‘Reliability Concepts in Quantile-based Analysis of Lifetime Data

Reliability analysis is a well established branch of statistics that deals with the statistical study of different aspects of lifetimes of a system of components. As we pointed out earlier that major part of the theory and applications in connection with reliability analysis were discussed based on the measures in terms of distribution function. In the beginning chapters of the thesis, we have described some attractive features of quantile functions and the relevance of its use in reliability analysis. Motivated by the works of Parzen (1979), Freimer et al. (1988) and Gilchrist (2000), who indicated the scope of quantile functions in reliability analysis and as a follow up of the systematic study in this connection by Nair and Sankaran (2009), in the present work we tried to extend their ideas to develop necessary theoretical framework for lifetime data analysis. In Chapter 1, we have given the relevance and scope of the study and a brief outline of the work we have carried out. Chapter 2 of this thesis is devoted to the presentation of various concepts and their brief reviews, which were useful for the discussions in the subsequent chapters .In the introduction of Chapter 4, we have pointed out the role of ageing concepts in reliability analysis and in identifying life distributions .In Chapter 6, we have studied the first two L-moments of residual life and their relevance in various applications of reliability analysis. We have shown that the first L-moment of residual function is equivalent to the vitality function, which have been widely discussed in the literature .In Chapter 7, we have defined percentile residual life in reversed time (RPRL) and derived its relationship with reversed hazard rate (RHR). We have discussed the characterization problem of RPRL and demonstrated with an example that the RPRL for given does not determine the distribution uniquely

Nonparametric Estimation of Survivor Function in Bivariate Competing Risk Models’

So far, in the bivariate set up, the analysis of lifetime (failure time) data with multiple causes of failure is done by treating each cause of failure separately. with failures from other causes considered as independent censoring. This approach is unrealistic in many situations. For example, in the analysis of mortality data on married couples one would be interested to compare the hazards for the same cause of death as well as to check whether death due to one cause is more important for the partners’ risk of death from other causes. In reliability analysis. one often has systems with more than one component and many systems. subsystems and components have more than one cause of failure. Design of high-reliability systems generally requires that the individual system components have extremely high reliability even after long periods of time. Knowledge of the failure behaviour of a component can lead to savings in its cost of production and maintenance and. in some cases, to the preservation of human life. For the purpose of improving reliability. it is necessary to identify the cause of failure down to the component level. By treating each cause of failure separately with failures from other causes considered as independent censoring, the analysis of lifetime data would be incomplete. Motivated by this. we introduce a new approach for the analysis of bivariate competing risk data using the bivariate vector hazard rate of Johnson and Kotz (1975).

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Modelling and Analysis of Bivariate Lifetime Data using Reversed Hazard Rates

Department of Statistics, Cochin University of Science and Technology

Theory of Breaking of a Potyrner Molecule under Tension

The thesis presents the dynamics of a polymer chain under tension. It includes existing theories of polymer fracture, important theories of reaction rates, the rate using multidimensional transition state theory and apply it to the case of polyethylene etc. The main findings of the study are; the life time of the bond is somewhat sensitive to the potential lead to rather different answers, for a given potential a rough estimate of the rate can be obtained by a simples approximation that considers the dynamics of only the bond that breaks and neglects the coupling to neighboring bonds. Dynamics of neighboring bonds would decrease the rate, but usually not more than by one order of magnitude, for the breaking of polyethylene, quantum effects are important only for temperatures below 150K, the lifetime strongly depends on the strain and as the strain varies over a narrow range, the life varies rapidly from 105 seconds to 10_5 seconds, if we change one unit of the polymer by a foreign atom, say by one sulphure atom, in the main chain itself, by a weaker bond, the rate is found to increase by orders of magnitude etc.

