In this paper, we suggest employing the exponential ratio estimator to estimate the mean of the study variable using a two-phase sample strategy with two modified auxiliary variables. Several researchers discussed the properties of the estimators they proposed and discovered that the estimators in their studies were relatively efficient. The estimators previously studied are listed chronologically in the appendix to this paper. In two phase sampling, the estimator's mean square errors and relative efficiencies are calculated using auxiliary variable information. To assess the properties of our proposed estimator, we noticed that it has a lower mean square error (MSE) than the classical ratio estimator and some other exponential ratio estimators. The estimator is more useful than other estimators in solving real-world issues, notably in engineering, environmental science, management, and biological sciences. The proposed estimator has been applied to real-world data sets such as BRICS, Son's Head Measurement, Number of Hospital Beds, Sale Price of Residence, Ambient Pressure (AP), and Heating Load. In survey research, our suggested estimator has also been demonstrated to be more effective.

In this study, we propose the combination of exponential and ln ratio type estimator to estimate the mean of Y (Study Variable) by incorporating two auxiliary variables in two phase sampling scheme. Under simple random sampling without replacement, the illustration for mean square error and mathematical comparisons are presented. Several approaches are available in literature to estimate the study variable by using information on the variable of interest. The performance of our proposed estimator is compared with other ratio type estimators theoretically and empirically. It is observed that ratio and exponential ratio estimators considered by various researchers and usual unbiased estimator is less efficient than our proposed estimator. An efficiency comparison is also given using five data sets and simulation studies for checking the merits of our proposed estimator and outcomes are sound and moderately illuminating in comparison to different estimators.

A completely regular topological space X is called a P-space if every zero-set in X is open. An intermediate ring is a ring A(X) of real-valued continuous functions on X containing all the bounded continuous functions. In this paper, we find new characterizations of P-spaces X in terms of properties of correspondences between ideals in A(X) and z-filters on X. We also show that some characterizations of P-spaces that are described in terms of properties of C(X) actually characterize C(X) among intermediate rings on X.

Globally, using the road is one of the most risky activities that most people undertake.  In the world of government and commerce, there are many societal, business, legal and  cost reasons for organisations to focus on road safety. With this societal and  organisational context in mind, the article sets out the business case for work-related  road safety. It aims to assist policy makers understand the importance of work-related  travel and of support managers (such as in fleet, transport or health u0026 safety) seeking  board authorisation to implement a sustainable long term work-related road safety policy  with supporting interventions. It focuses on why work-related road safety is important,  based on the authors company research and experiences il1 a number of organisations  over the past twenty years. This article also has links to other useful business case  documents, in the Appendix.

Safety is a key issue for transport policy globally. Work-related travel has a significant impact on both road and occupational safety. Implementing a long term, sustainable work-related road safety program is a complex process requiring careful management decision making. Despite an increasing interest in research, policy and practice, there remain few published studies of organisations that have effectively managed their travel risks. The aim of this paper is to review and evaluate the outcomes of a driver risk assessment, monitoring and improvement program undertaken by British Telecommunications throughout its UK operations. The material presented is based on a detailed case study of the policies, procedures and performance monitoring implemented to manage the road safety risks of approximately 95,000 workers over more than 10 years. From a review of processes and outcomes, a good practice data-led systems-based approach is identified, focusing on occupational health and safety principles, the Haddon Matrix, risk assessment and evaluation. The case, which has seen a halving of the company׳s collision rate and costs, provides access to large insurance claims and other data sets over a long term period. A number of potential lessons for researchers, policy makers and practitioners are identified relating to issues such as data, management, tools, frameworks and further opportunities to focus on improving both road and worker safety.

