Estimation of parameters of yamada et al. model and modification of the model

Yamada, Ohba and Osaki (1983) suggested an important NHPP model for software failure phenomenon. So far little work has been done on the problem of estimating its parameters. We present here some conditions for the likelihood estimates to be finite, positive and unique. We also suggest a modification of the model. The performance measures and statistical inferences of the modified model are discussed here. The modified model is applied to software failure data and the results are compared with Jelinski-Moranda [4] and some existing important NHPP models     

LASSO and shrinkage estimation in Weibull censored regression models

In this paper we address the problem of estimating a vector of regression parameters in the Weibull censored regression model. Our main objective is to provide natural adaptive estimators that significantly improve upon the classical procedures in the situation where some of the predictors may or may not be associated with the response. In the context of two competing Weibull censored regression models (full model and candidate submodel), we consider an adaptive shrinkage estimation strategy that shrinks the full model maximum likelihood estimate in the direction of the submodel maximum likelihood estimate. We develop the properties of these estimators using the notion of asymptotic distributional risk. The shrinkage estimators are shown to have higher efficiency than the classical estimators for a wide class of models. Further, we consider a LASSO type estimation strategy and compare the relative performance with the shrinkage estimators. Monte Carlo simulations reveal that when the true model is close to the candidate submodel, the shrinkage strategy performs better than the LASSO strategy when, and only when, there are many inactive predictors in the model. Shrinkage and LASSO strategies are applied to a real data set from Veteran's administration (VA) lung cancer study to illustrate the usefulness of the procedures in practice.     

Forecasting models for developing control scheme to improve furnace run length

In petrochemical industries, the gaseous feedstock like ethane and propane are cracked in furnaces to produce ethylene and propylene as main products and the inputs for the other plant in the downstream. A problem of low furnace run length (FRL) increases furnace decoking and reduces productivity along with the problem of reducing life of the coil. Coil pressure ratio (CPR) and tube metal temperature (TMT) are the two most important performance measures for the FRL to decide upon the need for furnace decoking. This article, therefore, makes an attempt to develop the prediction models for CPR and TMT based on the critical process parameters, which would lead to take the necessary control measures along with a prior indication for decoking. Regression-based time series and double exponential smoothing techniques are used to build up the models. The effective operating ranges of the critical process parameters are found using a simulation-based approach. The models are expected to be the guiding principles eventually to increase the average run length of furnace.