Modelling and Analysis of Bivariate Lifetime Data using Reversed Hazard Rates

Department of Statistics, Cochin University of Science and Technology

STUDY OF INFLUENCE OF SAFETY ENGINEERING AND MANAGEMENT PRACTICES IN SELECTED INDUSTRIES IN KERALA

In the twentieth century, as technology grew with it. This resulted in collective efforts and thinking in the direction of controlling work related hazards and accidents. Thus, safety management developed and became an important part of industrial management. While considerable research has been reported on the topic of safety management in industries from various parts of the world, there is scarcity of literature from India. It is logical to think that a clear understanding of the critical safety management practices and their relationships with accident rates and management system certifications would help in the development and implementation of safety management systems. In the first phase of research, a set of six critical safety management practices has been identified based on a thorough review of the prescriptive, practitioner, conceptual and empirical literature. An instrument for measuring the level of practice of these safety conduction a survey using questionnaire in chemical/process industry. The instrument has been empirically validated using Confirmatory Factor Analysis (CFA) approach. As the second step. Predictive validity of safety management practices and the relationship between safety management practices and self-reported accident rates and management system certifications have been investigated using ANOVA. Results of the ANOVA tests show that there is significant difference in the identified safety management practices and the determinants of safety performance have been investigated using Multiple Regression Analysis. The inter-relationships between safety management practices, determinants of safety performance and components of safety performance have been investigated with the help of structural equation modeling. Further investigations into engineering and construction industries reveal that safety climate factors are not stable across industries. However, some factors are found to be common in industries irrespective of the type of industry. This study identifies the critical safety management practices in major accident hazard chemical/process industry from the perspective of employees and the findings empirically support the necessity for obtaining safety specific management system certifications

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.

Consequence modelling,vulnerability assessment and fuzzy fault tree analysis of hazardous storages in an industrial area

The hazards associated with major accident hazard (MAH) industries are fire, explosion and toxic gas releases. Of these, toxic gas release is the worst as it has the potential to cause extensive fatalities. Qualitative and quantitative hazard analyses are essential for the identitication and quantification of the hazards associated with chemical industries. This research work presents the results of a consequence analysis carried out to assess the damage potential of the hazardous material storages in an industrial area of central Kerala, India. A survey carried out in the major accident hazard (MAH) units in the industrial belt revealed that the major hazardous chemicals stored by the various industrial units are ammonia, chlorine, benzene, naphtha, cyclohexane, cyclohexanone and LPG. The damage potential of the above chemicals is assessed using consequence modelling. Modelling of pool fires for naphtha, cyclohexane, cyclohexanone, benzene and ammonia are carried out using TNO model. Vapor cloud explosion (VCE) modelling of LPG, cyclohexane and benzene are carried out using TNT equivalent model. Boiling liquid expanding vapor explosion (BLEVE) modelling of LPG is also carried out. Dispersion modelling of toxic chemicals like chlorine, ammonia and benzene is carried out using the ALOHA air quality model. Threat zones for different hazardous storages are estimated based on the consequence modelling. The distance covered by the threat zone was found to be maximum for chlorine release from a chlor-alkali industry located in the area. The results of consequence modelling are useful for the estimation of individual risk and societal risk in the above industrial area.Vulnerability assessment is carried out using probit functions for toxic, thermal and pressure loads. Individual and societal risks are also estimated at different locations. Mapping of threat zones due to different incident outcome cases from different MAH industries is done with the help of Are GIS.Fault Tree Analysis (FTA) is an established technique for hazard evaluation. This technique has the advantage of being both qualitative and quantitative, if the probabilities and frequencies of the basic events are known. However it is often difficult to estimate precisely the failure probability of the components due to insufficient data or vague characteristics of the basic event. It has been reported that availability of the failure probability data pertaining to local conditions is surprisingly limited in India. This thesis outlines the generation of failure probability values of the basic events that lead to the release of chlorine from the storage and filling facility of a major chlor-alkali industry located in the area using expert elicitation and proven fuzzy logic. Sensitivity analysis has been done to evaluate the percentage contribution of each basic event that could lead to chlorine release. Two dimensional fuzzy fault tree analysis (TDFFTA) has been proposed for balancing the hesitation factor invo1ved in expert elicitation .

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.

Development of Safety and Quality Management System in Shrimp Farming

Shrimp Aquaculture has provided tremendous opportunity for the economic and social upliftment of rural communities in the coastal areas of our country Over a hundred thousand farmers, of whom about 90% belong to the small and marginal category, are engaged in shrimp farming. Penaeus monodon is the most predominant cultured species in India which is mainly exported to highly sophisticated, quality and safety conscious world markets. Food safety has been of concem to humankind since the dawn of history and the concern about food safety resulted in the evolution of a cost effective, food safety assurance method, the Hazard Analysis Critical Control Point (HACCP). Considering the major contribution of cultured Penaeus monodon to the total shrimp production and the economic losses encountered due to disease outbreak and also because traditional methods of quality control and end point inspection cannot guarantee the safety of our cultured seafood products, it is essential that science based preventive approaches like HACCP and Pre requisite Programmes (PRP) be implemented in our shrimp farming operations. PRP is considered as a support system which provides a solid foundation for HACCP. The safety of postlarvae (PL) supplied for brackish water shrimp farming has also become an issue of concern over the past few years. The quality and safety of hatchery produced seeds have been deteriorating and disease outbreaks have become very common in hatcheries. It is in this context that the necessity for following strict quarantine measures with standards and code of practices becomes significant. Though there were a lot of hue and cry on the need for extending the focus of seafood safety assurance from processing and exporting to the pre-harvest and hatchery rearing phases, an experimental move in this direction has been rare or nil. An integrated management system only can assure the effective control of the quality, hygiene and safety related issues. This study therefore aims at designing a safety and quality management system model for implementation in shrimp farming and hatchery operations by linking the concepts of HACCP and PRP.