A Study on the Reversed Lack of Memory Property and its Generalizations

In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ”addition”. In particular an associative, binary operator ” * ” is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

Excitation wavelength dependence of energy transfer in dye mixture doped polymer optical fibre preforms

Dependence of energy transfer parameters on excitation wavelength has been investigated in poly (methyl methacrylate) (PMMA) optical fibre preforms doped with C 540:Rh B dye mixture by studying the fluorescence intensity and the lifetime variations. A fluorescence spectrophotometer was used to record the excitation spectra of the samples for the emission wavelengths 495 and 580 nm. The fluorescence emission from the polymer rods was studied at four specific excitation wavelengths viz; 445, 465, 488 and 532 nm. The fluorescence lifetime of the donor molecule was experimentally measured in polymer matrix by time correlated single photon counting technique. The energy transfer rate constants and transfer efficiencies were calculated and their dependence on the acceptor concentration was analysed for three excitation wavelengths. It was found that any change in the excitation wavelength leads to significant variations in the quenching characteristics, which in turn affect the calculated energy transfer parameters.

Effect of Improving Energy Efficiency on System Reliability

In the present scenario of energy demand overtaking energy supply top priority is given for energy conservation programs and policies. Most of the process plants are operated on continuous basis and consumes large quantities of energy. Efficient management of process system can lead to energy savings, improved process efficiency, lesser operating and maintenance cost, and greater environmental safety. Reliability and maintainability of the system are usually considered at the design stage and is dependent on the system configuration. However, with the growing need for energy conservation, most of the existing process systems are either modified or are in a state of modification with a view for improving energy efficiency. Often these modifications result in a change in system configuration there by affecting the system reliability. It is important that system modifications for improving energy efficiency should not be at the cost of reliability. Any new proposal for improving the energy efficiency of the process or equipments should prove itself to be economically feasible for gaining acceptance for implementation. In order to arrive at the economic feasibility of the new proposal, the general trend is to compare the benefits that can be derived over the lifetime as well as the operating and maintenance costs with the investment to be made. Quite often it happens that the reliability aspects (or loss due to unavailability) are not taken into consideration. Plant availability is a critical factor for the economic performance evaluation of any process plant.The focus of the present work is to study the effect of system modification for improving energy efficiency on system reliability. A generalized model for the valuation of process system incorporating reliability is developed, which is used as a tool for the analysis. It can provide an awareness of the potential performance improvements of the process system and can be used to arrive at the change in process system value resulting from system modification. The model also arrives at the pay back of the modified system by taking reliability aspects also into consideration. It is also used to study the effect of various operating parameters on system value. The concept of breakeven availability is introduced and an algorithm for allocation of component reliabilities of the modified process system based on the breakeven system availability is also developed. The model was applied to various industrial situations.

Synthesis and Photochemistry of a few Olefin appended Dibenzobarrelenes and Bisdibenzobarrelenes

