Estimation and prediction for Chen distribution with bathtub shape under progressive censoring

We consider estimation of the unknown parameters of Chen distribution [Chen Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statist Probab Lett. 2000;49:155–161] with bathtub shape using progressive-censored samples. We obtain maximum likelihood estimates by making use of an expectation–maximization algorithm. Different Bayes estimates are derived under squared error and balanced squared error loss functions. It is observed that the associated posterior distribution appears in an intractable form. So we have used an approximation method to compute these estimates. A Metropolis–Hasting algorithm is also proposed and some more approximate Bayes estimates are obtained. Asymptotic confidence interval is constructed using observed Fisher information matrix. Bootstrap intervals are proposed as well. Sample generated from MH algorithm are further used in the construction of HPD intervals. Finally, we have obtained prediction intervals and estimates for future observations in one- and two-sample situations. A numerical study is conducted to compare the performance of proposed methods using simulations. Finally, we analyse real data sets for illustration purposes.     

A bivariate signed rank test for two sample location problem

An affine-invariant signed rank test for the difference in location between two symmetric populations is proposed. The proposed test statistic is compared with Hotelling's T2 test statistic, Mardia's(1967)test statistic, Peters-Randles(1991) test statistic and Wilcoxon's rank sum test statistic using a Monte Carlo Study. It performs better than Mardia's test statistic under almost all populations considered. Under the bivariate normal distribution, it performs better than other test statistics compared for small differences in location between two populations except Hotelling's T2. It performs better than all statistics, including Hotelling's T , for sample size 15 when samples are drawn from Pearson type.     

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.     

A two-stage unrelated randomized response model for estimating a rare sensitive attribute in probability proportional to size sampling using Poisson distribution

This paper describes the estimating procedures of mean number of entities that possess a rare sensitive attribute using the Mangat (1992) randomized device, when the population consists of some clusters and the population is again stratified with some clusters in each stratum. Unbiased estimation procedures for the mean number of individuals have been discussed and their properties are described when the parameter of a rare unrelated attribute is assumed to be known and unknown. An empirical study is carried out to show the dominance of the proposed estimator over Lee et al. (2013) estimator.     

The Slippage Problem for the Circular Normal Distribution

The slippage problem occurs when an unspecified observation in a given random sample is from a distribution other than that for all the remaining observations. This paper studies the problem in terms of the 'slip' in the mean direction of a circular normal distribution. The slippage problem is first treated as a multiple decision problem with a prior which is invariant under the permutations of the hypotheses. The probabilities of accepting the various hypotheses for the Bayes rule with respect to this prior are explicitly obtained. The likelihood ratio tests for this slippage problem, for the cases when the mean directions are both known and unknown, are shown to be easily computable. The tests are illustrated through two well-known datasets. The performances of a range of tests are compared using extensive simulation.     

Optimal Enhancement and Lifetime of Software Systems: A Control Theoretic Analysis

We develop an optimal control model to maximize the net value provided by a software system over its useful life. The model determines the initial number of features in the system, the level of dynamic enhancement effort, and the lifetime of the system. The various factors affecting these optimal choices are systems characteristics (e.g., complexity, age, quality), user learning, and process maturity. We also consider that there is a time lag between the addition of a feature and the realization of its benefit to users. The basic model is extended to consider the decision of replacing the existing system by a new one.