The Department has three major groups of researchers actively engaged in research related to the thrust area of statistical inference. These groups correspond to
- Survival analysis and Reliability
- Statistical Ecology
- Inference in Stochastic Processes
(i) Bounds on unidentifiable probabilistic functions based on the observations from coherent systems : Peterson like bounds for the joint and marginal survival functions of component lifetimes have been obtained for data on from coherent systems. There are already two schemes of observing data from coherent systems in the literature, viz., continuous monitoring and autopsy. Another one has been identified to be 'cuts and paths'. Under all the above schemes it has been shown that the joint distributions of the observations are collections of the relevant incidence functions.
The required bounds are based on these incidence functions. These are the `Worst case' bounds although pointwise sharp.
(ii) Inference based on incidence functions: As the incidence functions are the only identifiable probabilistic structure in these cases, it is natural to base inference on these.
Bayes estimates of the incidence functions have been obtained which may be subject to order restrictions. The features of the posterior distribution were estimated from simulated
data through the MCMC technique. These methods were applied to certain data on automobile failures provided by TELCO, Pune.
Asymptotic, conservative simultaneous confidence bands for the incidence functions have been obtained. These are based on the Peterson lower and upper bounds in the case of competing risks.
In addition, besides several parametric and semiparametric models are proposed for the family of incidence functions through intuitive arguments. These models are seen to fit well to certain data sets available in the literature.
In an earlier work, a statistical procedure has been proposed to test whether identical systems operating in different environments, show different failure patterns, where the structure function of the system may not be known.
(iii) Non-homogeneous Poisson processes have been employed as models for failures of repairable systems. A test for homogeneous Poisson process against non-homogeneous Poisson process alternatives have been obtained for data on such repairable systems.
(iv) Preservation of aging properties under formation of a system with repair facility and standby components, were established.
It is shown that the one component system supported by an inactive standby and a repair facility has NBUE life time as long as components of the system have NBUE life times.
(v) Designing experiments for reliability studies.
A procedure has been suggested to study the life time of several brands, say, n of a component which are operating in different, say m environments. Existing procedures to carry out the life study would require mn experiments. The suggested procedure is cost effective with respect to existing methods.
(vi) Testing equality of medians of k survival functions based on profile(empirical) likelihood in randomly right censored models. Unlike existing tests, equality of the underlying distributions is not assumed while obtaining the null asymptotic distribution.
(vii) Review of properties of renewal processes such as the monotonicity, the $Pf_2$ property etc. Also applications of these properties in preventive maintenance policies and machine scheduling processes are studied.
(viii) A sampling plan based on a more general symmetric family of distributions with the parameters estimated using the modified maximum likelihood (MML) procedure is proposed. This sampling plan performs well for most of the symmetric non-normal distribution.
Modified maximum likelihood estimation has been proposed for censored data, giving easily computable estimators as compared to the complexities involved in the usual maximum likelihood method.
(ix) Interactions with organizations like Kirloskar Oil Engines Limited, Crompton Greaves Limited, Automotive Research Association of India, Research and Development ( Engineers) ( DRDO), Dighi have been developed . The group has strengthened motivation for statistical thinking and methodology in such organizations.