An investigation of estimation performance for a multivariate Poisson-gamma model with parameter dependency

Statistical analysis can be overly reliant on naive assumptions of independence between different data generating processes. This results in having greater uncertainty when estimating underlying characteristics of processes as dependency creates an opportunity to boost sample size by incorporating more data into the analysis. However, this assumes that dependency has been appropriately specified, as mis-specified dependency can provide misleading information from the data. The main aim of this research is to investigate the impact of incorporating dependency into the data analysis. Our motivation for this work is concerned with estimating the reliability of items and as such we have restricted our investigation to study homogeneous Poisson processes (HPP), which can be used to model the rate of occurrence of events such as failures. In an HPP, dependency between rates can occur for numerous reasons. Whether it is similarity in mechanical designs, failure occurrence due to a common management culture or comparable failure count across machines for same failure modes. Multiple types of dependencies are considered. Dependencies can take different forms, such as simple linear dependency measured through the Pearson correlation, rank dependencies which capture non-linear dependencies and tail dependencies where the strength of the dependency may be stronger in extreme events as compared to more moderate one. The estimation of the measure of dependency between correlated processes can be challenging. We develop the research grounded in a Bayes or empirical Bayes inferential framework, where uncertainty in the actual rate of occurrence of a process is modelled with a prior probability distribution. We consider prior distributions to belong to the Gamma distribution given its flexibility and mathematical association with the Poisson process. For dependency modelling between processes we consider copulas which are a convenient and flexible way of capturing a variety of different dependency characteristics between distributions. We use a multivariate Poisson – Gamma probability model. The Poisson process captures aleatory uncertainty, the inherent variability in the data. Whereas the Gamma prior describes the epistemic uncertainty. By pooling processes with correlated underlying mean rate we are able to incorporate data from these processes into the inferential process and reduce the estimation error. There are three key research themes investigated in this thesis. First, to investigate the value in reducing estimation error by incorporating dependency within the analysis via theoretical analysis and simulation experiments. We show that correctly accounting for dependency can significantly reduce the estimation error. The findings should inform analysts a priori as to whether it is worth pursuing a more complex analysis for which the dependency parameter needs to be elicited. Second, to examine the consequences of mis-specifying the degree and form of dependency through controlled simulation experiments. We show the relative robustness of different ways of modelling the dependency using copula and Bayesian methods. The findings should inform analysts about the sensitivity of modelling choices. Third, to show how we can operationalise different methods for representing dependency through an industry case study. We show the consequences for a simple decision problem associated with the provision of spare parts to maintain operation of the industry process when depenency between event rates of the machines is appropriately modelled rather than being treated as independent processes.Statistical analysis can be overly reliant on naive assumptions of independence between different data generating processes. This results in having greater uncertainty when estimating underlying characteristics of processes as dependency creates an opportunity to boost sample size by incorporating more data into the analysis. However, this assumes that dependency has been appropriately specified, as mis-specified dependency can provide misleading information from the data. The main aim of this research is to investigate the impact of incorporating dependency into the data analysis. Our motivation for this work is concerned with estimating the reliability of items and as such we have restricted our investigation to study homogeneous Poisson processes (HPP), which can be used to model the rate of occurrence of events such as failures. In an HPP, dependency between rates can occur for numerous reasons. Whether it is similarity in mechanical designs, failure occurrence due to a common management culture or comparable failure count across machines for same failure modes. Multiple types of dependencies are considered. Dependencies can take different forms, such as simple linear dependency measured through the Pearson correlation, rank dependencies which capture non-linear dependencies and tail dependencies where the strength of the dependency may be stronger in extreme events as compared to more moderate one. The estimation of the measure of dependency between correlated processes can be challenging. We develop the research grounded in a Bayes or empirical Bayes inferential framework, where uncertainty in the actual rate of occurrence of a process is modelled with a prior probability distribution. We consider prior distributions to belong to the Gamma distribution given its flexibility and mathematical association with the Poisson process. For dependency modelling between processes we consider copulas which are a convenient and flexible way of capturing a variety of different dependency characteristics between distributions. We use a multivariate Poisson – Gamma probability model. The Poisson process captures aleatory uncertainty, the inherent variability in the data. Whereas the Gamma prior describes the epistemic uncertainty. By pooling processes with correlated underlying mean rate we are able to incorporate data from these processes into the inferential process and reduce the estimation error. There are three key research themes investigated in this thesis. First, to investigate the value in reducing estimation error by incorporating dependency within the analysis via theoretical analysis and simulation experiments. We show that correctly accounting for dependency can significantly reduce the estimation error. The findings should inform analysts a priori as to whether it is worth pursuing a more complex analysis for which the dependency parameter needs to be elicited. Second, to examine the consequences of mis-specifying the degree and form of dependency through controlled simulation experiments. We show the relative robustness of different ways of modelling the dependency using copula and Bayesian methods. The findings should inform analysts about the sensitivity of modelling choices. Third, to show how we can operationalise different methods for representing dependency through an industry case study. We show the consequences for a simple decision problem associated with the provision of spare parts to maintain operation of the industry process when depenency between event rates of the machines is appropriately modelled rather than being treated as independent processes

A systematic review of software development cost estimation studies

This paper aims to provide a basis for the improvement of software estimation research through a systematic review of previous work. The review identifies 304 software cost estimation papers in 76 journals and classifies the papers according to research topic, estimation approach, research approach, study context and data set. A web-based library of these cost estimation papers is provided to ease the identification of relevant estimation research results. The review results combined with other knowledge provide support for recommendations for future software cost estimation research, including: 1) Increase the breadth of the search for relevant studies, 2) Search manually for relevant papers within a carefully selected set of journals when completeness is essential, 3) Conduct more studies on estimation methods commonly used by the software industry, and, 4) Increase the awareness of how properties of the data sets impact the results when evaluating estimation methods

