RESEARCH ACTIVITIES

The post graduate Department of Mathematics was upgraded as a Research Department in 1999. The Department produced the first ever PhD in Mathematics from an affiliated college of the M.G. University. So far we have produced 8 PhD holders. Presently there are Five Research Guides, 14 scholars working in the department.

Research Guides

On going Projects

A major project of the NBHM of Rs. 6, 60,000 was undertaken by Dr. E.S.Jeevanand. The topic of the project is “SOME INFERENCE RESULTS RELATED TO RELIABILITY MEASURES OF LOMAX AND POWER FUNCTION DISTRIBUTIONS”.
A UGC Minor Project of Rs. 1, 50,000 on “APPLICATIONS OF EVIDENCE THEORY IN INTERNET USING FUZZY MATHEMATICS” was undertaken by Dr Sunny Kuriakose.

Summary of the UGC minor project entitled

“Estimation of time zo test transform  for Classical Pareto  distribution  IN some real data situation”

Dr.E.S.Jeevanand, Associate Professor, Department of Mathematics.

The field of reliability is of recent origin.  In the real world, all products and systems are unreliable in the sense that they degrade with age and ultimately fail.  Since the process of deterioration leading to failure occurs in a random manner, the concept of reliability requires a probabilistic framework.  With the wide spread manufacture and use of increasingly sophisticated mechanical, electrical and electronic equipment during the second half of the last century, questions of reliability became of interest.  The term reliability of a product (system) denotes the probability that the product (system) will perform its intended function for a specified time period when operating under normal environmental conditions.  Even though the above definition of reliability is explained with reference to the behavior or length of life of a system, it is equally applicable in the analysis of any duration variable that describes a well-defined population subject to decrement due to the operation of forces of attrition over time.  It may not be out of place to point out that the methods of lifetime analysis can be applied in many areas beyond survival analysis (and reliability which is concerned with failure of industrial objects).  It needs to be recognized that the data to be analyzed should be in the form of the time of occurrence of the event of interest.  Such events may be from economics – time spent in the state of unemployment, from sociology – time spent out of jail until next conviction, and from other disciplines.  In general, one may call this methodology as event time analysis.

 TTT-plot

The TTT-plot an empirical and scale invariant plot based on failure data, and the corresponding asymptotic curve, named the scaled TTT-Transform were introduced by Barlow and Campo (1975) and used for model identification purposes. Since then these tools have proven to be very useful in several applications in reliability. The TTT-Transform has also been found quite useful in theoretical applications such as looking for test statistics for particular purposes and to study their power. They are also been found quite useful in practical applications such as ageing properties, characterization of distributions, maintenance optimization and also in design of experiments (See Deshpande and Suresh (1990) and Bergman and Klefsjo(1998)). For more reliability application of the TTT one can refer the papers of Klefsjo and Bergman (1984), Gill (1986), Westberg and Klefsjo (1994), Csorgo and Zitikis (1998), Feng-Bin Sun and Kececloglu (1999), Kvaloslashy and Lindqvist (1998) and Raqabi and Madi(2002). The application of this transform in econometrics and its close relationship with the Lorenz curve have been studied by many authors including Chandra and Singpurwalla (1981), Klefsjo (1984), Pham and Turkkan (1994), Kochar et al. (2002), among others. The scaled total time on test (TTT) transform of F is defined as (Klefsjo(1984))

      f(p) =  for 0 £ p £ 1.                   (1.1)

 m =   and  = inf{x: F(x)³y} for 0 £ y £ 1.