Master-Degree-Project
Method of Negative Moments of Positive Random Variables
Recent experiments on the lifespan of products focus on measuring reliability characteristics by testing identical components under normal conditions and recording their "time to failure." This time is considered a random variable with a specific cumulative distribution function (CDF). The inverse moment of a positive random variable is used to estimate the lifespan and understand the distribution of failure times. Significant inverse moments can indicate a higher likelihood of early failures, providing valuable information for product design and reliability assessment.
This thesis consists of three chapters:
- Theoretical Overview: It explains statistical moments, their use in data analysis, and the formal definition and role of the inverse moment in characterizing distributions, compared to other moments like mean and variance.
- Interpretation of the Inverse Moment: It explores how the inverse moment helps interpret data, its relationship with the distribution shape (skewness), and examples in different contexts.
- Analysis in Various Distributions: This chapter analyzes the inverse moment in several distributions, its effect on skewed distributions, and provides practical examples.
The use of negative moments is important for understanding the behavior of random variables, especially in assessing the likelihood of extreme events, such as early failures or short lifespans. Negative moments help characterize the tail behavior of distributions, providing insights into the reliability and risk of systems. They are particularly useful in fields like:
- Reliability and Risk Analysis: Assessing product lifespans, system failures, and maintenance schedules.
- Life Testing: Estimating failure times in various products or systems.
- Survival Analysis: Analyzing time-to-event data in medical and healthcare settings.
- Finance and Insurance: Evaluating large losses and assessing financial risks.
Negative moments are essential for making informed decisions in engineering, healthcare, finance, and other industries where predicting failure or assessing risk is critical.