Abstract Recently, A. S. Krishnan, S. M. Sunoj and N. U. Nair [Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc. 2020, 10.1007/s42952-019-00023-x] introduced past extropy for measuring uncertainty contained in past lifetime of random variables. In the present study, we focus on the past extropy of k-records. The motivation for considering past extropy of k-records has been discussed in detail. We have also illustrated the merit of considering past extropy of k-records over past extropy of classical records and past extropy of original random sample using two real life data sets. Some important properties of past extropy of k-records are discussed in this work. We have expressed past extropy of k-records using past extropy of k-records arising from uniform distribution. The work proposes a simple estimator for past extropy of k-records as well.
{"title":"Past Extropy of 𝑘-Records","authors":"E. I. A. Sathar, Jitto Jose","doi":"10.1515/eqc-2019-0023","DOIUrl":"https://doi.org/10.1515/eqc-2019-0023","url":null,"abstract":"Abstract Recently, A. S. Krishnan, S. M. Sunoj and N. U. Nair [Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc. 2020, 10.1007/s42952-019-00023-x] introduced past extropy for measuring uncertainty contained in past lifetime of random variables. In the present study, we focus on the past extropy of k-records. The motivation for considering past extropy of k-records has been discussed in detail. We have also illustrated the merit of considering past extropy of k-records over past extropy of classical records and past extropy of original random sample using two real life data sets. Some important properties of past extropy of k-records are discussed in this work. We have expressed past extropy of k-records using past extropy of k-records arising from uniform distribution. The work proposes a simple estimator for past extropy of k-records as well.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"22 1","pages":"25 - 38"},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86165031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The concept of sequential order statistics were introduced by Kamps in 1995. In this article, we derive an acceptance sampling plan, for units having exponentially distributed lifetime, using sequential order statistics. Based on data obtained from progressive type II censoring using constant stress accelerated life tests, we obtain the maximum likelihood estimates of the parameters of the exponential distribution. Further, a log linear life-stress relationship is assumed to derive the exact distributions of the estimators of the parameters of exponential distribution. The parameters of the sampling scheme are obtained by minimizing expected total testing cost satisfying usual probability requirements. Some numerical results are presented in a table to illustrate our plans.
{"title":"Optimal Design of Reliability Acceptance Sampling Plan Based on Sequential Order Statistics","authors":"Mahesh Kumar, P. C. Ramyamol","doi":"10.1515/eqc-2019-0012","DOIUrl":"https://doi.org/10.1515/eqc-2019-0012","url":null,"abstract":"Abstract The concept of sequential order statistics were introduced by Kamps in 1995. In this article, we derive an acceptance sampling plan, for units having exponentially distributed lifetime, using sequential order statistics. Based on data obtained from progressive type II censoring using constant stress accelerated life tests, we obtain the maximum likelihood estimates of the parameters of the exponential distribution. Further, a log linear life-stress relationship is assumed to derive the exact distributions of the estimators of the parameters of exponential distribution. The parameters of the sampling scheme are obtained by minimizing expected total testing cost satisfying usual probability requirements. Some numerical results are presented in a table to illustrate our plans.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"29 1","pages":"87 - 94"},"PeriodicalIF":0.0,"publicationDate":"2019-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77459681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper deals with a new method of deriving the Process Capability Index (PCI) when the quality characteristic X follows a positively skewed distribution. The focus of the paper is to derive a new estimate of PCI by taking into account the 100 ( 1 - α ) {100(1-{alpha})} Confidence Intervals (CI) of the parameter (s) and arriving at a new expression. The formula C s {{C}_{{s}}} , proposed by Wright (1995) which contains a component for skewness, is reexamined and a new estimate is constructed by utilizing the lower, middle and upper values of the CI of the parameter. The weighted average of the three possible estimates of C s {{C}_{{s}}} is proposed as the new estimate by taking the weights inversely proportional to the squared deviation from the hypothetical value of C s {{C}_{{s}}} . The properties of the estimate are studied by simulation using one parameter exponential distribution.