Many studies have shown that driver attitude and behaviour are important determinants of the likelihood of collision involvement. Knowledge of the Rules of the Road and the perception of hazards are also associated with collision involvement. The aim of this paper is to review the practical application of an online fleet driver assessment program to help identify, target and reduce occupational road safety risks. A large and unique data set collected from online assessment of drivers employed in a UK telecommunications organisation is analyzed. Data was also collected on driver demographics and their driving and collision history. Analysis of the data revealed that attitude, behaviour, knowledge and hazard perception are highly correlated with self-reported collisions. The influence of these variables on collision involvement was assessed using a Poisson regression model. Both attitude and behaviour scores exhibit a statistically significant association with collision involvement, along with other variables such as mileage driven, driver age and personality. The findings lend support to the need to create a safety culture in which driver assessment and improvement is the norm, as well as reducing exposure to risk wherever possible through better ways of working and travelling.

As a component of its National Road Safety Partnership Program draft strategy, the Australian National Transport Commission (NTC) recently consulted with stakeholders regarding the future for Corporate Road Safety in Australia, focusing on the major role that industry can play in improving road safety in Australia. This paper draws on and extends our submission, which can be seen in full on the NTC website. Contemporary road safety focuses on key public safety factors, yet globally few governments have explored road safety from an occupational perspective. Road travel is the biggest traumatic cause of worker fatalities in most westernised countries, and an increasingly recognised injury and fatality burden in many others. Corporate road safety is poorly addressed in existing Australian and other international regulatory regimes, with the work-road injury burden frequently falling between work and road safety policy and regulatory practice. In contrast, Work Health and Safety (WHS) regimes are well established in many countries. It is proposed that these existing WHS systems could be effectively applied to work-road safety to provide a framework for co-ordinated policy and cost-effective strategies to reduce the road toll. Based on experience and a systematic literature analysis, gaps were identified in existing policy and practice. Evidence-based recommendations were then developed to focus on reducing the road toll and related business costs. These include the implementation of strategic corporate road safety systems underpinned by existing WHS data, systems, strategies and policies.

Internationally, few governments have explored road-safety from an occupational perspective, although road-use is the biggest traumatic cause of worker fatalities in most westernised countries, and an increasing risk in many others. Work-driving policy is poorly addressed in existing Workplace Health and Safety (WHS) practice. Work-road risk management frequently falls between WHS and work-road safety policy. Considerable opportunity exists to enhance road safety at work if existing mature WHS regimes could be effectively applied by organisations to work-road safety. Workplace road-safety is gaining recognition in many countries as a viable strategic focus to address a growing road toll. Most existing initiatives are applied on an individual employer basis rather than systematically across industries. The potential workplace integration of road-safety and WHS strategies presents a unique opportunity for significant reductions in both injury-burden and damage costs for organisations, nationally and internationally, whilst also reducing the road toll.

Since this paper was first presented at the American Society of Safety Engineers Safety 2012 Conference in Denver on June 3-6, 2012 the Pfizer global driver safety program has continued to develop, and has been further rolled out around the globe - including Australasia. Pfizer was also recognised at the 2012 Brake Fleet Safety Forum Annual road safety awards for the global and on-going nature of its program and achieving beneficial road safety outcomes in over 20 countries around the world. Pfizer has also worked tirelessly to benchmark and share good practice with others through the Fleet Safety Benchmarking project (www.fleetsafetybenchmarking.net).

Motor vehicle crashes are the leading cause of work-related fatalities in most high-income regions, including the European Union (EU). This research assesses transpositions of relevant EU directives by the United Kingdom (UK), France, and Sweden. The market-driven UK uses a business-led model to manage occupational road risk. Although technically correct, its transpositions were tempered by earlier legislation requiring employers to ensure a safe workplace lso far as is reasonably practicable.r French policymaking is dominated by government, with engagement of the lsocial partnersr (labor and industry). Transposition delays stemmed from domestic debates on the 35-hour workweek, existing collective agreements, and long-established structures of French codes of law. Swedish policymaking is consensual and corporatist, with road safety policy strongly influenced by the systems-based Vision Zero model. Transposition rarely required major changes to Swedish law. The main conclusion is that although member-state transpositions were generally technically accurate, they were influenced by domestic politics, institutional arrangements, and policy beliefs.

