School of Mathematics

In this paper, we establish reliability sampling plans for a two-parameter lognormal distribution when it is known that samples are progressive first-failure censored. An EM algorithm is developed to obtain maximum likelihood estimates of unknown parameters. Reliability sampling plans are obtained using two different criteria, namely minimizing the expected test time and minimizing the determinant of the variance covariance matrix of the maximum likelihood estimates, under a restriction on the total cost associated with the experiment and for given specifications on the operating characteristic curve. Finally, a numerical study is performed and specific comments are given.

For a lognormal distribution, in Bayesian framework, we consider estimation of unknown parameters, and prediction of future observable, when it is known that samples are hybrid censored. We derive Bayes estimates with respect to the squared error loss function under both informative and non-informative prior situations. These estimates are then computed using Lindley method, importance sampling, and OpenBUGS software. For comparison purpose, we also obtain maximum likelihood estimates using expectation-maximization (EM) algorithm, and compute Fisher information matrix as well. Predictive estimates of future observable are obtained under the setup of one-and two-sample prediction problems. We further compute equal-tail and highest posterior density predictive intervals, the corresponding average interval length and coverage percentage. Proposed methods of estimation and prediction are compared numerically, and comments are made based on a simulation study. Two real data sets are also analyzed for illustration purpose.

In this paper, we consider the problem of estimating unknown parameters of an inverse Weibull distribution when it is known that samples are progressive type-I interval censored. We propose an EM algorithm to obtain maximum likelihood estimates and mid point estimates. For comparison purpose Bayes estimates are also obtained under the square error loss function using non-informative and informative prior situations. A simulation study is conducted to access the performance of the proposed estimators and recommendations are made on the basis of simulation results. A real data set is also analyzed in detail for an illustration purpose. Finally, by making use of expected Fisher information matrix various inspection times and optimal censoring schemes are obtained.

In this paper, we develop double acceptance sampling plan and group acceptance sampling plan for an inverse Weibull distribution based on a truncated life test. We consider the median lifetime of the test units as a quality parameter and obtain the design parameters such as sample size and acceptance number. These plans are obtained under the consumer's risk and the producer's risk simultaneously involved at a certain confidence level. We present a simulation study to support the proposed methods and a comparison between single and double acceptance sampling plans is made. A real data set is also analyzed to illustrate the implementation of the proposed sampling plans. Further, the situation under which the proposed samplings plans can also be used for other percentiles points is discussed. Finally a conclusion is presented.

This article deals with problems of estimation and prediction under classical and Bayesian approaches when lifetime data following a lognormal distribution are observed under type-I progressive hybrid censoring. We first obtain maximum likelihood estimates, Bayes estimates, and corresponding interval estimates of unknown lognormal parameters. We then develop predictors to predict censored observations and construct prediction intervals. Further, we analyze two real data sets and conduct a simulation study to compare the performance of proposed methods of estimation and prediction. Finally, optimal censoring schemes are constructed under cost constraints and a conclusion is presented.

This article addresses the problems of estimation and prediction when the lifetime data following Poisson-Exponential distribution are observed under type-II censoring. We obtain maximum likelihood estimates and associated interval estimates under a classical approach, and Bayes estimates using various loss functions and associated highest posterior density interval estimates. Maximum likelihood estimates are obtained using the Newton-Raphson method and Expectation Maximization (EM) algorithm, and Bayes estimates are computed using importance sampling and Lindley approximation. We also compute shrinkage preliminary test estimates based on maximum likelihood and Bayes estimates. Further, we provide inference on the censored observations by making use of best unbiased and condition median predictors under a classical approach, and predictive estimates under the Bayesian paradigm using importance sampling. The associated predictive interval estimates are also obtained using different methods. Finally, we conduct a simulation study to compare the performance of all the proposed methods of estimation and prediction, and analyze a real data set for illustration purpose.

Objectives: This paper presents an up-to-date overview of research performed in the Virtual Reality (VR) environment ranging from definitions, its presence in the various fields, and existing market players and their projects in the VR technology. Further an attempt is made to gain an insight on the psychological mechanism underlying experience in using VR device. Methods: Our literature survey is based on the research articles, analysis of the projects of various companies and their findings for different areas of interest. Findings: In our literature survey we observed that the recent advances in virtual reality enabling technologies have led to variety of virtual devices that facilitate people to interact with the digital world. In fact in the past two decades researchers have tried to integrate reality and VR in the form of intuitive computer interface. Improvements: This has led to variety of potential benefits of VR in many applications such as News, Healthcare, Entertainment, Tourism, Military and Defence etc. However despite the extensive research efforts in creating virtual system environments it is yet to become apparent in normal daily life.

In this paper, we develop double acceptance sampling plan and group acceptance sampling plan for an inverse Weibull distribution based on a truncated life test. We consider the median lifetime of the test units as a quality parameter and obtain the design parameters such as sample size and acceptance number. These plans are obtained under the consumer's risk and the producer's risk simultaneously involved at a certain confidence level. We present a simulation study to support the proposed methods and a comparison between single and double acceptance sampling plans is made. A real data set is also analyzed to illustrate the implementation of the proposed sampling plans. Further, the situation under which the proposed samplings plans can also be used for other percentiles points is discussed. Finally a conclusion is presented.