摘要本文研究了当质量特性X服从正偏态分布时，求过程能力指数(PCI)的一种新方法。本文的重点是通过考虑参数(s)的100次方(1- α) {100(1-{alpha})}置信区间(CI)并得到一个新的表达式，推导出PCI的一个新的估计。对Wright(1995)提出的包含偏度分量的公式C s {{C}_{{s}}}进行重新检验，并利用参数CI的下、中、上值构造新的估计。将C s {{C}_{{s}}}的三个可能估计的加权平均值作为新的估计，其权重与C s {{C}_{{s}}}的假设值的方差成反比。通过单参数指数分布的仿真研究了估计的性质。
{"title":"A New Method of Estimating the Process Capability Index with Exponential Distribution Using Interval Estimate of the Parameter","authors":"S. Vedururu, M. Subbarayudu, K. Sarma","doi":"10.1515/eqc-2019-0005","DOIUrl":"https://doi.org/10.1515/eqc-2019-0005","url":null,"abstract":"Abstract This paper deals with a new method of deriving the Process Capability Index (PCI) when the quality characteristic X follows a positively skewed distribution. The focus of the paper is to derive a new estimate of PCI by taking into account the 100 ( 1 - α ) {100(1-{alpha})} Confidence Intervals (CI) of the parameter (s) and arriving at a new expression. The formula C s {{C}_{{s}}} , proposed by Wright (1995) which contains a component for skewness, is reexamined and a new estimate is constructed by utilizing the lower, middle and upper values of the CI of the parameter. The weighted average of the three possible estimates of C s {{C}_{{s}}} is proposed as the new estimate by taking the weights inversely proportional to the squared deviation from the hypothetical value of C s {{C}_{{s}}} . The properties of the estimate are studied by simulation using one parameter exponential distribution.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"19 1","pages":"102 - 95"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81722940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Recently, G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini [G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini, On dynamic weighted survival entropy of order α, Comm. Statist. Theory Methods 46 2017, 5, 2139–2150] proposed a measure of uncertainty based on the survival function called weighted survival entropy of order α. They have also introduced the dynamic form of a measure called dynamic weighted survival entropy of order α and studied various properties in the context of reliability modeling. In this paper, we extend these measures into the bivariate setup and study its properties. We also look into the problem of extending the same measure for conditionally specified models. Empirical and non-parametric estimators are suggested for the proposed measure using the conditionally specified model, and the effect of the proposed estimators is illustrated using simulated and real data sets.
最近，G. Rajesh, E. I.;Abdul-Sathar和S. Nair Rohini [G.]拉杰什，e。王晓明，一种动态加权生存熵的研究方法，数学学报。理论方法[46,2017,5,2139-2150]提出了一种基于生存函数的不确定性度量，称为阶α加权生存熵。他们还介绍了一种称为阶α动态加权生存熵的度量的动态形式，并研究了可靠性建模背景下的各种特性。在本文中，我们将这些度量推广到二元设置中，并研究了它的性质。我们还研究了对条件指定模型的相同测度的扩展问题。利用条件指定模型提出了经验估计量和非参数估计量，并用模拟和实际数据集说明了所提出估计量的效果。
{"title":"Bivariate Dynamic Weighted Survival Entropy of Order 𝛼","authors":"S. Nair Rohini, E. I. Abdul Sathar","doi":"10.1515/eqc-2018-0032","DOIUrl":"https://doi.org/10.1515/eqc-2018-0032","url":null,"abstract":"Abstract Recently, G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini [G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini, On dynamic weighted survival entropy of order α, Comm. Statist. Theory Methods 46 2017, 5, 2139–2150] proposed a measure of uncertainty based on the survival function called weighted survival entropy of order α. They have also introduced the dynamic form of a measure called dynamic weighted survival entropy of order α and studied various properties in the context of reliability modeling. In this paper, we extend these measures into the bivariate setup and study its properties. We also look into the problem of extending the same measure for conditionally specified models. Empirical and non-parametric estimators are suggested for the proposed measure using the conditionally specified model, and the effect of the proposed estimators is illustrated using simulated and real data sets.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"27 1","pages":"67 - 85"},"PeriodicalIF":0.0,"publicationDate":"2019-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76026638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Simultaneous optimization of multiple quality characteristics (responses) of a product or process is required in many real-world problems. Multiresponse optimization (MRO) techniques tries to solve such problems; the ultimate objective of which is to adjust control factors that provides most desired values for the responses. Regression techniques are most commonly used methods to identify and estimate relationships between control variables and responses. Due to the industrial advances and hence the complexity of processes and systems, many relationships between input variables and quality characteristics have become much more complex. In such circumstances, classic regression techniques encounter difficulties to create a well-fitted model which can be easily optimized. The alternative approach proposed in this study is a regression tree method called CART, which is a data mining method. Since the output of CART consists of several if-then terms, NSGA-II algorithm was considered to solve the model and achieve the optimal solutions. Finally, we evaluate performance of the proposed method with a real data set about modeling and improvement of automotive engines.