Fleet, work-related or occupational road safety has the potential to make a major contribution to reducing both human harm and asset damage. To date, however, there would appear to be a dearth of well researched and evaluated case studies in the public domain in this area.This paper provides an on-going, documented, real-world case study of work-related road safety within an Australian company that has sought to manage, monitor and improve its road safety performance over the last 5 years through a range of proactive, fleet manager, insurance and risk-led initiatives.Roche Australia has successfully implemented a Company Motor Vehicle Safety Program with support from its fleet insurers and risk management advisors. Four key initiatives are set out covering: (1) Driver risk assessment, monitoring and improvement. (2) Policy development and communications. (3) Process and outcomes evaluation. (4) Continuous review and refinement of policies, processes, programs and future developments.The program has led to a range of process and performance-based outcomes. Typical barriers to success in work-related road safety have been identified and overcome. Almost 100% risk assessment and improvement process compliance by drivers has been achieved. A predictive relationship between risk assessment outcomes and collision history has been identified. Reductions in insurance claims, collision costs and claims ratio have been sustained. A detailed project plan is in place to continue the program for the next 3 years.The paper concludes that with effective management, a well developed work-related road safety program can result in performance improvements within the initiating organisation. Several limitations in the case study methodology, as well as areas for further work and lessons for policy makers, researchers and practitioners are also identified. (C), 2011 Elsevier Ltd. All rights reserved.

Implementing a long term, sustainable work related road safety program throughout a whole supply chain from door to door, rather than just gate to gate requires a constant balancing act between the needs of business, the economy and the environment. Despite an increasing interest in research, policy and practice in the area of work-related road safety, there remains few published case studies of organisations that have effectively managed this risk. The aim of this paper is to directly address this gap, by reviewing and evaluating a risk led approach to occupational driver management, risk assessment, monitoring and improvement undertaken by BT throughout its UK, and increasingly global, supply chain. The paper is based on a detailed chronological case study of the policies, processes and procedures implemented to manage the road safety risks of 100,000 BT workers over an 8 year period. From a review of processes and outcomes data available, a good practice model and lessons for occupational road safety researchers, policy makers and practitioners are identified – including a halving of the collision rate and costs, and significant environmental improvements thorough improved business practices, more sustainable ways of working and changing manager and driver behaviours.

It has been estimated that 25% of collisions on UK roads and 30% of US occupational fatalities involve someone driving for work. Across the EU the figure is worse with 34% of work fatalities involving road traffic or transport accidents. These collisions are not confined to large trucks but also include many smaller vehicles where driving is secondary to the employees' main task. In general employees driving for work have an increased risk of involvement in a fatal or serious road traffic accident. Increasingly fleet management has focused on safety and the behaviour of drivers rather than asset management and cost control. Studies have shown that changing the behaviour of both drivers and the rest of the organisation can make a large improvement in safety. This paper reports on a study of insurance claims made by employees driving for a large UK company. The company uses a fleet of approximately 40,000 vehicles and has made significant progress in applying a range of strategies to driver safety. As part of the research, claims were clustered using latent class analysis based on crash and driver characteristics. A multinomial logit model was then used to predict crash severity within each class thus identifying previously obscured driver risk dependencies. It is concluded that specific interventions could be aimed at the risks faced by these drivers and that this approach may aid the company in continuing to improve its safety record.

We introduce the Möbius polynomial M_n(x) = ∑_d|nμ( n/d) x^d, which gives the number of aperiodic bracelets of length n with x possible types of gems, and therefore satisfies M_n(x) ≡ 0 (mod n) for all x ∈ℤ. We derive some key properties, analyze graphs in the complex plane, and then apply Möbius polynomials combinatorially to juggling patterns, irreducible polynomials over finite fields, and Euler's totient theorem.

