This research focuses on stochastic modeling of the evolution over time of biological populations through branching processes. We introduce a new class of discrete time two-sex branching processes with random mating and overlapping generations. Mating and reproduction are considered to be influenced by the numbers of females and males existing in the population. This evolution over time with generational overlap is a novel research in two-sex branching process literature. We study general probabilistic properties and establish some limiting results of biological interest.
{"title":"Population Dependent Two-Sex Branching Process with Random Mating and Overlapping Generations","authors":"Manuel Molina, Manuel Mota","doi":"10.1515/eqc-2024-0008","DOIUrl":"https://doi.org/10.1515/eqc-2024-0008","url":null,"abstract":"\u0000 This research focuses on stochastic modeling of the evolution over time of biological populations through branching processes. We introduce a new class of discrete time two-sex branching processes with random mating and overlapping generations. Mating and reproduction are considered to be influenced by the numbers of females and males existing in the population. This evolution over time with generational overlap is a novel research in two-sex branching process literature. We study general probabilistic properties and establish some limiting results of biological interest.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"13 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140963416","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}
Fatemeh Eskandari-Kataki, M. Owlia, samrad Jafarian-Namin
We aim to extend the Markov System Dynamic method (MSD) to evaluate the reliability of repairable systems in two-state weather (2SW) models. Increasing the number of components in real practices has limited the use of the Markov method, because of increasing the number of equations and the complexity of the problem. There is no such restriction in the MSD method. Thus, it can be applied to complex systems. Theoretically, we indicate that the 2SW model is a type of linear dynamical system. Therefore, we can use MSD to solve it. Through an example, the validity of the proposed method is confirmed in comparison to the Markov method for the 2SW model. Since the MSD method does not use equations, it can be a preferred alternative for calculating the reliability of 2SW models. Accordingly, we apply the MSD method for assessing the reliability of a four-component system.
{"title":"Assessment of Reliability of Power Systems Under Adverse Weather Condition Using Markov System Dynamic Method","authors":"Fatemeh Eskandari-Kataki, M. Owlia, samrad Jafarian-Namin","doi":"10.1515/eqc-2023-0022","DOIUrl":"https://doi.org/10.1515/eqc-2023-0022","url":null,"abstract":"\u0000 We aim to extend the Markov System Dynamic method (MSD) to evaluate the reliability of repairable systems in two-state weather (2SW) models. Increasing the number of components in real practices has limited the use of the Markov method, because of increasing the number of equations and the complexity of the problem. There is no such restriction in the MSD method. Thus, it can be applied to complex systems. Theoretically, we indicate that the 2SW model is a type of linear dynamical system. Therefore, we can use MSD to solve it. Through an example, the validity of the proposed method is confirmed in comparison to the Markov method for the 2SW model. Since the MSD method does not use equations, it can be a preferred alternative for calculating the reliability of 2SW models. Accordingly, we apply the MSD method for assessing the reliability of a four-component system.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"12 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141004877","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}
The probability generating function (pgf) B(s){B(s)} of the limiting conditional law (LCL) of a subcritical Markov branching process (Zt:t≥0){(Z_{t}:tgeq 0)} (MBP) has a certain integral representation and it satisfies B(0)
