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Design and Optimization of c-Control Chart Using a Triple Sampling Scheme 三次抽样c-控制图的设计与优化
Q3 Mathematics Pub Date : 2023-07-25 DOI: 10.1515/eqc-2023-0012
José Jorge Muñoz, Manuel J. Campuzano, Verónica Deibe-Blanco
Abstract In this paper, a c-control chart using a triple sampling scheme (TS-c) is studied. The chart design, procedure, and a bi-objective optimization model are given to optimize the TS-c-chart. The Average Run Length for in-control and out-of-control ( ARL 1 mathrm{ARL}_{1} ), and Average Sample Number metrics are calculated. A Comparison among TS-c, Fixed parameters c (FP-c), VSS-c, EWMA-c, and Double Sampling c (DS-c) control charts are carried out in terms of ARL 1 mathrm{ARL}_{1} . The proposed TS-c-chart has lower ARL 1 mathrm{ARL}_{1} values for detecting small and moderate shifts in the mean number of non-conformities in control compared with FP-c, VSS-c, EWMA-c, and DS-c.
摘要本文研究了一种采用三重采样方案(TS-c)的c控制图。给出了ts -c图的设计、流程和双目标优化模型。计算控制和失控的平均运行长度(ARL 1 mathm {ARL}_{1})和平均样本数指标。比较了TS-c、固定参数c (FP-c)、VSS-c、EWMA-c和双采样c (DS-c)控制图在ARL 1 数学{ARL}_{1}下的性能。与FP-c、VSS-c、EWMA-c和DS-c相比,所提出的ts -c图具有较低的ARL 1 数学{ARL}_{1}值,用于检测控制中不符合项平均数量的微小和中等变化。
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引用次数: 0
Frontmatter 头版头条
Q3 Mathematics Pub Date : 2023-06-01 DOI: 10.1515/eqc-2023-frontmatter1
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引用次数: 0
An Extension of Yang and Rahim’s Model to Determine Design Parameters in Multivariate Control Charts Under Multiple Assignable Causes and Weibull Shock Model 多可分配原因下多元控制图设计参数确定的Yang和Rahim模型的推广及威布尔冲击模型
Q3 Mathematics Pub Date : 2023-05-31 DOI: 10.1515/eqc-2022-0053
Rahmat Shojaei, M. Bameni Moghadam
Abstract One of the most important issues in the operation of any one- or multi-variable control chart is to determine the design parameters. Because in practice, production processes are affected by several assignable causes, several papers have been published to determine the design parameters. In all the papers presented so far, it has been assumed that after the occurrence of one of the assignable causes until the issuance of the true alarm, no other assignable cause occurs. Contrary to popular opinion, this paper argues that the formulas presented under this assumption for the average cost and quality cycle time in previous papers are incorrect and shows how the formula can be corrected. Therefore, this paper theoretically and numerically examines the conditions of occurrence of this assumption and its relationship with the design parameters in the design of multivariate control charts. A new economic model for determining design parameters is also presented. Numerical results show that the old formulas have a significant under-estimation of the average cost per unit time of the quality cycle. Also, a numerical study for economic and economic-statistical design of T 2 {T^{2}} control chart is presented under the proposed model.
摘要设计参数的确定是任何单变量或多变量控制图运行中最重要的问题之一。因为在实践中,生产过程受到几个可分配原因的影响,已经发表了几篇论文来确定设计参数。在目前发表的所有论文中,都假设在其中一个可分配原因发生后,直到真警报发出为止,没有其他可分配原因发生。与流行的观点相反,本文认为在此假设下提出的以往文献中的平均成本和质量周期时间公式是不正确的,并说明了公式的修正方法。因此,本文从理论上和数值上考察了多元控制图设计中该假设发生的条件及其与设计参数的关系。提出了一种新的确定设计参数的经济模型。数值结果表明,旧公式对质量周期单位时间的平均成本有明显的低估。在此基础上,对t2 {T^{2}}控制图的经济和经济统计设计进行了数值研究。
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引用次数: 0
Reliability Estimation of Parallel Repairable System under Uncertainty in Lifetime Data 寿命数据不确定下并联可修系统可靠性估计
Q3 Mathematics Pub Date : 2023-05-03 DOI: 10.1515/eqc-2022-0044
Sruthi K., Mahesh Kumar
Abstract Reliability is a popular concept that has been used in the manufacturing industry. In this paper, we consider a parallel system containing n non-identical and independent components in which each component is repairable except when all components are failed. As a special case, estimating the reliability of the system with identical components is considered. In real life, the data obtained for repair rate and failure rate could be subject to uncertainty. Here, to address this situation, failure and repair rates are considered as fuzzy numbers to estimate the reliability of the system. Fuzzy system reliability is estimated using fuzzy failure and repair rates, which are obtained by using confidence intervals and point estimators of failure rate and repair rate.
