Pub Date : 2022-01-03DOI: 10.1080/16843703.2021.2015834
Somayeh Khalili, R. Noorossana
ABSTRACT Multivariate multiple profile monitoring has been studied extensively over the past few years. Most of these studies assumed that the observations are uncorrelated, which could be violated in practice. In this paper, multivariate linear mixed model is proposed to allow correlation among observations of the multivariate multiple linear profiles. In order to monitor random effects and process variability in phase II, three control charts are suggested. The results of performance comparisons with an existing method show the superiority of the proposed control chart. Finally, the applicability of the proposed method is illustrated using a real case.
{"title":"Online monitoring of autocorrelated multivariate linear profiles via multivariate mixed models","authors":"Somayeh Khalili, R. Noorossana","doi":"10.1080/16843703.2021.2015834","DOIUrl":"https://doi.org/10.1080/16843703.2021.2015834","url":null,"abstract":"ABSTRACT Multivariate multiple profile monitoring has been studied extensively over the past few years. Most of these studies assumed that the observations are uncorrelated, which could be violated in practice. In this paper, multivariate linear mixed model is proposed to allow correlation among observations of the multivariate multiple linear profiles. In order to monitor random effects and process variability in phase II, three control charts are suggested. The results of performance comparisons with an existing method show the superiority of the proposed control chart. Finally, the applicability of the proposed method is illustrated using a real case.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"319 - 340"},"PeriodicalIF":2.8,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41340321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-03DOI: 10.1080/16843703.2021.2015826
Shanshan Lv, Zhen He, Guodong Wang, G. Vining
ABSTRACT Product quality and reliability characteristics are important considerations for all manufacturers in the product and process design. Industrial experiments may include both quality and reliability characteristics with the goal to obtain a compromise optimization of the two responses. In many cases, such experiments do not use a completely randomized design. Instead, they involve a more complicated experimental protocol, for example, subsampling, blocking, and split-plot structure. This paper presents a framework for the simultaneous optimization of quality and reliability characteristics with random effects. The paper provides a linear mixed model for quality characteristic and a nonlinear mixed model for Type I censored lifetime to incorporate random effects in the analysis. Subsequently, the desirability function approach is used to obtain a trade-off between the quality and reliability characteristics. The mixed models in this paper can incorporate information from all censored test stands and random effects. The proposed framework provides engineers with an appropriate approach to simultaneously optimize the quality and reliability characteristics with random effects. The paper used a case study to illustrate the proposed framework. A simulation study is also considered to present the necessary of incorporating random effects in the modelling stage.
{"title":"Simultaneous optimization of quality and censored reliability characteristics with constrained randomization experiment","authors":"Shanshan Lv, Zhen He, Guodong Wang, G. Vining","doi":"10.1080/16843703.2021.2015826","DOIUrl":"https://doi.org/10.1080/16843703.2021.2015826","url":null,"abstract":"ABSTRACT Product quality and reliability characteristics are important considerations for all manufacturers in the product and process design. Industrial experiments may include both quality and reliability characteristics with the goal to obtain a compromise optimization of the two responses. In many cases, such experiments do not use a completely randomized design. Instead, they involve a more complicated experimental protocol, for example, subsampling, blocking, and split-plot structure. This paper presents a framework for the simultaneous optimization of quality and reliability characteristics with random effects. The paper provides a linear mixed model for quality characteristic and a nonlinear mixed model for Type I censored lifetime to incorporate random effects in the analysis. Subsequently, the desirability function approach is used to obtain a trade-off between the quality and reliability characteristics. The mixed models in this paper can incorporate information from all censored test stands and random effects. The proposed framework provides engineers with an appropriate approach to simultaneously optimize the quality and reliability characteristics with random effects. The paper used a case study to illustrate the proposed framework. A simulation study is also considered to present the necessary of incorporating random effects in the modelling stage.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"299 - 318"},"PeriodicalIF":2.8,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42916403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-23DOI: 10.1080/16843703.2021.2015827
Florence Leony, Chen-ju Lin
ABSTRACT Process selection has been a focal task in operation management. This research focuses on finding alternatives to the current process that have to be at least as capable as the current process. Having multiple alternative processes available enables the manufacturers to have better resource utilization and scheduling flexibility. However, selecting the right process under non-normal data remains a challenge. Quality loss is a popular criterion because of its direct relationship with cost objectives. In this research, we propose the Cpp -based PO bootstrap approach to evaluate candidate processes based on quality loss by utilizing the incapability index. The Cpp index represents Taguchi’s Loss function k(x – T)2, which is suitable for the nominal-the-best type of quality characteristic. It measures production loss caused by process inaccuracy and imprecision. The experiments show that the proposed method can loosen up the reliance on normal assumption by controlling type I error and providing higher power compared to the extended method from the literature. The application to amplifier circuits manufacturing showed that the proposed method is effective to identify the inferior processes despite the severe departure of data from normal, while the opposed method built under normality assumption fails to do so.