亚临界马尔可夫分支过程（ Z t : t ≥ 0 ）的极限条件律（ LCL ）的概率产生函数（ pgf ） B ( s ) {B(s)} 具有一定的积分表示，它满足 B ( 0 ) = 0 {B(0)=0} 和 B ′ ( 0 ) > 0 {B(0)=0} 的条件。 {(Z_{t}:tgeq 0)} (MBP) 有一定的积分表示，它满足 B ( 0 ) = 0 {B(0)=0} 和 B ′ ( 0 ) > 0 {B^{prime}(0)>0} 。这里提出的一般问题是逆问题：如果给定的 pgf B 满足这两个条件，那么它是否与某个 MBP 有关联呢？我们将得到一些必要条件，并用简单的例子和反例来说明这个问题。博尔定律的特殊情况被证明是 MBP 家族的 LCL，并且概率 P 1 ( Z t = j ) {P_{1}(Z_{t}=j)} 具有简单明了的代数表达式。我们还找到了移位负二项式定律成为 LCL 的精确条件。最后，探讨了相关 LCL 的无限可分性对子代规律的影响。
{"title":"On Subcritical Markov Branching Processes with a Specified Limiting Conditional Law","authors":"Assen Tchorbadjieff, Penka Mayster, A. Pakes","doi":"10.1515/eqc-2023-0043","DOIUrl":"https://doi.org/10.1515/eqc-2023-0043","url":null,"abstract":"\u0000 <jats:p>The probability generating function (pgf) <jats:inline-formula id=\"j_eqc-2023-0043_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mi>B</m:mi>\u0000 <m:mo></m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mi>s</m:mi>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_eqc-2023-0043_eq_0176.png\" />\u0000 <jats:tex-math>{B(s)}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> of the limiting conditional law (LCL) of a subcritical Markov branching process <jats:inline-formula id=\"j_eqc-2023-0043_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mrow>\u0000 <m:msub>\u0000 <m:mi>Z</m:mi>\u0000 <m:mi>t</m:mi>\u0000 </m:msub>\u0000 <m:mo>:</m:mo>\u0000 <m:mrow>\u0000 <m:mi>t</m:mi>\u0000 <m:mo>≥</m:mo>\u0000 <m:mn>0</m:mn>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_eqc-2023-0043_eq_0131.png\" />\u0000 <jats:tex-math>{(Z_{t}:tgeq 0)}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> (MBP) has a certain integral representation and it satisfies <jats:inline-formula id=\"j_eqc-2023-0043_ineq_9997\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mrow>\u0000 <m:mi>B</m:mi>\u0000 <m:mo></m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mn>0</m:mn>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 ","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"123 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140380321","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}
In this study, we propose a Bayesian Extended Exponentially Weighted Moving Average (BEEWMA) control chart. We have considered that the control chart statistic follows a normal distribution and the location parameter has an informative prior (normal). Average run length (ARL) has been used to evaluate the performance of the BEEWMA control chart. A simulation study has been performed to evaluate the new BEEWMA control chart’s performance for different smoothing constants values. The performance of the proposed control chart is also measured using a real-life application.
{"title":"A Bayesian Extended Exponentially Weighted Moving Average Control Chart","authors":"Souradeep Das, Sudhansu S. Maiti","doi":"10.1515/eqc-2023-0021","DOIUrl":"https://doi.org/10.1515/eqc-2023-0021","url":null,"abstract":"\u0000 In this study, we propose a Bayesian Extended Exponentially Weighted Moving Average (BEEWMA) control chart. We have considered that the control chart statistic follows a normal distribution and the location parameter has an informative prior (normal). Average run length (ARL) has been used to evaluate the performance of the BEEWMA control chart.\u0000A simulation study has been performed to evaluate the new BEEWMA control chart’s performance for different smoothing constants values. The performance of the proposed control chart is also measured using a real-life application.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"17 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140477504","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}
We consider a special class of Galton–Watson theta-processes in a varying environment fully defined by four parameters, with two of them (θ,r){(theta,r)} being fixed over time n, and the other two (an,cn){(a_{n},c_{n})} characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton–Watson processes in a varying environment.
