American Journal of Mathematical and Management Sciences

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  • ISSN
    0196-6324

Publications in this journal

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    ABSTRACT: The additive reversed hazards model relates the conditional reversed hazard function of the lifetime linearly to the covariates. It describes the association between the lifetime and covariates in terms of risk difference. In the present work, we introduce an additive reversed hazards model for modeling and analysis of lifetime in the presence of covariates under left censoring. We develop a closed form semiparametric estimator of the regression parameter. We also provide a Breslow-type estimator for a cumulative baseline reversed hazard function. Asymptotic properties of the estimators are studied. Simulation studies are conducted to assess the finite sample properties of the estimators. Finally, we apply the proposed model to real-life data.
    American Journal of Mathematical and Management Sciences 10/2014; 33(4).
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    ABSTRACT: Balakrishnan and Li (2005) introduced the use of ordered ranked set sampling (ORSS) and derived the best linear unbiased estimators (BLUEs) under ORSS (BLUEs-ORSS). In this study, we extend the work to ordered double ranked set sampling (ODRSS) scheme by using the idea of order statistics from independent and nonidentically distributed random variables. The BLUEs of the location and the scale parameters of a location-scale family of distributions are derived using ODRSS (BLUEs-ODRSS). It is shown that the BLUEs-ODRSS are uniformly better than the BLUEs-ORSS for the two-parameter exponential, normal, and generalized geometric distributions. Furthermore, we also study the properties of the distribution-free confidence intervals for quantiles and tolerance intervals based on ODRSS. We show that the confidence and tolerance intervals under the ODRSS scheme are more precise than their counterparts based on the ORSS scheme.
    American Journal of Mathematical and Management Sciences 10/2014; 33(4).
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    ABSTRACT: The aim of this article is to present a fuzzy programming approach to a single-sink, fixed-charge, multiobjective, multi-index stochastic transportation problem (SSMISTP). This article focuses on the minimization of the transportation cost, deterioration rate, and underused capacity for transportation of raw materials from different sources to the ”Single-Sink” by different transportation modes. The parameters of the proposed problem are transportation cost, fixed-charge, deterioration rate, and underused capacity. These parameters are to be treated here as random variables. Because of the globalization of the market, assume that the “Sink” demand is an interval representing the inexact demand component for the SSMISTP. By considering the uncertainties of these parameters, we formulate the mathematical model of the proposed problem. Using a stochastic programming approach, all the stochastic objective functions are converted into deterministic objective functions. Again using the interval concept, the proposed interval-valued sink constraint decomposes into two deterministic constraints. Finally, using all deterministic objective functions and constraints, we design a multiobjective transportation problem(MOTP). The optimal compromise solution to the MOTP has been obtained by using a fuzzy programming technique. We demonstrate the feasibility of the proposed problem using a real-life practical example.
    American Journal of Mathematical and Management Sciences 10/2014; 33(4).
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    ABSTRACT: In this article we propose a new scheduling model in which two agents share a common machine to process their respective jobs. Each agent has its own objective function to optimize, and the job processing times are subject to cumulative deteriorating. The task is to minimize one agent's total completion time with the restriction that another agent's maximum cost cannot exceed a given upper bound. We analyze some properties on the optimal solution and then propose an optimal polynomial-time solution algorithm followed by a numerical example.
    American Journal of Mathematical and Management Sciences 10/2014; 33(4).
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    ABSTRACT: In this article we consider various methods of estimation of the unknown parameters of a generalized inverted exponential distribution from a frequentist as well as Bayesian perspective. With regard to Bayes estimation of the unknown parameters under squared error loss function, we assume that the scale and shape parameters of the distribution have a gamma prior and are independently distributed. Under these priors, we use an importance sampling technique to calculate Bayes estimates and the corresponding highest posterior density intervals. We also compute approximate Bayes estimates using Lindley’s approximation. Besides Bayes estimation, we introduce maximum likelihood estimates and estimates based on percentiles. Monte Carlo simulations are performed to compare the performance of the Bayes estimates with the classical estimates. Two datasets have been analyzed for illustrative purposes.
    American Journal of Mathematical and Management Sciences 07/2014; 33(3).
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    ABSTRACT: In this article we study the problem of selecting among k independent Bernoulli populations whose success probabilities are unknown, and the sample size for each population is assumed to follow a discrete uniform distribution with known range. We consider two goals and propose procedures for each goal: (1) selecting the best and (2) selecting the best in comparison with a standard. The “best” is defined as that having the highest success probability. We derive the probability of a correct selection and the least favorable configuration for each procedure by using the exact binomial distribution, without any approximation. Simulations and examples are provided to illustrate our procedures.
    American Journal of Mathematical and Management Sciences 07/2014; 33(3).
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    ABSTRACT: In this article, we consider the problem of testing for mean vector and simultaneous confidence intervals when the data have a three-step monotone pattern that is missing observations. The maximum likelihood estimators of the mean vector and the covariance matrix with a three-step monotone missing data pattern are presented based on the derivation of Jinadasa and Tracy (1992). We propose an approximate upper percentile of Hotelling’s T 2-type statistic to test the mean vector. Further, we obtain the approximate simultaneous confidence intervals for any and all linear compounds of the mean and the testing equality of mean components. Finally, the accuracy of the approximation is investigated by Monte Carlo simulation, and a numerical example is given to illustrate the method.