{"title":"Developing a Flexible Methodology for Modeling and Solving Multiple Response Optimization Problems","authors":"T. Hejazi, M. Moradpour","doi":"10.1515/eqc-2018-0024","DOIUrl":"https://doi.org/10.1515/eqc-2018-0024","url":null,"abstract":"Abstract Simultaneous optimization of multiple quality characteristics (responses) of a product or process is required in many real-world problems. Multiresponse optimization (MRO) techniques tries to solve such problems; the ultimate objective of which is to adjust control factors that provides most desired values for the responses. Regression techniques are most commonly used methods to identify and estimate relationships between control variables and responses. Due to the industrial advances and hence the complexity of processes and systems, many relationships between input variables and quality characteristics have become much more complex. In such circumstances, classic regression techniques encounter difficulties to create a well-fitted model which can be easily optimized. The alternative approach proposed in this study is a regression tree method called CART, which is a data mining method. Since the output of CART consists of several if-then terms, NSGA-II algorithm was considered to solve the model and achieve the optimal solutions. Finally, we evaluate performance of the proposed method with a real data set about modeling and improvement of automotive engines.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"24 1","pages":"103 - 113"},"PeriodicalIF":0.0,"publicationDate":"2019-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75944825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The production network under examination consists of a number of workstations. Each workstation is a parallel configuration of machines performing the same kind of tasks on a given part. Parts move from one workstation to another and at each workstation a part is assigned randomly to a machine. We assume that the production network is acyclic, that is, a part does not return to a workstation where it previously received service. Furthermore, we assume that the quality of the end product is additive, that is, the sum of the quality contributions of the machines along the production path. The contribution of each machine is modeled by a separate random variable. Our main result is the construction of estimators that allow pairwise and multiple comparison of the means and variances of machines in the same workstation. These comparisons then may lead to the identification of unreliable machines. We also discuss the asymptotic distributions of the estimators that allow the use of standard statistical tests and decision making.
{"title":"Quality Analysis in Acyclic Production Networks","authors":"Abraham Gutierrez, Sebastian Mueller","doi":"10.1515/eqc-2019-0014","DOIUrl":"https://doi.org/10.1515/eqc-2019-0014","url":null,"abstract":"Abstract The production network under examination consists of a number of workstations. Each workstation is a parallel configuration of machines performing the same kind of tasks on a given part. Parts move from one workstation to another and at each workstation a part is assigned randomly to a machine. We assume that the production network is acyclic, that is, a part does not return to a workstation where it previously received service. Furthermore, we assume that the quality of the end product is additive, that is, the sum of the quality contributions of the machines along the production path. The contribution of each machine is modeled by a separate random variable. Our main result is the construction of estimators that allow pairwise and multiple comparison of the means and variances of machines in the same workstation. These comparisons then may lead to the identification of unreliable machines. We also discuss the asymptotic distributions of the estimators that allow the use of standard statistical tests and decision making.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"31 8","pages":"59 - 66"},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/eqc-2019-0014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72412892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The major drawback of wind energy relies in its variability in time, which necessitates specific strategies to be settled. One such strategy can be the coordination of wind power production with a co-located power generation of dispatchable energy source (DES), e.g., thermal power station, combined heat and power plant, gas turbine or compressed air energy storage. In this paper, we consider an energy producer that generates power by means of a wind park and of a DES and sells the produced energy to an isolated grid. We determine the optimal quantity of energy produced by a DES, given the unit cost of this energy, that a power producer should buy and use to hedge against the risk inherent in the production of energy through wind turbines. We determine the optimal quantity by solving a static optimization problem taking into account the possible dependence between the amount of energy produced by wind turbines and electricity prices by using a copula function. Several particular cases are studied that allow the determination of the optimal solution in an analytical closed form. Finally, a numerical example concerning a real 48 MW wind farm located in Poland and Polish Power Exchange shows the possibility of implementing the model in real-life problems.