This paper provides a background to Brake and its initiatives, including the Fleet Safety Forum. It explores the many financial as well as safety benefits of investing in road risk management measures relating to systems, drivers and vehicles, as realised by members of the international Fleet Safety Forum, coordinated by Brake. It also explores how, at the heart of the efforts to achieve these financial as well as safety benefits, is a social and cultural investment and change by companies in road risk management and the wider societal benefits of putting safety first. Finally, it looks at the results of Brakers initiatives in fleet safety, and more widely in road safety, alongside successful initiatives undertaken by organisations in addressing their road risk.

The Haddon Matrix was developed in the 1960s road safety arena, and has since been used in many public health settings. The literature and two specific case studies are reviewed to describe the background to the Haddon Matrix, identify how it has been critiqued and developed over time and practical applications in the work-related road safety context. Haddon’s original focus on the road, vehicle and driver has been extended and applied to include organisational safety culture, journey management and wider issues in society that affect occupational drivers and the communities in which they work. The paper shows that the Haddon Matrix has been applied in many projects and contexts. Practical work-related road safety applications include providing a comprehensive systems-based safety management framework to inform strategy. It has also been used to structure the review or gap analysis of current programs and processes, identify and develop prevention measures and as a tool for effective post-event investigations.

Work related road traffic fatalities are the largest cause of work fatalities in the UK. It is estimated that 25% of UK road accidents involve someone driving for work. This risk profile makes fleet safety an important topic for study as it can have a significant impact on the overall road toll, and on worker safety. Although many regulations relate to the operation of large trucks and buses there are fewer special regulations for those driving for work in other contexts. Fleet risk management has traditionally focused on cost control rather than employee and public safety although this has been changing. Studies have shown that changing behaviors in both drivers and the rest of the organization can make a large improvement in outcomes. This study has unique access to the detailed insurance claims data from a large UK telecoms fleet of approximately 40,000 vehicles since 2001 and information on interventions applied to manage this risk. A range of interventions have been applied to claim reduction which are based on published work. Interventions include driver training, building safety into management performance metrics and risk assessments yet it is unclear as to which intervention shows most or any impact on safety outcomes. This study outlines these actions and quantifies the effectiveness of driver training using a statistical modeling approach. The complex data represents a wide range of vehicle types (e.g. trucks and white vans and personal cars) which could be used for work related journeys, commuting or pleasure. Performance is shown to be statistically significant reduction in collisions after exposure to training. Although data consistency issues have obscured the investigation, this study has shown that management strategies and the safety culture are worthy investments

SummaryConsider a system of n players in which each initially starts on a different team. At each time step, we select an individual winner and an individual loser randomly and the loser joins the winner's team. The resulting Markov chain and stochastic matrix clearly have one absorbing state, in which all players are on the same team, but the combinatorics along the way are surprisingly elegant. The expected number of time steps until each team is eliminated is a ratio of binomial coefficients. When a team is eliminated, the probabilities that the players are configured in various partitions of n into t teams are given by multinomial coefficients. The expected value of the time to absorbtion is (n - 1)2 steps. The results depend on elementary combinatorics, linear algebra, and the theory of Markov chains.

Since the formation of the coalition government in the UK there has been increasing focus on, and debate about, cuts in the road safety budget. Such cuts will have many knock-on effects for road safety, including the work-related or fleet sector. This means that it is increasingly important for all sectors of the fleet industry, and its suppliers, to fully understand the external context in which they find themselves, particularly when trying to make long term plans. Work-related road safety is influenced by external economic, legal and political factors which operate at local, national and international levels. These factors influence organisational changes such as management structures, which in turn influence work context and job characteristics at organisational and individual levels. When developing a work-related road safety program - for all vehicle types from heavy trucks and buses, right down to couriers on two wheeled machines - it is vital to understand and allow for such external factors. During the 1980s, a PEST (political, economic, social and technological) analysis was developed as the way to do this. Then in the 1990s, this concept expanded into a PESTEL (political, economic, social, technological, environmental and legal) analysis. Now the tool has further evolved into a PESTELED (political, economic, social, technological, environmental, legal, ethical and demographic) analysis.