    American Journal of Mathematical and Management Sciences 07/2014; 33(3).
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    ABSTRACT: Sousa, Shabbir, Corte-Real, and Gupta (2010) and Gupta, Shabbir, Sousa, and Corte-Real (2012) have presented ratio and regression estimators for the finite population mean of a sensitive study variable utilizing nonsensitive auxiliary information. We improve the results further by using optional scrambling. In the process, we also estimate the sensitivity level of the underlying sensitive question. We compare the proposed method with Sousa et al. (2010) and Gupta et al. (2012) estimators.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
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    ABSTRACT: In this article, we propose a double acceptance sampling plan based on the truncated life test for Maxwell distribution. By fixing the consumer’s confidence level, the minimum sample sizes of the first and second samples necessary to ensure the specified mean life are obtained. The operating characteristic values and the minimum ratios of the mean life to the specified life are also analyzed. Several useful tables are provided. We illustrate the double acceptance sampling plan with a numerical example.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
  • American Journal of Mathematical and Management Sciences 01/2014; Taylor & Francis, In Press,.
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    ABSTRACT: Redundancy allocation, being an important and effective way to improve system reliability, has been discussed by many authors. The main idea, which has been advocated in this article, lies in the fact that some components have more significance in the functioning of the system than the others; because of this, it is expected that if allocation of the redundant component is made according to some component-importance measure, optimality can be achieved easily. The novelty of this study is that the problem of redundancy allocation has been solved by allocating redundant components according to some component-importance measures that are not very difficult to obtain and comprehend for an engineered system, even when there is no information about the reliability of the components. The component structural-importance measure and reliability-importance measure have been used in this work for the purpose of allocating redundancy. The results derived can be used to maximize system reliability using redundancy allocation for a general n-component coherent system. Applications of the results have been illustrated with examples of coherent systems.
    American Journal of Mathematical and Management Sciences 01/2014; 33(1).
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    ABSTRACT: In this study, an acceptance sampling plan is developed for a truncated life test when the lifetime of a product follows exponentiated inverse Rayleigh distribution. The minimum sample size required and the acceptance number are determined for various combinations of shape parameters of the exponentiated inverse Rayleigh distribution when the consumer's risk and the test termination time are specified. The operating characteristic values according to various quality levels are also obtained. The results obtained are compared with ordinary inverse Rayleigh distribution.
    American Journal of Mathematical and Management Sciences 01/2014; 33(1).
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    ABSTRACT: The purpose of this work is to study an inventory model for a deteriorating item considering time-quadratic demand and time-dependent partial backlogging, which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. The model is solved analytically to obtain the optimal solution of the problem. The sufficient condition of the optimal solution is also studied. It is then illustrated with the help of numerical examples.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
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    ABSTRACT: In this study we have considered different methods of estimation of the unknown parameters of a two-parameter Rayleigh distribution from both the frequentists' and the Bayesian view points. First, we briefly describe different frequentists' approaches: maximum likelihood estimators, method of moments estimators, L-moment estimators, percentile-based estimators, and least squares estimators, and we compare them using extensive numerical simulations. We have also considered Bayesian inferences of the unknown parameters. It is observed that the Bayes estimates and the associated credible intervals cannot be obtained in explicit forms, and we have suggested using an importance sampling technique to compute the Bayes estimates and the associated credible intervals. We analyze one dataset for illustrative purposes.
    American Journal of Mathematical and Management Sciences 01/2014; 33(1).
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    ABSTRACT: The purpose of this paper is to present a linear integer programming approach to construct efficient binary incomplete block designs for any given number of treatments v, number of blocks b, with common block-size k, and with a nearly balanced concurrence matrix. The proposed approach is illustrated by constructing an efficient incomplete block design. A-efficient and D-efficient incomplete block designs have been constructed and catalogued using the proposed algorithm for a restricted range of parameters 3 v 20, b v, and 2 k min(10, v − 1), with vb1, 000. An R package is developed to implement the proposed approach.
    American Journal of Mathematical and Management Sciences 01/2014; 33(2).
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    ABSTRACT: Redundancy is an important aspect of system design. The use of redundancy improves system reliability. In the case of systems whose cost of failure is very high, redundancy may be used to make the system fail-safe, and thus, in any safety-critical systems, a proper use of redundancy is essential. Because adding redundancy increases the total cost and complexity of a system design, it should be used wisely, taking the cost and other constraints into account. The question arises with regard to how many redundant components should be added to different components or subsystems of a coherent system in order to maximize the system reliability. The problem becomes more difficult when the maximization is to be done under various constraints. The present study solves a redundancy allocation problem (RAP) in a complex system in an optimal way under various constraints involving cost, weight, volume, and so forth. The rule developed here can be used to maximize the reliability of any simple or complex coherent systems under any number of constraints. A numerical example has been included to illustrate the method.
    American Journal of Mathematical and Management Sciences 01/2013; 32(4).