{"title":"Optimal Control of a Dispatchable Energy Source for Wind Energy Management","authors":"G. D’Amico, F. Petroni, R. A. Sobolewski","doi":"10.1515/eqc-2019-0001","DOIUrl":"https://doi.org/10.1515/eqc-2019-0001","url":null,"abstract":"Abstract The major drawback of wind energy relies in its variability in time, which necessitates specific strategies to be settled. One such strategy can be the coordination of wind power production with a co-located power generation of dispatchable energy source (DES), e.g., thermal power station, combined heat and power plant, gas turbine or compressed air energy storage. In this paper, we consider an energy producer that generates power by means of a wind park and of a DES and sells the produced energy to an isolated grid. We determine the optimal quantity of energy produced by a DES, given the unit cost of this energy, that a power producer should buy and use to hedge against the risk inherent in the production of energy through wind turbines. We determine the optimal quantity by solving a static optimization problem taking into account the possible dependence between the amount of energy produced by wind turbines and electricity prices by using a copula function. Several particular cases are studied that allow the determination of the optimal solution in an analytical closed form. Finally, a numerical example concerning a real 48 MW wind farm located in Poland and Polish Power Exchange shows the possibility of implementing the model in real-life problems.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"11 1","pages":"19 - 34"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79788250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Di Crescenzo and Longobardi [Di Crescenzo and Longobardi, On cumulative entropies, J. Statist. Plann. Inference 139 2009, 12, 4072–4087] proposed the cumulative entropy (CE) as an alternative to the differential entropy. They presented an estimator of CE using empirical approach. In this paper, we consider a risk measure based on CE and compare it with the standard deviation and the Gini mean difference for some distributions. We also make empirical comparisons of these measures using samples from stock market in members of the Organization for Economic Co-operation and Development (OECD) countries.
[摘要]Di Crescenzo and Longobardi, On cumulative entropy， [j]。Plann。[j] [Inference][139, 2009, 12, 4072-4087]提出累积熵(CE)作为微分熵的替代方法。他们提出了一个使用经验方法的CE估计。在本文中，我们考虑了一种基于CE的风险度量，并将其与一些分布的标准差和基尼均值差进行了比较。我们还利用经济合作与发展组织(OECD)成员国股票市场的样本对这些措施进行了实证比较。
{"title":"Notes on Cumulative Entropy as a Risk Measure","authors":"S. Tahmasebi, H. Parsa","doi":"10.1515/eqc-2018-0019","DOIUrl":"https://doi.org/10.1515/eqc-2018-0019","url":null,"abstract":"Abstract Di Crescenzo and Longobardi [Di Crescenzo and Longobardi, On cumulative entropies, J. Statist. Plann. Inference 139 2009, 12, 4072–4087] proposed the cumulative entropy (CE) as an alternative to the differential entropy. They presented an estimator of CE using empirical approach. In this paper, we consider a risk measure based on CE and compare it with the standard deviation and the Gini mean difference for some distributions. We also make empirical comparisons of these measures using samples from stock market in members of the Organization for Economic Co-operation and Development (OECD) countries.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"35 1","pages":"1 - 7"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73722068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract If the distribution of the linear combination of two independent and identically distributed random variables from a distribution belongs to the same distribution, then we call that distribution a stable distribution. The Levy distribution is a member of the family of stable distributions. In this paper, we will present some basic distributional properties and characterizations of the Levy distribution.
{"title":"On Some Characterizations of the Levy Distribution","authors":"M. Ahsanullah, V. Nevzorov","doi":"10.1515/eqc-2018-0031","DOIUrl":"https://doi.org/10.1515/eqc-2018-0031","url":null,"abstract":"Abstract If the distribution of the linear combination of two independent and identically distributed random variables from a distribution belongs to the same distribution, then we call that distribution a stable distribution. The Levy distribution is a member of the family of stable distributions. In this paper, we will present some basic distributional properties and characterizations of the Levy distribution.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"27 1","pages":"53 - 57"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82385708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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