我们考虑一类特殊的加尔顿-沃森 Theta 过程，它处于完全由四个参数定义的变化环境中，其中两个参数 ( θ , r ) {(theta,r)} 在时间 n 上是固定的，另外两个 ( a n , c n ) {(a_{n},c_{n})}表征不断变化的再生产规律。我们为可能存在缺陷的再生产规律的θ过程建立了一系列透明极限定理。这些结果可以作为通向变化环境中加尔顿-沃森过程的精辟一般结果的垫脚石。
{"title":"Galton–Watson Theta-Processes in a Varying Environment","authors":"S. Sagitov, Yerakhmet Zhumayev","doi":"10.1515/eqc-2024-0001","DOIUrl":"https://doi.org/10.1515/eqc-2024-0001","url":null,"abstract":"\u0000 <jats:p>We consider a special class of Galton–Watson theta-processes in a varying environment fully defined by four parameters, with two of them <jats:inline-formula id=\"j_eqc-2024-0001_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mi>θ</m:mi>\u0000 <m:mo>,</m:mo>\u0000 <m:mi>r</m:mi>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_eqc-2024-0001_eq_0224.png\" />\u0000 <jats:tex-math>{(theta,r)}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> being fixed over time <jats:italic>n</jats:italic>, and the other two <jats:inline-formula id=\"j_eqc-2024-0001_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:msub>\u0000 <m:mi>a</m:mi>\u0000 <m:mi>n</m:mi>\u0000 </m:msub>\u0000 <m:mo>,</m:mo>\u0000 <m:msub>\u0000 <m:mi>c</m:mi>\u0000 <m:mi>n</m:mi>\u0000 </m:msub>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_eqc-2024-0001_eq_0227.png\" />\u0000 <jats:tex-math>{(a_{n},c_{n})}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton–Watson processes in a varying environment.</jats:p>","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"45 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140507898","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 Artificial neural networks (NNs) have been extensively studied for their application to quality control (QC) to monitor the conformity of processes to quality specifications. However, the requirement of at least five QC measurements increases the associated costs. This study explores the potential of using NNs on samples of QC measurements of very small size. To achieve this, three one-dimensional (1-D) convolutional NNs (CNNs) were designed, trained, and tested on datasets of n -tuples of simulated, standardized, normally distributed QC measurements, where 2≤n≤4 {2leq nleq 4} . The performance of the designed CNNs was compared to that of statistical QC functions applied to samples of equal sizes, maintaining equal probabilities for false rejection. The results demonstrated that for n -tuples of QC measurements distributed as 𝒩(0,s2) mathscr{N}(0,s^{2}) , where 1.2<s≤9.0 1.2
{"title":"Quality Control Using Convolutional Neural Networks Applied to Samples of Very Small Size","authors":"Rallou A. Chatzimichail, Aristides T. Hatjimihail","doi":"10.1515/eqc-2023-0001","DOIUrl":"https://doi.org/10.1515/eqc-2023-0001","url":null,"abstract":"Abstract Artificial neural networks (NNs) have been extensively studied for their application to quality control (QC) to monitor the conformity of processes to quality specifications. However, the requirement of at least five QC measurements increases the associated costs. This study explores the potential of using NNs on samples of QC measurements of very small size. To achieve this, three one-dimensional (1-D) convolutional NNs (CNNs) were designed, trained, and tested on datasets of n -tuples of simulated, standardized, normally distributed QC measurements, where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>2</m:mn> <m:mo>≤</m:mo> <m:mi>n</m:mi> <m:mo>≤</m:mo> <m:mn>4</m:mn> </m:mrow> </m:math> {2leq nleq 4} . The performance of the designed CNNs was compared to that of statistical QC functions applied to samples of equal sizes, maintaining equal probabilities for false rejection. The results demonstrated that for n -tuples of QC measurements distributed as <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"script\">𝒩</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:msup> <m:mi>s</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> mathscr{N}(0,s^{2}) , where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>1.2</m:mn> <m:mo><</m:mo> <m:mi>s</m:mi> <m:mo>≤</m:mo> <m:mn>9.0</m:mn> </m:mrow> </m:math> 1.2<sleq 9.0 , the designed CNNs outperformed their statistical QC functions counterparts. Therefore, the use of 1-D CNNs applied to samples of two to four QC measurements can effectively enhance the detection of nonconformity of a process to quality specifications. This approach has the potential to significantly reduce the costs of QC measurements and improve the overall efficiency of the QC process.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135875198","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 We given an elementary proof that in a Markov chain with absorbing states, and positive probability of absorption at some time t>0 {t>0} , time to absorption follows a mixture distribution of hypo-exponential random variables. We use this fact to show that early approximations of such a distribution yield the length of the shortest path from an initial state to an absorbing state. Thus different Markov chains with the same distance of shortest paths can yield identical first order approximations. Our work is motivated by the classical Armitage and Doll model of carcinogenesis.