摘要可靠性是一个广泛应用于制造业的概念。本文考虑一个包含n个不相同且独立的组件的并行系统,其中每个组件都是可修复的,除非所有组件都失效。作为一种特殊情况,考虑了具有相同部件的系统的可靠性估计。在实际生活中,获得的修理率和故障率数据可能存在不确定性。这里,为了解决这种情况,故障率和修复率被视为模糊数来估计系统的可靠性。利用模糊故障率和修复率的置信区间和点估计得到模糊故障率和修复率,对模糊系统可靠性进行估计。
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引用次数: 0
An ARL-Unbiased Modified np-Chart for Autoregressive Binomial Counts 自回归二项计数的arl无偏修正np图
Q3 Mathematics Pub Date : 2023-03-31 DOI: 10.1515/eqc-2022-0052
M. Morais, P. Wittenberg, Camila Jeppesen Cruz
Abstract Independence between successive counts is not a sensible premise while dealing, for instance, with very high sampling rates. After assessing the impact of falsely assuming independent binomial counts in the performance of np-charts, such as the one with 3-σ control limits, we propose a modified np-chart for monitoring first-order autoregressive counts with binomial marginals. This simple chart has an in-control average run length (ARL) larger than any out-of-control ARL, i.e., it is ARL-unbiased. Moreover, the ARL-unbiased modified np-chart triggers a signal at sample t with probability one if the observed value of the control statistic is beyond the lower and upper control limits L and U. In addition to this, the chart emits a signal with probability γ L {gamma_{L}} (resp. γ U {gamma_{U}} ) if that observed value coincides with L (resp. U). This randomization allows us to set the control limits in such a way that the in-control ARL takes the desired value ARL 0 {operatorname{ARL}_{0}} , in contrast to traditional charts with discrete control statistics. Several illustrations of the ARL-unbiased modified np-chart are provided, using the statistical software R and resorting to real and simulated data.
例如,在处理非常高的采样率时,连续计数之间的独立性不是一个明智的前提。在评估了错误假设独立二项计数对np图性能的影响后,例如具有3 σ控制极限的np图,我们提出了一种改进的np图,用于监测具有二项边缘的一阶自回归计数。这个简单的图表有一个可控的平均运行长度(ARL)大于任何失控的ARL,也就是说,它是ARL无偏的。此外,如果控制统计量的观测值超出控制下限L和上限u,则arl无偏修正np图在样本t处触发一个概率为1的信号,此外,图表发出一个概率为γ L {gamma_{L}}的信号(resp。γ U {gamma_{U}}),如果观测值与L (resp。这种随机化允许我们以这样一种方式设置控制限制,即控制中的ARL取期望值ARL 0 {operatorname{ARL}_{0}},与具有离散控制统计的传统图表相反。利用统计软件R,结合真实数据和模拟数据,给出了arl无偏修正np图的几个例子。
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引用次数: 0
General Independent Competing Risks for Maintenance Analysis 维护分析的一般独立竞争风险
Q3 Mathematics Pub Date : 2022-11-25 DOI: 10.1515/eqc-2022-0029
Makram Krit
Abstract Repairable systems are submitted to corrective maintenance and condition-based preventive maintenance actions. Condition-based preventive maintenance occurs at times which are determined according to the results of inspections and degradation or operation controls. The generalization of the models suggested makes it possible to integrate the dependence between corrective and preventive maintenances. In order to take into account this dependency and the possibility of imperfect maintenances, generalized competing risks models have been presented in Doyen and Gaudoin (2006). In this study, we revise the general case in which the potential times to next corrective and preventive maintenance are independent conditionally to the past of the maintenance process. We address the identifiability issue and we find a result similar to that of Zhou, Lu, Shi and Cheng (2018) for usual competing risks. We propose realistic models with exponential risks and derive their likelihood functions.