Estimating software project effort using analogies

Accurate project effort prediction is an important goal for the software engineering community. To date most work has focused upon building algorithmic models of effort, for example COCOMO. These can be calibrated to local environments. We describe an alternative approach to estimation based upon the use of analogies. The underlying principle is to characterise projects in terms of features (for example, the number of interfaces, the development method or the size of the functional requirements document). Completed projects are stored and then the problem becomes one of finding the most similar projects to the one for which a prediction is required. Similarity is defined as Euclidean distance in n-dimensional space where n is the number of project features. Each dimension is standardised so all dimensions have equal weight. The known effort values of the nearest neighbours to the new project are then used as the basis for the prediction. The process is automated using a PC based tool known as ANGEL. The method is validated on nine different industrial datasets (a total of 275 projects) and in all cases analogy outperforms algorithmic models based upon stepwise regression. From this work we argue that estimation by analogy is a viable technique that, at the very least, can be used by project managers to complement current estimation techniques

Intelligent systems in manufacturing: current developments and future prospects

Global competition and rapidly changing customer requirements are demanding increasing changes in manufacturing environments. Enterprises are required to constantly redesign their products and continuously reconfigure their manufacturing systems. Traditional approaches to manufacturing systems do not fully satisfy this new situation. Many authors have proposed that artificial intelligence will bring the flexibility and efficiency needed by manufacturing systems. This paper is a review of artificial intelligence techniques used in manufacturing systems. The paper first defines the components of a simplified intelligent manufacturing systems (IMS), the different Artificial Intelligence (AI) techniques to be considered and then shows how these AI techniques are used for the components of IMS

Risk Assessment of a Wind Turbine: A New FMECA-Based Tool With RPN Threshold Estimation

A wind turbine is a complex system used to convert the kinetic energy of the wind into electrical energy. During the turbine design phase, a risk assessment is mandatory to reduce the machine downtime and the Operation & Maintenance cost and to ensure service continuity. This paper proposes a procedure based on Failure Modes, Effects, and Criticality Analysis to take into account every possible criticality that could lead to a turbine shutdown. Currently, a standard procedure to be applied for evaluation of the risk priority number threshold is still not available. Trying to fill this need, this paper proposes a new approach for the Risk Priority Number (RPN) prioritization based on a statistical analysis and compares the proposed method with the only three quantitative prioritization techniques found in literature. The proposed procedure was applied to the electrical and electronic components included in a Spanish 2 MW on-shore wind turbine

Multi-criteria decision making support tools for maintenance of marine machinery systems

PhD ThesisFor ship systems to remain reliable and safe they must be effectively maintained through a sound maintenance management system. The three major elements of maintenance management systems are; risk assessment, maintenance strategy selection and maintenance task interval determination. The implementation of these elements will generally determine the level of ship system safety and reliability. Reliability Centred Maintenance (RCM) is one method that can be used to optimise maintenance management systems. However the tools used within the framework of the RCM methodology have limitations which may compromise the efficiency of RCM in achieving the desired results. This research presents the development of tools to support the RCM methodology and improve its effectiveness in marine maintenance system applications. Each of the three elements of the maintenance management system has been considered in turn. With regard to risk assessment, two Multi-Criteria Decision Making techniques (MCDM); Vlsekriterijumska Optimizacija Ikompromisno Resenje, meaning: Multi-criteria Optimization and Compromise Solution (VIKOR) and Compromise Programming (CP) have been integrated into Failure Mode and Effects Analysis (FMEA) along with a novel averaging technique which allows the use of incomplete or imprecise failure data. Three hybrid MCDM techniques have then been compared for maintenance strategy selection; an integrated Delphi-Analytical Hierarchy Process (AHP) methodology, an integrated Delphi-AHP-PROMETHEE (Preference Ranking Organisation METHod for Enrichment Evaluation) methodology and an integrated Delphi-AHP-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) methodology. Maintenance task interval determination has been implemented using a MCDM framework integrating a delay time model to determine the optimum inspection interval and using the age replacement model for the scheduled replacement tasks. A case study based on a marine Diesel engine has been developed with input from experts in the field to demonstrate the effectiveness of the proposed methodologies.Tertiary Education Trust Fund (TETFUND), a scholarship body of the Federal Republic of Nigeria for providing the fund for this research. My gratitude also goes to Federal University of Petroleum Resource, Effurun, Nigeria for giving me the opportunity to be a beneficiary of the scholarship

An Expert Based Methodology for Cost Oriented Analysis of Machine Tool Reliability

Abstract: This paper proposes an improved methodology for machine tool reliability analysis. The overall objective of the proposed methodology is to provide the machine tool manufacturers with the approach that will help them in making cost driven decisions while improving the performance of their machines in the field. The methodology consists of three parts viz., modified fault tree diagram, simulation based data analysis and cost based Failure Modes and Effects Analysis (FMEA). Modified fault tree diagram found useful in providing better insight into the failures and their impact. The simulation based approach helps in obtaining time to failure distribution parameters for each failure events using expert's judgements. The effect of uncertainty in the experts' judgements is also quantified in terms of 90 per cent confidence interval values of the parameters. Finally, the cost based FMEA proposed in this paper will help the manufacturer in identifying the critical failure events based on actual cost of failures to the users. The methodology is illustrated with the help of an example of a CNC grinding machine