{"title":"Time to Absorption in Markov Chains as a Mixture Distribution of Hypo-Exponential Distributions","authors":"Josh Hiller","doi":"10.1515/eqc-2023-0028","DOIUrl":"https://doi.org/10.1515/eqc-2023-0028","url":null,"abstract":"Abstract We given an elementary proof that in a Markov chain with absorbing states, and positive probability of absorption at some time <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>t</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {t>0} , time to absorption follows a mixture distribution of hypo-exponential random variables. We use this fact to show that early approximations of such a distribution yield the length of the shortest path from an initial state to an absorbing state. Thus different Markov chains with the same distance of shortest paths can yield identical first order approximations. Our work is motivated by the classical Armitage and Doll model of carcinogenesis.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"79 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234072","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 Many quality characteristics in manufacturing industry are of one sided specifications. The well-known process capability indices CPU C_{PU} and CPL C_{PL} are often used to measure the performance of such type of production process. It is usually assumed that process observations are independent and measurement system is free of errors. But actually in many industry it has been proven that auto-correlation is an inherent nature of the production process, especially for chemical processes. Moreover, even with the use of highly sophisticated advanced measuring instruments some amount of measurement error is always present in the observed data. Hence gauge measurement error also needs to be considered. In this paper we discuss some inferential properties of one-sided process capability indices for a stationary Gaussian process in the presence of measurement errors. As a particular case of a stationary Gaussian process, we discuss the case of a stationary AR(1) operatorname{AR}(1) process where measurement error follows an independent Gaussian distribution.
制造业的许多质量特征都是片面的。众所周知的过程能力指标cp _ U C_{PU}和cp _ L C_{PL}经常被用来衡量这类生产过程的性能。通常假设过程观测是独立的，测量系统没有误差。但实际上，在许多行业中已经证明，自相关是生产过程的固有性质，特别是对于化学过程。此外，即使使用高度精密的先进测量仪器，在观测数据中也总是存在一定数量的测量误差。因此，还需要考虑量规测量误差。本文讨论了存在测量误差的平稳高斯过程单侧过程能力指标的一些推论性质。作为平稳高斯过程的一个特例，我们讨论了测量误差服从独立高斯分布的平稳AR (1) operatorname{AR}(1)过程的情况。
{"title":"Measuring One-Sided Process Capability Index for Autocorrelated Data in the Presence of Random Measurement Errors","authors":"Kuntal Bera, M. Z. Anis","doi":"10.1515/eqc-2023-0020","DOIUrl":"https://doi.org/10.1515/eqc-2023-0020","url":null,"abstract":"Abstract Many quality characteristics in manufacturing industry are of one sided specifications. The well-known process capability indices <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>C</m:mi> <m:mrow> <m:mi>P</m:mi> <m:mo></m:mo> <m:mi>U</m:mi> </m:mrow> </m:msub> </m:math> C_{PU} and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>C</m:mi> <m:mrow> <m:mi>P</m:mi> <m:mo></m:mo> <m:mi>L</m:mi> </m:mrow> </m:msub> </m:math> C_{PL} are often used to measure the performance of such type of production process. It is usually assumed that process observations are independent and measurement system is free of errors. But actually in many industry it has been proven that auto-correlation is an inherent nature of the production process, especially for chemical processes. Moreover, even with the use of highly sophisticated advanced measuring instruments some amount of measurement error is always present in the observed data. Hence gauge measurement error also needs to be considered. In this paper we discuss some inferential properties of one-sided process capability indices for a stationary Gaussian process in the presence of measurement errors. As a particular case of a stationary Gaussian process, we discuss the case of a stationary <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>AR</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mn>1</m:mn> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> operatorname{AR}(1) process where measurement error follows an independent Gaussian distribution.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135548687","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 Classical Hotelling’s T2 T^{2} control chart is frequently used for monitoring a multivariate process. The existence of outlying observations in the Phase I data used to determine the control limit can have a significant impact on the accuracy of such control charts, as is well known. Based on the robust reweighted orthogonalized comedian estimates, a robust multivariate quality control chart for individual observations is proposed in this study. Control limit of the proposed robust control chart is estimated by modelling the simulated quantiles for any sample size. A Simulation study has been conducted to examine the performance of the proposed method and compare it with the performances of the classical Hotelling T2 T^{2} control chart, a robust control chart based on shrinkage reweighted estimator and two robust control charts based on the reweighted minimum covariance determinant estimator. The results demonstrate the effectiveness of the proposed method, even under high-dimensional settings or when the contamination in the Phase I data is high, with both independent and correlated variables. Performance of the proposed method is also illustrated by implementing in a real-world example