This article addresses the problems of estimation and prediction when the lifetime data following Poisson-Exponential distribution are observed under type-II censoring. We obtain maximum likelihood estimates and associated interval estimates under a classical approach, and Bayes estimates using various loss functions and associated highest posterior density interval estimates. Maximum likelihood estimates are obtained using the Newton-Raphson method and Expectation Maximization (EM) algorithm, and Bayes estimates are computed using importance sampling and Lindley approximation. We also compute shrinkage preliminary test estimates based on maximum likelihood and Bayes estimates. Further, we provide inference on the censored observations by making use of best unbiased and condition median predictors under a classical approach, and predictive estimates under the Bayesian paradigm using importance sampling. The associated predictive interval estimates are also obtained using different methods. Finally, we conduct a simulation study to compare the performance of all the proposed methods of estimation and prediction, and analyze a real data set for illustration purpose.

This article deals with problems of estimation and prediction under classical and Bayesian approaches when lifetime data following a lognormal distribution are observed under type-I progressive hybrid censoring. We first obtain maximum likelihood estimates, Bayes estimates, and corresponding interval estimates of unknown lognormal parameters. We then develop predictors to predict censored observations and construct prediction intervals. Further, we analyze two real data sets and conduct a simulation study to compare the performance of proposed methods of estimation and prediction. Finally, optimal censoring schemes are constructed under cost constraints and a conclusion is presented.

Purpose -The purpose of this paper is to present a technique for analyzing the behavior of an industrial system utilizing vague, imprecise, and uncertain data. The synthesis unit of a urea plant situated in northern part of India has been considered to demonstrate the proposed approach. Sensitivity analysis of system's behaviour has also been done in it. Design/methodology/approach -In the proposed approach, traditional Lambda-Tau technique is used to analyze the behavior of a complex repairable synthesis unit of a fertilizer industry up to a desired degree of accuracy. This technique has been demonstrated by computing eight well-known reliability indices which are used for behaviour analysis of the considered system in a more promising way. Findings -The study of analysis of reliability, availability, maintainability etc can help in increasing the production and quality of synthesis. To ensure the system performance throughout its service life, it is necessary to set up proper maintenance, planning and control which can be done after studying the variation of reliability, availability with respect to time. Thus, it may be a more useful analysis tool to access the current system condition and involved uncertainties. The present paper suggested an approach to improve the system's performance. Originality/value -The paper suggests a technique for analyzing the stochastic behavior of an industrial subsystem by computing eight well-known reliability indices in the form of fuzzy membership function. The benefits for the methodology include the ability to model and deal with highly complex system as fuzzy sets can deal easily with approximations and it helps in improving and handling the uncertainties and possibilities.

Reliability, availability and maintainability (RAM) analysis of a system is helpful in carrying out design modifications, if any, and it is required to achieve minimum failures or to increase mean time between failures (MTBF), and thus it is used to plan maintainability requirements, optimise reliability and maximum equipment availability. To this effect, this paper presents the application of RAM analysis in the process industry. Fuzzy Lambda?Tau methodology is used here to model the system behaviour. Each system components, failure rate and repair time are represented by triangular fuzzy numbers with known spread. The methodology uses Petri nets to model the system instead of fault tree because it allows efficient simultaneous generation of minimal cuts and path sets. Various reliability parameters such as MTBF, expected number of failures (ENOF), reliability, availability, etc. are calculated. The computed results are presented to plant personnel for their performance considerably by adopting and practicing suitable maintenance policies/strategies.

In a real life situation, due to the complexity of the industrial systems andnon-linearity of their behavior, it is very difficult to achieve optimum performance of system fordesired industrial goals using uncertain, vague and imprecise data. Herein, an approach has beenproposed through which the behavior of the system is analyzed in the form of well- known sixreliability indices by using triangular fuzzy numbers which allow the consideration of expertopinions, linguistic variables, operating conditions in reliability information. Using their behav-ior analysis a fuzzy multi-objective optimization problem (FMOOP) has been formulated. Due tothe conflicting nature of the multiple objectives, the decision making is difficult and it leads tothe Pareto optimal solutions instead of single optimal solutions. Many evolutionary algorithms(EAs) already exist in the literature for solving a multi-objective optimization problem (MOOP),and are termed as multi-objective evolutionary algorithms (MOEAs). Particle swarm optimiza-tion (PSO) is one of such MOEA which demonstrates the ability to identity a Pareto-optimalfront efficiently. Here, a crisp optimization problem is reformulated from FMOOP by taking intoaccount the preference of decision maker (DM) and then PSO is applied to solve the resultingfuzzified MOOP. The presented approach is applied in order to solve the multi-objective se-ries-parallel system reliability optimization problem for a crystallization unit of a urea plant.

Probability distributions play an important role in the reliability studies and have many applications in engineering. Estimation of the distribution parameters is also significant for making a decision. It is difficult to trap the global solution for the estimation of parameters by the traditional methods such as maximum likelihood estimator (MLE), as these methods trap a local solution. To get the global values of these parameters is complicated. In this paper, we have developed a two-phase approach by taking the advantages of one of the evolutionary algorithms, namely the particle swarm optimization (PSO) for getting the global values of the distribution parameters. PSO exploits the concept of the moment method to estimate the distribution parameters by using mean, standard deviation, coefficient of variation (CV) and Anderson–Darling (AD) statistics for the best fitting of the distribution to failure data. In comparison with the widely used algorithms, a meta-heuristic algorithm (PSO) offers much more choices for system designers.