Reliability Is An Important And Challenging Subject, Which Involves The Disciplines Of Science And Engineering. Researchers In Both These Fields Have Been Working On Reliability Problems For Several Decades. Reliability Is The Ability Of A System Or Component To Perform Its Required Functions Under Stated Conditions For A Specified Period Of Time. It Plays A Key Role In Monitoring The Quality Of Various Systems Which Is Primarily Due To Complexity, Sophistication, And Automation Inherent In Modern Technology. A Product Has Value As A Result Of Its Utility Or Performance In Satisfying A Need Or Requirement. For Most Products, Customers See Reliability As One Of The Important Quality Characteristics. Evaluation Of Reliability Involves The Use Of Many Statistical Tools. We Confine Ourselves To Those Of Direct Importance In Reliability Theory. Some Of The Tools For Studying The Reliability Characteristics Of A System Are The Failure Rate, The Mean Residual Lifetime, The Reversed Hazard Rate And The Expected Inactivity Time. These Four Measures Are The Most Important Notions In The Area Of Engineering, Biomedical Science, Actuarial Science, Forensic Science, Reliability Theory, Survival Studies, Business, Social Sciences And Many Other Fields. In View Of The Growing Importance, Here We Make An Attempt To Study These Four Measures In Different Directions. We Study The Entropy For Inactivity Time, And Based On This, A Conditional Measure Of Uncertainty Has Been Defined, Which Has Helped In Defining A New Stochastic Order And An Ageing Class. Some Characterization Results Are Also Provided Here. We Also Study The Higher Order Moments And Partial Moments Of The Inactivity Time. Some Results On Decreasing Reversed Hazard Rate Property Of Order Statistics And Record Values Are Also Provided. We Discuss The Mean Residual Life Of Record Values For A General Set Up. A General Class Of Failure Rate Model Is Estimated Under Different Loss Functions Using Bayesian Approach. Key Words And Phrases: Ageing Class, Characterization, Reliability, Stochastic Ordering, Order Statistics And Record Values.