Classical and Bayesian Approach in Estimation of Scale Parameter of Inverse Weibull Distribution

In this paper, Inverse Weibull Distribution is considered. The classical Maximum likelihood estimator has been obtained. Bayesian method of estimation has been employed in order to estimate the scale parameter of Inverse Weibull Distribution by using Jeffery’s and Quasi’s prior under three different loss functions. Also these methods are compared by using mean square error with varying sample sizes through simulation study conducted in R software. Keywords: Inverse Weibull Distribution, Jeffrey’s and Quasi’s prior, loss functions and R software

A New Class of Generalized Modified Weibull Distribution with Applications

A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented

Inferential Survival Analysis for Type II Censored Truncated Exponential Topp Leone Exponential Distribution with Application to Engineering Data

This study focuses on estimating the unknown parameters of the truncated exponential Topp-Leon distribution using a type II scheme. We estimate the unknown parameters, survival, and hazard functions using maximum likelihood estimation methods. Additionally, we derive the approximate variance covariance matrix and asymptotic confidence intervals. Furthermore, we compute Bayesian estimates of the unknown parameters under squared error and linear loss functions. To generate samples from the posterior density functions, we use the Metropolies-Hastings algorithm. We demonstrate the effectiveness of the proposed distribution by applying it to two data sets: Monte Carlo simulation and real data set. Our results show that the proposed distribution provides accurate estimates of the unknown parameters and performs well in fitting the data. Our findings also indicate that Bayesian estimation can provide more precise estimates with narrower confidence intervals compared to maximum likelihood estimation method. In summary, the study provides a comprehensive analysis of the estimation of the unknown parameters for the truncated exponential Topp-Leone distribution using a type II scheme. Also, the results demonstrate the potential of this distribution in modeling real data and the usefulness of both maximum likelihood and Bayesian estimation methods in obtaining accurate parameter estimates

Data analysis and simulation for warranties and golf handicaps

In this dissertation, we discuss the application of data analysis and numerical simulation in order to gain insight into problems related to warranty cost management and the effectiveness of the golf handicap system. Despite the commonalities of the approaches, we will discuss these problems in turn. For many moderately high value items with a substantial sales volume (such as automobiles), a warranty is used as an important element of marketing products as a better warranty typically signals higher product quality to customers. Much recent research on modeling and optimization of servicing costs for Non-Renewing Free Replacement Warranties (NR-FRW) assumes that the consumers’ usage profile is known. Such an assumption is unrealistic for many consumer durables. In such cases, it would be pragmatic to assume that the usage rate should be modeled by a probability distribution. This research seeks to model and minimize the expected costs of servicing strategies for NR-FRW; this is accomplished using a numerical technique known as simulated annealing while considering a variety of usage rate distributions. The relationship between the usage rate distribution and product life-length is modeled using the Accelerated Failure Time (AFT) formulation. We use a copula based approach to capture the adverse impact of increasing product usage rate on its time-to-failure. We obtain a unique copula based on the marginal distributions of both the usage rate and the product life-length, which we call the AFT Copula. The underlying dependency of our copula is evaluated using non-parametric measures of association. The Mean Time to First Failure (MTTF) indicates which usage rate distributions most likely correspond to highly reliable products. We found that certain warranty servicing strategies were more cost efficient than other commonly used approaches. We use data analysis techniques on a traction motor data set to study the practicality of our approach. The results obtained from this data are in qualitative agreement with our previous results. The ability of a golfer is measured by a player’s handicap which is an estimate of his/her potential based on previously played games. The handicap system is administered by the United States Golf Association (USGA); it is designed to enable players of differing abilities to compete against each other on an equitable basis. Most previous studies in golf have focused on analyzing golf scores. The goal of this research is to study the effectiveness of the current handicapping system. We use the AT&T Golf Tournament League data set for our study; this data set contains scores and handicaps of golfers from almost 100 different tournaments. In this study, we use data analysis methods including filtering to remove outliers and goodness of fit tests to determine the most appropriate distribution for the golf scores. Because each handicap requires a separate fit, we develop a technique of minimizing the average ranks of the candidate distributions in order to obtain the single best distribution for all handicaps. For this data set, the generalized extreme value distribution is the most appropriate. In order to investigate the effectiveness of the handicap system, we conduct simulations of competitions between golfers with varying handicaps based on the empirical and fitted data for golf scores. These simulations indicate that a player with a lower handicap has an advantage over a player with a higher handicap

