits in relation to the youngest 1965 cohort. This is basically due to thegap between current wages and the contribution bases established in the 60s and 70s in Spain during the early stages of the Social Security System, and to the worsening shortfall in Social Security funding, combined with the longer of life expectancy.In addition, intragenerational effects exist by income levels. For contributors who pay between the minimum and the maximum allowable contribution bases, net transfers and rates of return are higher in actuarial terms for high incomecontributors. The social security `dealï is again more profitable for highincome individuals since they contribute at the maximum basis, with respect tolow income contributors at the minimum basis. This is due to the late entry and a higher survival rate for high income contributors.The system tends to favour women, given that they generally live longer than men and this factor is only partially offset by their lower wages. Married males, given the fact that they have longer life expectancy and leave a pension to their spouse, obtain higher present net transfers too than do single contributors.We close the paper with some comments on the slight impact and moderate effects of proposals for Social Security reform and on how these may change the previously observed redistribution effects.

Life-time growth patterns of pumpkinseed Lepomis gibbosus introduced to Europe, relative to North American populations

The pumpkinseed Lepomis gibbosus, an omnivorous, nest guarding North American sunfish, was introduced into European waters about 100 years ago. To assess growth performance following introduction, we reviewed the available data for North American and European populations of pumpkinseed and compared the back-calculated age-specific growth for juveniles (standard length, SL, at age two) and adults (age two to five increment) as well as adult body size (SL at age five), von Bertalanffy growth model parameters and the index of growth (in length) performance (φ′). For continental comparisons of growth trajectory, mean growth curves for North American and Europe were calculated with the von Bertalanffy model using pooled data sets for each continent. Juvenile growth rate did not differ between European and North American pumpkinseed, but mean adult body size and adult growth rate were both significantly greater in North American than European populations. Adult body size decreased with increasing latitude (ANOVA) in North American populations, but this was not observed with adult growth rate. In contrast, adult body size tended to increase with latitude in European populations. Adult body size correlated significantly with φ′. The von Bertalanffy model described the overall growth patterns of North American and European populations reasonably well, but on the individual population level, length asymptotes were unrealistic (estimates that were > 20 % of the mean back-calculated size for the oldest age class) for a third of European populations and 80% of the North American populations. In contrast to North American pumpkinseed populations, somatic growth in European populations appears to be compromised by limited, but adequate, food resources, probably due to strong intraspecific interactions. This appears to be especially acute in adults, having potential ramifications for life span and reproductive allocation

The Effect of Operational Disturbances on Reliability and Operation Time Distribution of NCmachine Tools in FMS

This thesis concentrates on studying the operational disturbance behavior of machine tools integrated into FMS. Operational disturbances are short term failures of machine tools which are especially disruptive to unattended or unmanned operation of FMS. The main objective was to examine the effect of operational disturbances on reliability and operation time distribution for machine tools. The theoretical part of the thesis covers the fimdamentals of FMS relating to the subject of this study. The concept of FMS, its benefits and operator's role in FMS operation are reviewed. The importance of reliability is presented. The terms describing the operation time of machine tools are formed by adopting standards and references. The concept of failure and indicators describing reliability and operational performance for machine tools in FMSs are presented. The empirical part of the thesis describes the research methodology which is a combination of automated (ADC) and manual data collection. By using this methodology it is possible to have a complete view of the operation time distribution for studied machine tools. Data collection was carried out in four FMSs consisting of a total of 17 machine tools. Each FMS's basic features and the signals of ADC are described. The indicators describing the reliability and operation time distribution of machine tools were calculated according to collected data. The results showed that operational disturbances have a significant influence on machine tool reliability and operational performance. On average, an operational disturbance occurs every 8,6 hours of operation time and has a down time of 0,53 hours. Operational disturbances cause a 9,4% loss in operation time which is twice the amount of losses caused by technical failures (4,3%). Operational disturbances have a decreasing influence on the utilization rate. A poor operational disturbance behavior decreases the utilization rate. It was found that the features of a part family to be machined and the method technology related to it are defining the operational disturbance behavior of the machine tool. Main causes for operational disturbances were related to material quality variations, tool maintenance, NC program errors, ATC and machine tool control. Operator's role was emphasized. It was found that failure recording activity of the operators correlates with the utilization rate. The more precisely the operators record the failure, the higher is the utilization rate. Also the FMS organizations which record failures more precisely have fewer operational disturbances.

Gap effect and reaction time distribution: simple vs choice manual responses

It is well known that saccadic reaction times (SRT) are reduced when the target is preceded by the offset of the fixation point (FP) - the gap effect. Some authors have proposed that the FP offset also allows the saccadic system to generate a separate population of SRT, the express saccades. Nevertheless, there is no agreement as to whether the gap effect and express responses are also present for manual reaction times (MRT). We tested the gap effect and the MRT distribution in two different conditions, i.e., simple and choice MRT. In the choice MRT condition, subjects need to identify the side of the stimulus and to select the appropriate response, while in the simple MRT these stages are not necessary. We report that the gap effect was present in both conditions (22 ms for choice MRT condition; 15 ms for simple MRT condition), but, when analyzing the MRT distributions, we did not find any clear evidence for express manual responses. The main difference in MRT distribution between simple and choice conditions was a shift towards shorter values for simple MRT.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. © 2010 Elsevier B.V. All rights reserved.

Residence Time Distribution Models Derived from Non-Ideal Laminar Velocity Profiles in Tubes

The theoretical E-curve for the laminar flow of non-Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks-in-series models of residence time distribution (RTD). In this work, four RTD models derived from non-ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

A life time in South Africa; being the recollections of the first premier of Natal,

Mode of access: Internet.