This book collects select chapters on modern industrial problems related to uncertainties and vagueness in the expert domain of knowledge. The book further provides the knowledge related to application of various mathematical and statistical tools in these areas. The results presented in the book help the researchers and scientists in handling complicated projects in their domains. Useful to industrialists, academicians, researchers and students alike, the book aims to help managers and technical specialists in designing and implementation of reliability and risk programs as below: Ensure the system safety and risk informed asset management Follow a proper strategy to maintain the mechanical components of the system Schedule the proper actions throughout the product life cycle Understand the structure and cost of a complex system Plan the proper schedule to improve the reliability and life of the system Identify unwanted failures and set up preventive and correction action .