可修系统被提交到纠正性维护和基于状态的预防性维护行动中。基于状态的预防性维护发生的时间是根据检查和退化或操作控制的结果确定的。所提出的模型的泛化使得校正维修和预防性维修之间的依赖关系得以整合。为了考虑到这种依赖性和不完全维护的可能性,Doyen和Gaudoin(2006)提出了广义竞争风险模型。在本研究中,我们修正了一般情况下,下一次纠正和预防性维修的潜在时间是有条件地独立于过去的维修过程。我们解决了可识别性问题,并发现了与Zhou, Lu, Shi和Cheng(2018)的结果相似的通常竞争风险。我们提出了具有指数风险的现实模型,并推导了它们的似然函数。
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引用次数: 0
On Normal-Laplace Stochastic Volatility Model 关于正态拉普拉斯随机波动模型
Q3 Mathematics Pub Date : 2022-11-23 DOI: 10.1515/eqc-2022-0013
Shiji Kavungal, Rahul Thekkedath
Abstract This paper analyses a stochastic volatility model generated by first order normal-Laplace autoregressive process. The model parameters are estimated by the generalized method of moments. A simulation experiment is carried out to check the performance of the estimates. Finally, a real data analysis is provided to illustrate the practical utility of the proposed model and show that it captures the stylized factors of the financial return series.
摘要本文分析了一阶正态拉普拉斯自回归过程生成的随机波动模型。采用广义矩量法对模型参数进行估计。通过仿真实验验证了估计的性能。最后,提供了一个真实的数据分析,以说明所提出的模型的实际效用,并表明它捕获了财务回报系列的风格化因素。
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引用次数: 0
Estimation and Confidence Intervals of Modified Process Capability Index Using Robust Measure of Variability 基于鲁棒变异性的改进过程能力指数估计及置信区间
Q3 Mathematics Pub Date : 2022-11-02 DOI: 10.1515/eqc-2022-0014
Mahendra Saha, S. Dey
Abstract The process capability index (PCI), denoted by 𝐼, is a well-known characteristic in quality control analysis. Using Gini’s mean difference, we construct a new PCI, I G I_{G} say, assuming the two-parameter Weibull distribution (WD). In order to estimate the proposed I G I_{G} when the process follows the WD, we use five classical methods of estimation and compare the performance of the obtained estimators with respect to their mean squared errors (MSEs) through a simulation study. Confidence intervals for the proposed PCI are constructed based on five bootstrap confidence intervals (BCIs) methods. Monte Carlo simulation study has been carried out to compare the performance of these five BCIs in terms of average widths and coverage probabilities. Finally, three real data sets from electronic and food industries are employed for illustrating the effectiveness of the proposed study. All these data sets show that the width of bias-corrected accelerated bootstrap interval is minimum among all other considered BCIs.
过程能力指数(PCI)是质量控制分析中一个众所周知的特征,用𝐼表示。利用基尼均值差,假设双参数威布尔分布(WD),我们构造了一个新的PCI, I G I_{G}。为了在过程遵循WD时估计所提出的I G I_{G},我们使用了五种经典的估计方法,并通过仿真研究比较了所得到的估计器的均方误差(MSEs)的性能。基于五种自举置信区间(bci)方法构建了PCI的置信区间。通过蒙特卡罗模拟研究,比较了这五种bci在平均宽度和覆盖概率方面的性能。最后,采用来自电子和食品行业的三个真实数据集来说明所提出研究的有效性。所有这些数据集表明,在所有其他考虑的bci中,偏差校正加速自举间隔的宽度是最小的。
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引用次数: 0
Robust Optimization of an Imperfect Process when the Mean and Variance are Jointly Monitored under Dependent Multiple Assignable Causes 多可分配原因下均值和方差联合监测不完美过程的鲁棒优化
Q3 Mathematics Pub Date : 2022-10-28 DOI: 10.1515/eqc-2022-0018
A. Salmasnia, samrad Jafarian-Namin, Behnam Abdzadeh
Abstract Imperfect processes experience fault productions over time due to specific causes. Integrating the statistical process control, maintenance policy, and economic production quantity has led to more favorable results for the imperfect processes in literature. When monitoring a process, multiple assignable causes (ACs) may shift it to an out-of-control state. As indicated recently, if the interdependency of ACs is neglected, the total cost will be underestimated. Moreover, the mean and variance can simultaneously be affected by the occurrence of ACs. A non-central chi-square (NCS) chart was suggested for its decent performance against X-R chart in detecting the process disturbances and lowering quality loss cost. Besides, the increased occurrence rate of ACs over time leads to higher quality and maintenance costs. Employing a non-uniform sampling (NUS) scheme can significantly reduce costs. In the literature of modeling for imperfect processes under multiple ACs, all input parameters have always been fixed. The effectiveness of the models depends somewhat on the accurate estimates of these parameters. In reality, the estimation of parameters may be associated with uncertainty. For the first time, a robust design approach is proposed for designing NCS chart by considering the interval estimation of uncertain parameters. A particle swarm optimization (PSO) algorithm is used to present solutions. The proposed model is investigated through a real numerical example.