{"title":"The PO bootstrap approach for comparing process incapability applied to non-normal process selection","authors":"Florence Leony, Chen-ju Lin","doi":"10.1080/16843703.2021.2015827","DOIUrl":"https://doi.org/10.1080/16843703.2021.2015827","url":null,"abstract":"ABSTRACT Process selection has been a focal task in operation management. This research focuses on finding alternatives to the current process that have to be at least as capable as the current process. Having multiple alternative processes available enables the manufacturers to have better resource utilization and scheduling flexibility. However, selecting the right process under non-normal data remains a challenge. Quality loss is a popular criterion because of its direct relationship with cost objectives. In this research, we propose the Cpp -based PO bootstrap approach to evaluate candidate processes based on quality loss by utilizing the incapability index. The Cpp index represents Taguchi’s Loss function k(x – T)2, which is suitable for the nominal-the-best type of quality characteristic. It measures production loss caused by process inaccuracy and imprecision. The experiments show that the proposed method can loosen up the reliance on normal assumption by controlling type I error and providing higher power compared to the extended method from the literature. The application to amplifier circuits manufacturing showed that the proposed method is effective to identify the inferior processes despite the severe departure of data from normal, while the opposed method built under normality assumption fails to do so.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"215 - 233"},"PeriodicalIF":2.8,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60299981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-13DOI: 10.1080/16843703.2021.1944966
Sumit Kumar, A. Yadav, S. Dey, Mahendra Saha
ABSTRACT In this article, to estimate the generalized process capability index (GPCI) Cpyk when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI Cpyk is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI Cpyk, and coverage probabilities (CPs), and average width (AW) for interval estimates. It is found that the Bayes estimates performed better than the considered classical estimates in terms of their corresponding MSEs. Further, the Bayes estimates based on linear-exponential loss function are more efficient than the squared error loss function under informative prior. To illustrate the performance of the proposed methods, two real data sets are analyzed.In this article, to estimate the generalized process capability index (GPCI) when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI , and coverage probabilities (CPs), and average width (AW) Abbreviations: AW : Average width; : Bias-corrected percentile bootstrap; BCI : Bootstrap confidence interval; CDF : Cumulative distribution function; CI : Confidence interval; CK : Coefficient of kurtosis; CP : Coverage probability; CS : Coefficient of skewness; GGD : Generalized gamma distribution; GPCI : Generalized process capability index; GLD : Generalized lindley distribution; SWCI : Shortest width credible interval; IS : Importance sampling; K-S : Kolmogorov-Smirnov; : Lower specification limi; LD : Lindley distribution; LDL : Lower desired limit LLF : Linex loss function; MCMC : Markov Chain Monte Carlo; MH : Metr
{"title":"Parametric inference of generalized process capability index Cpyk for the power Lindley distribution","authors":"Sumit Kumar, A. Yadav, S. Dey, Mahendra Saha","doi":"10.1080/16843703.2021.1944966","DOIUrl":"https://doi.org/10.1080/16843703.2021.1944966","url":null,"abstract":"ABSTRACT In this article, to estimate the generalized process capability index (GPCI) Cpyk when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI Cpyk is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI Cpyk, and coverage probabilities (CPs), and average width (AW) for interval estimates. It is found that the Bayes estimates performed better than the considered classical estimates in terms of their corresponding MSEs. Further, the Bayes estimates based on linear-exponential loss function are more efficient than the squared error loss function under informative prior. To illustrate the performance of the proposed methods, two real data sets are analyzed.In this article, to estimate the generalized process capability index (GPCI) when the process follows the power Lindley distribution, we have used five methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares method of estimation, the maximum product of spacings method of estimation, and Bayesian method of estimation. