Mathematics Applied to Engineering and Management

Mangey Ram, S.B. Singh, Mangey Ram, S.B. Singh

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781351123280
• Edition: 1
• Topic: Matemáticas
• Subtopic: Matemática aplicada

This book offers the latest research advances in the field of mathematics applications in engineering sciences and provides a reference with a theoretical and sound background, along with case studies.

In recent years, mathematics has had an amazing growth in engineering sciences. It forms the common foundation of all engineering disciplines. This new book provides a comprehensive range of mathematics applied to various fields of engineering for different tasks in fields such as civil engineering, structural engineering, computer science, electrical engineering, among others. It offers articles that develop the applications of mathematics in engineering sciences, conveys the innovative research ideas, offers real-world utility of mathematics, and plays a significant role in the life of academics, practitioners, researchers, and industry leaders.

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• Focuses on the latest research in the field of engineering applications
• Includes recent findings from various institutions
• Identifies the gaps in the knowledge of the field and provides the latest approaches
• Presents international studies and findings in modelling and simulation
• Offers various mathematical tools, techniques, strategies, and methods across different engineering fields

1

Geometric and Geometric-Like Processes and Their Applications in Warranty Analysis

Richard Arnold, Stefanka Chukova, Yu Hayakawa, and Sarah Marshall

CONTENTS

1.1 Introduction

1.2 GPs and GLPs: An Overview and Applications

1.2.1 Geometric Process

1.2.2 Classification of GLPs

1.2.3 Applications of GLPs

1.3 Applications of GPs in Warranty Analysis

1.3.1 Basics of Warranty Analysis

1.3.2 A Warranty Cost Model for Non-zero Repair Times

1.3.2.1 An Alternating Process (AP) Model

1.3.2.2 Three AP Models

1.3.3 Nonrenewing Free Repair Warranty Cost Analysis

1.3.3.1 Expected Warranty Costs Over the Warranty Period (0,T)

1.3.3.2 Expected Warranty Costs Over the Product Lifecycle (0,L)

1.3.4 RFRW and RRFRW(n) Cost Analysis

1.3.4.1 Expected Warranty Costs Over (0,W_T)

1.3.4.2 Expected Warranty Costs Over Product Life Cycle (0,L)

1.4 Data Analysis

1.4.1 Fitting APs to Warranty Claims Data

1.4.1.1 Hypothesis Testing

1.4.1.2 Comparing the Fit of the Models

1.4.1.3 Identifying a Parametric Form for the RP and GP

1.4.2 Estimation of Expected Warranty Cost Over (0,T)

1.5 Conclusion

References

1.1 Introduction

Stochastic processes, such as renewal processes, are often used to model the occurrence of recurrent events over time. Under the assumption of a renewal process, the time between events are modeled to be independent and identically distributed random variables. In many scenarios, this assumption is justifiable and reflects the modeled situation well. However, if trends over time are observed, this assumption does not hold. These types of trends can be observed in many practical problems in a variety of fields (e.g., engineering—a system’s lifetime is stochastically decreasing because of aging or imperfect repairs, and at the same time the maintenance/repair time required to keep an aging system operational is stochastically increasing; in epidemiology—the number...