Al-Anood Abd-ALLAH

DISSERTATION TITLE:

"Reliability Analysis for Some Stochastic Orders and Ageing Notions"

INTRODUCTION:

Reliability theory was historically developed to describe the failure and ageing of complex electronic (military) equipment, but the theory itself is a very general theory based on mathematics (probability theory) and a systems approach. The theory may therefore also be useful in describing and understanding the ageing and failure of biological systems. Reliability theory is a body of ideas, mathematical models, and methods aimed at predicting, estimating, understanding, and optimizing the life span and failure distributions of systems and their components. Also, it allows researchers to predict the age-related failure kinetics for a system of given architecture (reliability structure) and given reliability of its components. Recently, some authors introduced some new stochastic orders and ageing criteria and studied their inter-relations as well as their statistical analysis (estimation-testing-prediction and forecasting) under different types of sampling schemes, including random sampling, random or fixed censoring (right or left), truncated observations and Panel sampling. Ageing properties of various types of models were addressed; including shock models and wear processes, a mixture of life models.

Much of the stochastic orders and ageing classes that introduced recently will be developed statistically in details through estimating its survival function or doing testing of it. When this is done, the procedures will be used on real data situations from areas such as medicine, manufacturing, and economics. Thus, we will be able to tell the type of ageing a set of data exhibits and hence things like product warranties can be designed and the private sector will be the beneficiary.

OBJECTIVE:

Our first tasks is to develop new practical notions of ageing using new stochastic orders and study their basic proberties, such as preservation under modeling by adding lives, composing systems, or building shock models. We then shall test and estimate the survival function of these ageing notions and then find out what types of industrial, medical or life data can be best described by those ageing notions. This should help the private industrial sector build warranties for their products and expect when major repairs will be needed.

RRSEARCH PLAN:

1. Studying related published literature.

2. Identifying the required mathematical and simulation tools.

3. Developing and analyzing the proposed schemes.

4. Developing the simulation work.

5. Evaluting the efficiency and importance of the proposed schemes.

APPLIED FIELDS:

The expected results may be will find practical applications in reliability theory and life testing.

EXPECTED TIME OF FINALIZATION:

JANUARY, 2009

REFERENCES:

- Shaked, M. and Shanthikumar, J.G. (2007). Stochastic Orders. Springer, New-York.