Stochastics and Quality Control最新文献

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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>&gt;</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {t&gt;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}

{"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}

{"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}

{"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}