Dynamic safety analysis of decommissioning and abandonment of offshore oil and gas installations

The global oil and gas industry have seen an increase in the number of installations moving towards decommissioning. Offshore decommissioning is a complex, challenging and costly activity, making safety one of the major concerns. The decommissioning operation is, therefore, riskier than capital projects, partly due to the uniqueness of every offshore installation, and mainly because these installations were not designed for removal during their development phases. The extent of associated risks is deep and wide due to limited data and incomplete knowledge of the equipment conditions. For this reason, it is important to capture every uncertainty that can be introduced at the operational level, or existing hazards due to the hostile environment, technical difficulties, and the timing of the decommissioning operations. Conventional accident modelling techniques cannot capture the complex interactions among contributing elements. To assess the safety risks, a dynamic safety analysis of the accident is, thus, necessary. In this thesis, a dynamic integrated safety analysis model is proposed and developed to capture both planned and evolving risks during the various stages of decommissioning. First, the failure data are obtained from source-to-source and are processed utilizing Hierarchical Bayesian Analysis. Then, the system failure and potential accident scenarios are built on bowtie model which is mapped into a Bayesian network with advanced relaxation techniques. The Dynamic Integrated Safety Analysis (DISA) allows for the combination of reliability tools to identify safetycritical causals and their evolution into single undesirable failure through the utilisation of source to-source variability, time-dependent prediction, diagnostic, and economic risk assessment to support effective recommendations and decisions-making. The DISA framework is applied to the Elgin platform well abandonment and Brent Alpha jacket structure decommissioning and the results are validated through sensitivity analysis. Through a dynamic-diagnostic and multi-factor regression analysis, the loss values of accident contributory factors are also presented. The study shows that integrating Hierarchical Bayesian Analysis (HBA) and dynamic Bayesian networks (DBN) application to modelling time-variant risks are essential to achieve a well-informed decommissioning decision through the identification of safety critical barriers that could be mitigated against to drive down the cost of remediation.The global oil and gas industry have seen an increase in the number of installations moving towards decommissioning. Offshore decommissioning is a complex, challenging and costly activity, making safety one of the major concerns. The decommissioning operation is, therefore, riskier than capital projects, partly due to the uniqueness of every offshore installation, and mainly because these installations were not designed for removal during their development phases. The extent of associated risks is deep and wide due to limited data and incomplete knowledge of the equipment conditions. For this reason, it is important to capture every uncertainty that can be introduced at the operational level, or existing hazards due to the hostile environment, technical difficulties, and the timing of the decommissioning operations. Conventional accident modelling techniques cannot capture the complex interactions among contributing elements. To assess the safety risks, a dynamic safety analysis of the accident is, thus, necessary. In this thesis, a dynamic integrated safety analysis model is proposed and developed to capture both planned and evolving risks during the various stages of decommissioning. First, the failure data are obtained from source-to-source and are processed utilizing Hierarchical Bayesian Analysis. Then, the system failure and potential accident scenarios are built on bowtie model which is mapped into a Bayesian network with advanced relaxation techniques. The Dynamic Integrated Safety Analysis (DISA) allows for the combination of reliability tools to identify safetycritical causals and their evolution into single undesirable failure through the utilisation of source to-source variability, time-dependent prediction, diagnostic, and economic risk assessment to support effective recommendations and decisions-making. The DISA framework is applied to the Elgin platform well abandonment and Brent Alpha jacket structure decommissioning and the results are validated through sensitivity analysis. Through a dynamic-diagnostic and multi-factor regression analysis, the loss values of accident contributory factors are also presented. The study shows that integrating Hierarchical Bayesian Analysis (HBA) and dynamic Bayesian networks (DBN) application to modelling time-variant risks are essential to achieve a well-informed decommissioning decision through the identification of safety critical barriers that could be mitigated against to drive down the cost of remediation

On the upper truncated Weibull distribution and its reliability implications

10.1016/j.ress.2010.09.004Reliability Engineering and System Safety961194-200RESS