‘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).

Bivarite burr distributions

The present work is organized into six chapters. Bivariate extension of Burr system is the subject matter of Chapter II. The author proposes to introduce a general structure for the family in two dimensions and present some properties of such a system. Also in Chapter II some new distributions, which are bivariate extension of univariate distributions in Burr (1942) is presented.. In Chapter III, concentrates on characterization problems of different forms of bivariate Burr system. A detailed study of the distributional properties of each member of the Burr system has not been undertaken in literature. With this aim in mind in Chapter IV is discussed with two forms of bivariate Burr III distribution. In Chapter V the author Considers the type XII, type II and type IX distributions. Present work concludes with Chapter VI by pointing out the multivariate extension for Burr system. Also in this chapter the concept of multivariate reversed hazard rates as scalar and vector quantity is introduced.

“Stress Responses of Stinging Catfish Heteropneustes fassilis (Bloch) to Organophosphorus Insecticide Monocrotophos”

Poisoning by pesticides from agricultural fields is a serious water pollution problem and its environmental long-term effect may result in the incidence of poisoning of fish and other aquatic life forms (jyothi and Narayan, 1999). Fishes like Heteropneustesfbssilis and C/arius batrac/nus are especially prone to serious pesticide pollution as their habitat is mostly the agriculture area. Though only few studies are conducted in this area, it can be assessed from the local information that, population of such fish is on the verge of vulnerability due to extensive use of pesticides. The knowledge of sublethal effects of xenobiotic compounds on hematological parameters, enzyme activities and metabolite concentrations is very important to delineate the fish health status and provide a future understanding of ecological impacts. These pesticides act by causing inhibition of cholinesterase enzymes (ChE) by formation of enzyme inhibitor complex (O'Brien, 1976) and damaging the nervous system. These effects may result in metabolic disorders. Associated to cholinesterase activities, a study of other enzymes such as phosphatases and aminotransferases close to intermediary metabolite determination provides a wider view of metabolism. Interest in toxicological aspects has grown in recent years and research is now increasingly focused on mechanistic aspects of oxidative damage and cellular responses in biological system. The term ‘biomarker’ is generally used in a broad sense to include almost any measurement reflecting an interaction between a biological system and a potential hazard, which may be chemical, physical or biological (WHO, 1993). As biomarker stands for immediate responses, they are used as early warning signals of biological effects caused by environmental pollutants. The present work attempts to assess the toxicity of organophosphorus insecticide monocrotophos on the experimental organism selected for this study namely stinging catfish (Heteropneustesfossi/is) (Bloch), and to probe into the stress responses of the organism

An assessment of potential public health risk associated with the extended survival of indicator and pathogenic bacteria in freshwater lake sediments

Microcosm studies were performed to evaluate the survival of Escherichia coli, Salmonella paratyphi and Vibrio parahaemolyticus in water and sediment collected from the freshwater region of Vembanad Lake (9 35◦N 76 25◦E) along the south west coast of India. All three test microorganisms showed significantly (p < 0.01) higher survival in sediment compared to overlying water. The survival in different sediment types with different particle size and organic carbon content revealed that sediment with small particle size and high organic carbon content could enhance their extended survival (p < 0.05). The results indicate that sediments of the Lake could act as a reservoir of pathogenic bacteria and exhibit a potential health hazard from possible resuspension and subsequent ingestion during recreational activities. Therefore, the assessment of bacterial concentration in freshwater Lake sediments used for contact and non contact recreation has of considerable significance for the proper assessment of microbial pollution of the overlying water, and for the management and protection of related health risk at specific recreational sites. Besides, assessment of the bacterial concentration in sediments can be used as a relatively stable indicator of long term mean bacterial concentration in the water column above

Potential Exposure Risk Associated with the High Prevalence and Survival of Indicator and Pathogenic Bacteria in the Sediment of Vembanadu Lake, India

Prevalence of faecal coliform bacteria and the survival of Escherichia coli, Vibrio parahaemolyticus and Salmonella paratyphi were studied in the water and sediment from Vembanadu Lake in the presence and absence of protozoan predators. The density of faecal coliform bacteria ranged between mean MPN value 5080–9000/100 ml in water and 110,000–988,000/1 g in sediment (p <0.01), which was 110 times greater than in overlying water. The laboratory microcosm studies revealed that E. coli, V. parahaemolyticus and S. paratyphi showed significantly higher survival (p <0.05) potential in sediment than in overlying water both in the presence and absence of protozoan predators. The results indicate that Vembanadu Lake sediment constitutes a reservoir of pathogenic bacteria and exhibits potential health hazard from possible resuspension and subsequent ingestion during recreational activities. Therefore, assessment of bacterial concentration in freshwater lake sediments used for contact and non-contact recreation is of considerable significance for the proper assessment of microbial pollution of the overlying water and the management and protection of related health risk at specific recreational sites. In addition, assessment of the bacterial concentration in sediments can be used as a relatively stable indicator of long-term mean bacterial concentration in the water column above.

Some Properties of Weighted Distributions in the Context of Repairable Systems

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables

Characterizations of bivariate models using dynamic Kullback–Leibler discrimination measures

In this paper, the residual Kullback–Leibler discrimination information measure is extended to conditionally specified models. The extension is used to characterize some bivariate distributions. These distributions are also characterized in terms of proportional hazard rate models and weighted distributions. Moreover, we also obtain some bounds for this dynamic discrimination function by using the likelihood ratio order and some preceding results.

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.