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential) loss functions with the help of the Metropolis-Hastings algorithm and importance sampling method. The confidence intervals for the GPCI is constructed based on three bootstrap methods and Bayesian methods. Besides, asymptotic confidence intervals based on maximum likelihood method is also constructed. We studied the performances of these estimators based on their corresponding biases and MSEs for the point estimates of GPCI , and coverage probabilities (CPs), and average width (AW) Abbreviations: AW : Average width; : Bias-corrected percentile bootstrap; BCI : Bootstrap confidence interval; CDF : Cumulative distribution function; CI : Confidence interval; CK : Coefficient of kurtosis; CP : Coverage probability; CS : Coefficient of skewness; GGD : Generalized gamma distribution; GPCI : Generalized process capability index; GLD : Generalized lindley distribution; SWCI : Shortest width credible interval; IS : Importance sampling; K-S : Kolmogorov-Smirnov; : Lower specification limi; LD : Lindley distribution; LDL : Lower desired limit LLF : Linex loss function; MCMC : Markov Chain Monte Carlo; MH : Metr","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"153 - 186"},"PeriodicalIF":2.8,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42593432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-01DOI: 10.1080/16843703.2021.1927295
Shih-Wen Liu, Chien-Wei Wu, Zih-Huei Wang
ABSTRACT A flexible sampling policy integrated with the consideration of past records is discussed in this paper for the quality evaluation of submission based on process yield. Lot sentencing plays the main role in buyer-seller business contracts for deliveries. A continuous partnership between the vendor and buyer can help in maintaining historically traceable results whereby the recording information is considered valuable. Hence, we propose a new sampling strategy with an integrated operating mechanism that considers the preceding inspection results to lessen the required average sample number based on process yield. Compared with the conventional methods, the proposed modified sampling strategy has the advantage of having a small number of samples for inspection while providing desirable protection under the same quality requirements and tolerable sampling risks. An application taken from the contact lens industry is presented to demonstrate the practicability of this research.
{"title":"An integrated operating mechanism for lot sentencing based on process yield","authors":"Shih-Wen Liu, Chien-Wei Wu, Zih-Huei Wang","doi":"10.1080/16843703.2021.1927295","DOIUrl":"https://doi.org/10.1080/16843703.2021.1927295","url":null,"abstract":"ABSTRACT A flexible sampling policy integrated with the consideration of past records is discussed in this paper for the quality evaluation of submission based on process yield. Lot sentencing plays the main role in buyer-seller business contracts for deliveries. A continuous partnership between the vendor and buyer can help in maintaining historically traceable results whereby the recording information is considered valuable. Hence, we propose a new sampling strategy with an integrated operating mechanism that considers the preceding inspection results to lessen the required average sample number based on process yield. Compared with the conventional methods, the proposed modified sampling strategy has the advantage of having a small number of samples for inspection while providing desirable protection under the same quality requirements and tolerable sampling risks. An application taken from the contact lens industry is presented to demonstrate the practicability of this research.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"139 - 152"},"PeriodicalIF":2.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48210269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-28DOI: 10.1080/16843703.2021.1948952
O. T. Omolofe, N. Adegoke, O. A. Adeoti, O. Fasoranbaku, S. Abbasi
ABSTRACT Multivariate control charts are generally used in industries for monitoring and diagnosing processes characterized by several process variables. The applications of charts assume that the in-control process parameters are known and the charts’ limits are obtained from the known parameters. The parameters are typically unknown in practice, and the charts’ limits are usually based on estimated parameters from some historical in-control datasets in the Phase I study. The performance of the charts for monitoring future observation depends on efficient estimates of the process parameters from the historical in-control process. When only a few historical observations are available, the performance of the charts based on the empirical estimates of the process mean vector and covariance matrix have been shown to deviate from the desired performance of the charts based on the true parameters. We investigate the performance of the multivariate Shewhart control charts based on several shrinkage estimates of the covariance matrix when only a few in-control observations are available to estimate the parameters. Simulation results show that the control charts based on the shrinkage estimators outperform the charts based on existing classical estimators. An example involving high-dimensional monitoring is provided to illustrate the performance of the proposed Shrinkage-based Shewhart chart.