The thesis entitled: ‘Synthesis and Photochemistry of a few Olefin appended Dibenzobarrelenes and Bisdibenzobarrelenes’ is divided into 5 chapters.In Chapter 1, the fundamental concepts of Diels-Alder reaction, di-r:methane rearrangement and energy transfer process in organic photochemistry is discussed.Chapter 2 presents the synthesis of 9-olefin appended anthracenes and bisanthracenes. The target of synthesising various bridgehead olefin appended dibenzobarrelenes and some novel bisdibenzobarrelenes, led us to the synthesis of the appropriate alkenylanthracenes and bisanthracenes as precursor molecules. Diels-Alder reaction was the synthetic tool for the preparation of the target olefin appended dibenzobarrelenes and bisdibenzobarrelenes. This chapter attempts to throw light on our endeavours in synthesising the various 9-alkenylanthracenes and bisanthracenes.Chapter 3 deals with the synthesis of olefin appended dibenzobarrelenes and bisdibenzobarrelenes. Ever since the discovery of di-It-methane rearrangement dibenzobarrelenes, tailored with dijferent substituents at various positions have always been a tool to photochemists in unravelling the mechanisms of light induced reactions. Our intention of analysing the role of a It-moiety at the bridgehead position of the dibenzobarrelene, was synthetically envisaged via the Diels-Alder reaction. Bisdibenzobarrelenes were synthesised through tandem Diels-Alder reaction. Various alkenylanthracenes and bisanthracenes were employed as dienes and the dienophiles used were dimethyl acetylenedicarboxylate and dibenzoylacetylene. In this chapter, we report our venture in synthesising the various olefin appended dibenzobarrelenes and bisdibenzobarrelenes. Chapter 4 describes the preliminary time-resolved fluorescence studies of some olefin appended dibenzobarrelenes and bisdibenzobarrelenes.To understand the primary and secondary physicochemical processes in a photochemical reaction it is necessary to characterise the excited states and the transient intermediates during their short lifetime. A number of methods developed on the basis of the physical properties of the transient species are available for their detection. Time-correlated single-photon counting technique has been utilised in the present study of the excited states of olefin appended dibenzobarrelenes and bisdibenzobarrelenes. To understand the primary and secondary physicochemical processes in a photochemical reaction it is necessary to characterise the excited states and the transient intermediates during their short lifetime. A number of methods developed on the basis of the physical properties of the transient species are available for their detection. Time-correlated single-photon counting technique has been utilised in the present study of the excited states of olefin appended dibenzobarrelenes and bisdibenzobarrelenes.Chapter 5 portrays the photochemistry of olefin appended dibenzobarrelenes and bisdibenzobarrelenes. Dibenzocyclooctatetraene and dibenzosemibullvalene are the photoproducts obtained respectively through the singlet excited state and the triplet excited state of dibenzobarrelenes. Chemical literature shows evidences of the photoreactivity of dibenzobarrelenes generating both the singlet and triplet mediated photoproducts, in a single photoreaction. Our research target in synthesising various bridgehead olefin appended dibenzobarrelenes and bisdibenzobarrelenes, was based on the perception that olefins are eflicient triplet quenchers, thereby quenching intramolecularly the triplet excited state of the barrelenes. A It-moiety at the bridgehead position of the dibenzobarrelene, creates a tetra tr-methane system, which similar to a 6li—7l' or tri-tr-methane systems, could be the fertile ground for interesting photochemical rearrangements. Our attempts in deciphering the photochemistry of the olefin appended dibenzobarrelenes and bisdibenzobarrelenes is the substance of this chapter.

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

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.

‘Modeling and Analysis of Competing Risks Data’

there has been much research on analyzing various forms of competing risks data. Nevertheless, there are several occasions in survival studies, where the existing models and methodologies are inadequate for the analysis competing risks data. ldentifiabilty problem and various types of and censoring induce more complications in the analysis of competing risks data than in classical survival analysis. Parametric models are not adequate for the analysis of competing risks data since the assumptions about the underlying lifetime distributions may not hold well. Motivated by this, in the present study. we develop some new inference procedures, which are completely distribution free for the analysis of competing risks data.

Evaluation of the Power Consumption of Routing Protocols for Wireless Sensor Networks

Sensor networks are one of the fastest growing areas in broad of a packet is in transit at any one time. In GBR, each node in the network can look at itsneighbors wireless ad hoc networking (? Eld. A sensor node, typically'hop count (depth) and use this to decide which node to forward contains signal-processing circuits, micro-controllers and a the packet on to. If the nodes' power level drops below a wireless transmitter/receiver antenna. Energy saving is one certain level it will increase the depth to discourage trafiE of the critical issue forfor sensor networks since most sensors are equipped with non-rechargeable batteries that have limited lifetime.

Evaluation of the Power Consumption of Routing Protocols for Wireless Sensor Networks

Sensor networks are one of the fastest growing areas in broadwireless ad hoc networking (?Eld. A sensor node, typically'contains signal-processing circuits, micro-controllers and awireless transmitter/receiver antenna. Energy saving is oneof the critical issue for sensor networks since most sensorsare equipped with non-rechargeable batteries that have limited lifetime.In thiswork, four routing protocols for wireless sensor networks vizFlooding, Gossiping, GBR and LEACH have been simulated using Tiny OS and their power consumption is studied usingcaorwreiredTOoSuStIuMs.ingAMirceaal2izMaotitoens.of these protocols has been carried out using mica 2 motes