由于特定的原因,不完美的过程随着时间的推移会产生故障。将统计过程控制、维护政策和经济生产数量相结合,为文献中不完善的过程带来了更有利的结果。当监控一个过程时,多个可分配原因(ac)可能会将其转移到失控状态。正如最近所指出的,如果忽略了ac的相互依赖性,总费用将被低估。此外,平均值和方差可能同时受到ACs发生的影响。非中心卡方(NCS)图在检测过程干扰和降低质量损失成本方面优于X-R图。此外,随着时间的推移,空调的发生率增加,导致更高的质量和维护成本。采用非均匀采样(NUS)方案可以显著降低成本。在多ac条件下的不完善过程建模文献中,所有输入参数都是固定的。模型的有效性在某种程度上取决于对这些参数的准确估计。在现实中,参数的估计可能与不确定性有关。首次提出了一种考虑不确定参数区间估计的网络控制系统图的鲁棒设计方法。采用粒子群优化(PSO)算法求解。通过一个实际的数值算例对该模型进行了验证。
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引用次数: 1
The 𝑛𝑝-Chart with 3-𝜎 Limits and the ARL-Unbiased 𝑛𝑝-Chart Revisited 重新考察了3-限的𝑛𝑝-Chart和arl无偏的𝑛𝑝-Chart
Q3 Mathematics Pub Date : 2022-10-27 DOI: 10.1515/eqc-2022-0032
M. Morais, P. Wittenberg, Camila Jeppesen Cruz
Abstract In the statistical process control literature, counts of nonconforming items are frequently assumed to be independent and have a binomial distribution with parameters ( n , p ) (n,p) , where 𝑛 and 𝑝 represent the fixed sample size and the fraction nonconforming. In this paper, the traditional n ⁢ p np -chart with 3-𝜎 control limits is reexamined. We show that, even if its lower control limit is positive and we are dealing with a small target value p 0 p_{0} of the fraction nonconforming ( p ) (p) , this chart average run length (ARL) function achieves a maximum to the left of p 0 p_{0} . Moreover, the in-control ARL of this popular chart is also shown to vary considerably with the fixed sample size 𝑛. We also look closely at the ARL function of the ARL-unbiased n ⁢ p np -chart proposed by Morais [An ARL-unbiased n ⁢ p np -chart, Econ. Qual. Control 31 (2016), 1, 11–21], which attains a pre-specified maximum value in the in-control situation. This chart triggers a signal at sample 𝑡 with probability one if the observed number of nonconforming items, x t x_{t} , is beyond the lower and upper control limits (𝐿 and 𝑈), probability γ L gamma_{L} (resp. γ U gamma_{U} ) if x t x_{t} coincides with 𝐿 (resp. 𝑈). A graphical display for the ARL-unbiased n ⁢ p np -chart is proposed, taking advantage of the qcc package for the statistical software R. Furthermore, as far as we have investigated, its control limits can be obtained using three different search algorithms; their computation times are thoroughly compared.
在统计过程控制文献中,经常假定不合格品的数量是独立的,具有参数(n,p) (n,p)的二项分布,其中𝑛和𝑝代表固定的样本量和不合格品的比例。本文对传统的具有3- φ控制限的n ^ p np图进行了重新检验。我们表明,即使它的下控制极限是正的,并且我们处理的是不符合分数(p) (p) (p)的一个小目标值p0 p_{0},这个图表平均运行长度(ARL)函数在p0 p_{0}的左边达到最大值。此外,这个流行图表的控制ARL也显示出随固定样本量𝑛变化很大。我们还仔细研究了Morais提出的ARL-无偏n减去p - np -图的ARL函数[An ARL-无偏n减去p - np -图,经济学]。[q] . Control 31(2016), 1,11 - 21],在控制状态下达到预定最大值。如果观察到的不合格品数量x t x_{t}超出控制下限和上限(𝐿和𝑈),则该图表在样本𝑡触发一个信号,概率为1,概率为γ L gamma_{L} (resp. 1)。γ U gamma_{U}),如果x t x_{t}与𝐿(p。𝑈)。利用统计软件r的qcc包,提出了一种arl -无偏n≠p np -图的图形显示方法。此外,就我们所研究的,它的控制极限可以使用三种不同的搜索算法获得;它们的计算时间进行了彻底的比较。
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引用次数: 1
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Stochastics and Quality Control
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