{"title":"Multivariate control charts for monitoring process mean vector of individual observations under regularized covariance estimation","authors":"O. T. Omolofe, N. Adegoke, O. A. Adeoti, O. Fasoranbaku, S. Abbasi","doi":"10.1080/16843703.2021.1948952","DOIUrl":"https://doi.org/10.1080/16843703.2021.1948952","url":null,"abstract":"ABSTRACT Multivariate control charts are generally used in industries for monitoring and diagnosing processes characterized by several process variables. The applications of charts assume that the in-control process parameters are known and the charts’ limits are obtained from the known parameters. The parameters are typically unknown in practice, and the charts’ limits are usually based on estimated parameters from some historical in-control datasets in the Phase I study. The performance of the charts for monitoring future observation depends on efficient estimates of the process parameters from the historical in-control process. When only a few historical observations are available, the performance of the charts based on the empirical estimates of the process mean vector and covariance matrix have been shown to deviate from the desired performance of the charts based on the true parameters. We investigate the performance of the multivariate Shewhart control charts based on several shrinkage estimates of the covariance matrix when only a few in-control observations are available to estimate the parameters. Simulation results show that the control charts based on the shrinkage estimators outperform the charts based on existing classical estimators. An example involving high-dimensional monitoring is provided to illustrate the performance of the proposed Shrinkage-based Shewhart chart.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"277 - 298"},"PeriodicalIF":2.8,"publicationDate":"2021-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46263124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-22DOI: 10.1080/16843703.2021.1963032
Mohammad Vali Ahmadi, M. Doostparast
ABSTRACT In manufacturing industries, indices such as the lifetime performance index ( ) are utilized to assess whether products’ quality meets the required level. This article deals with the Bayesian inferences about on the basis of progressively censored data when the product’s lifetime follows the Weibull distribution. The Bayesian analysis is based on a conjugate prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are studied to assess the sensitivity of results to the prior parameters and the underlying distribution of the observed data. Finally, a simulation study is conducted to carry out the performance of the obtained results.
{"title":"Bayesian analysis of the lifetime performance index on the basis of progressively censored Weibull observations","authors":"Mohammad Vali Ahmadi, M. Doostparast","doi":"10.1080/16843703.2021.1963032","DOIUrl":"https://doi.org/10.1080/16843703.2021.1963032","url":null,"abstract":"ABSTRACT In manufacturing industries, indices such as the lifetime performance index ( ) are utilized to assess whether products’ quality meets the required level. This article deals with the Bayesian inferences about on the basis of progressively censored data when the product’s lifetime follows the Weibull distribution. The Bayesian analysis is based on a conjugate prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are studied to assess the sensitivity of results to the prior parameters and the underlying distribution of the observed data. Finally, a simulation study is conducted to carry out the performance of the obtained results.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"187 - 214"},"PeriodicalIF":2.8,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42980243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-12DOI: 10.1080/16843703.2021.1989141
Vasileios Alevizakos, K. Chatterjee, C. Koukouvinos
ABSTRACT The exponentially weighted moving average (EWMA) control chart is a very popular memory-type chart and also effective in detecting small shifts in the process mean. Several modifications of the EWMA chart, such as the double and triple EWMA charts (regarded as DEWMA and TEWMA charts, respectively) have been developed to enhance its performance in detecting small shifts. In the present article, we propose the quadruple EWMA chart (regarded as QEWMA chart) in order to improve much more the detection ability of the EWMA chart. The run-length characteristics of the proposed chart are evaluated by performing Monte Carlo simulations. Comparing with the EWMA, DEWMA and TEWMA charts, it is found that the QEWMA chart outperforms its competitors for small shifts. Moreover, it is shown that the proposed chart is more in-control (IC) robust under several non-normal distributions than the other charts, especially for a medium value of the smoothing parameter. The effect of inertia on the performance of the QEWMA chart is also investigated as a part of this article. Finally, two examples are provided to demonstrate the application of the proposed chart.