经典的Hotelling的T^{2}控制图经常用于监测一个多变量过程。众所周知，用于确定控制极限的第一阶段数据中存在的外围观测值会对此类控制图的准确性产生重大影响。基于鲁棒的重加权正交喜剧演员估计，本文提出了一个鲁棒的多变量质量控制图。通过对任意样本量的模拟分位数进行建模来估计所提出的鲁棒控制图的控制极限。通过仿真研究验证了该方法的性能，并将其与经典的Hotelling T 2 T^{2}控制图、基于收缩再加权估计量的鲁棒控制图和基于再加权最小协方差行列估计量的两种鲁棒控制图的性能进行了比较。结果证明了所提出方法的有效性，即使在高维设置或第一阶段数据中的污染很高的情况下，具有独立和相关变量。最后，通过实例验证了该方法的性能
{"title":"Enhancing Multivariate Control Charts for Individual Observations Using ROC Estimates","authors":"S. Vijayalakshmi, Nicy Sebastian, T. A. Sajesh","doi":"10.1515/eqc-2023-0023","DOIUrl":"https://doi.org/10.1515/eqc-2023-0023","url":null,"abstract":"Abstract Classical Hotelling’s <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>T</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> T^{2} control chart is frequently used for monitoring a multivariate process. The existence of outlying observations in the Phase I data used to determine the control limit can have a significant impact on the accuracy of such control charts, as is well known. Based on the robust reweighted orthogonalized comedian estimates, a robust multivariate quality control chart for individual observations is proposed in this study. Control limit of the proposed robust control chart is estimated by modelling the simulated quantiles for any sample size. A Simulation study has been conducted to examine the performance of the proposed method and compare it with the performances of the classical Hotelling <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>T</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> T^{2} control chart, a robust control chart based on shrinkage reweighted estimator and two robust control charts based on the reweighted minimum covariance determinant estimator. The results demonstrate the effectiveness of the proposed method, even under high-dimensional settings or when the contamination in the Phase I data is high, with both independent and correlated variables. Performance of the proposed method is also illustrated by implementing in a real-world example","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135548386","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 study develops a higher-order Markov model (HOM) for an inventory system with remanufacturing, substitution, and lost sales. Defective and disposed items are other factors that are considered in addition to probabilistic demand for both manufacturing and remanufacturing items. One year is the warranty period for items manufactured, and items sold return from customers to the manufacturer in increasing cumulative percentages over the months of the year. To the best our knowledge, a higher-order Markov model has rarely been used in a hybrid inventory system. The challenge is how to determine the steady state of the system with the probable demand for manufacturing and remanufacturing. We propose a new search algorithm to select the best control strategy from several strategies, and then compare it with the two-phase local search algorithm. Each state deals with (12) a probabilistic demand (policy), so the system steady state is set to (22632) policies in total for each production plan. The results showed profit maximization using the new search algorithm compared with the two-phase local search algorithm. Also, an increase in defective and returned items over time, and therefore an increase in remanufactured items. But it does not satisfy all the demand, so manufacturing increases over time due to substitution. Substitution strategy leads to increase the expected average profit.
{"title":"A Higher-Order Markov Model for a Hybrid Inventory System with Probabilistic Remanufacturing Demand","authors":"Ali Khaleel Dhaiban","doi":"10.1515/eqc-2022-0050","DOIUrl":"https://doi.org/10.1515/eqc-2022-0050","url":null,"abstract":"Abstract This study develops a higher-order Markov model (HOM) for an inventory system with remanufacturing, substitution, and lost sales. Defective and disposed items are other factors that are considered in addition to probabilistic demand for both manufacturing and remanufacturing items. One year is the warranty period for items manufactured, and items sold return from customers to the manufacturer in increasing cumulative percentages over the months of the year. To the best our knowledge, a higher-order Markov model has rarely been used in a hybrid inventory system. The challenge is how to determine the steady state of the system with the probable demand for manufacturing and remanufacturing. We propose a new search algorithm to select the best control strategy from several strategies, and then compare it with the two-phase local search algorithm. Each state deals with (12) a probabilistic demand (policy), so the system steady state is set to (22632) policies in total for each production plan. The results showed profit maximization using the new search algorithm compared with the two-phase local search algorithm. Also, an increase in defective and returned items over time, and therefore an increase in remanufactured items. But it does not satisfy all the demand, so manufacturing increases over time due to substitution. Substitution strategy leads to increase the expected average profit.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83710368","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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