{"title":"The quadruple exponentially weighted moving average control chart","authors":"Vasileios Alevizakos, K. Chatterjee, C. Koukouvinos","doi":"10.1080/16843703.2021.1989141","DOIUrl":"https://doi.org/10.1080/16843703.2021.1989141","url":null,"abstract":"ABSTRACT The exponentially weighted moving average (EWMA) control chart is a very popular memory-type chart and also effective in detecting small shifts in the process mean. Several modifications of the EWMA chart, such as the double and triple EWMA charts (regarded as DEWMA and TEWMA charts, respectively) have been developed to enhance its performance in detecting small shifts. In the present article, we propose the quadruple EWMA chart (regarded as QEWMA chart) in order to improve much more the detection ability of the EWMA chart. The run-length characteristics of the proposed chart are evaluated by performing Monte Carlo simulations. Comparing with the EWMA, DEWMA and TEWMA charts, it is found that the QEWMA chart outperforms its competitors for small shifts. Moreover, it is shown that the proposed chart is more in-control (IC) robust under several non-normal distributions than the other charts, especially for a medium value of the smoothing parameter. The effect of inertia on the performance of the QEWMA chart is also investigated as a part of this article. Finally, two examples are provided to demonstrate the application of the proposed chart.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"50 - 73"},"PeriodicalIF":2.8,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45689569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1080/16843703.2021.1892907
Vijayashree K. V., A. K
ABSTRACT In this work, we consider an M/M/1 queueing model subject to differentiatedvacations. When the server is idle, he takes a break for a specific duration(termed Type I vacation). Upon completing the vacation, he takes another short break if the server stillfinds an empty system (termed as Type IIvacation). Both types of vacation follow an exponential distribution. As TypeI vacation persists for an extended period, it is reasonable to assume that theservice continues during this vacation by an alternate server at a slower rate,unlike the Type II vacation. Also, Type II being a shorter duration vacation,we assume that the Type II vacation is interrupted when the queue size reaches a predefined threshold value. Further, the arriving customers willwait only for a fixed duration of time, and if the service is incomplete by then,they leave the system permanently. We obtain an exact analytical expressionfor the transient state probabilities using Laplace transform, generatingfunctions, and continued fraction methodology. We also derive some useful measuresof effectiveness like the time-dependent mean and variance andillustrate their variations graphically.
在本文中，我们考虑一个具有微分假期的M/M/1排队模型。当服务器空闲时，他会休息一段特定的时间(称为Type I vacation)。在完成假期后，如果服务器仍然发现一个空系统(称为Type IIvacation)，他将进行另一次短暂的休息。两种类型的假期都遵循指数分布。由于TypeI假期持续了一段较长的时间，因此可以合理地假设，与typeii假期不同，在此假期期间，服务将由备用服务器以较慢的速度继续提供。此外，Type II是一个持续时间较短的假期，我们假设当队列大小达到预定义的阈值时，Type II假期被中断。此外，到达的客户只会等待一段固定的时间，如果到那时服务还没有完成，他们就会永久地离开系统。我们利用拉普拉斯变换、生成函数和连分式方法得到了暂态概率的精确解析表达式。我们还推导了一些有用的有效性度量，如时间相关的均值和方差，并以图形方式说明了它们的变化。
{"title":"AN M/M/1 QUEUE SUBJECT TO DIFFERENTIATED VACATION WITH PARTIAL INTERRUPTION AND CUSTOMER IMPATIENCE","authors":"Vijayashree K. V., A. K","doi":"10.1080/16843703.2021.1892907","DOIUrl":"https://doi.org/10.1080/16843703.2021.1892907","url":null,"abstract":"ABSTRACT In this work, we consider an M/M/1 queueing model subject to differentiatedvacations. When the server is idle, he takes a break for a specific duration(termed Type I vacation). Upon completing the vacation, he takes another short break if the server stillfinds an empty system (termed as Type IIvacation). Both types of vacation follow an exponential distribution. As TypeI vacation persists for an extended period, it is reasonable to assume that theservice continues during this vacation by an alternate server at a slower rate,unlike the Type II vacation. Also, Type II being a shorter duration vacation,we assume that the Type II vacation is interrupted when the queue size reaches a predefined threshold value. Further, the arriving customers willwait only for a fixed duration of time, and if the service is incomplete by then,they leave the system permanently. We obtain an exact analytical expressionfor the transient state probabilities using Laplace transform, generatingfunctions, and continued fraction methodology. We also derive some useful measuresof effectiveness like the time-dependent mean and variance andillustrate their variations graphically.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"18 1","pages":"657 - 682"},"PeriodicalIF":2.8,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60299255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-01DOI: 10.1080/16843703.2021.1949825
Mosquera Jaime, Aparisi Francisco, Epprecht K. Eugenio
ABSTRACT Quality control charts are widely used to monitor production processes. To fix the control limits, the distribution of the statistic being controlled must be known. For using and S control charts together, when the parameters are unknown, the mean and standard deviation of the process must be estimated. Errors in these estimates can cause the real performance of the joint charts to be different from that expected by the user, and the in-control and out-of-control ARL may therefore be very different from the theoretical values. To date, only the effect of the estimation errors on the in-control performance of the joint charts has been studied in the literature. In this article, we study jointly this effect on both performance measures, the in-control and out-of-control ARLs for joint charts, and estimate the number of samples needed in Phase I to guarantee a required level in the probability of obtaining joint charts with acceptable in-control and out-of-control performances.
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