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CPV Monitoring - Optimization of Control Chart Design by Reducing the False Alarm Rate and Nuisance Signal CPV 监测 - 通过降低误报率和干扰信号优化控制图设计
Pub Date : 2024-04-02 DOI: 10.11648/j.sjams.20241202.11
Naveenganesh Muralidharan, Thatsinee Johnson, Leyla Rose, Mark Davis
The Food and Drug Administration’s 2011 Process Validation Guidance and International Council for Harmonization Quality Guidelines recommend continued process verification (CPV) as a mandatory requirement for pharmaceutical, biopharmaceutical, and other regulated industries. As a part of product life cycle management, after process characterization in stage 1 and process qualification and validation in stage-2, CPV is performed as stage-3 validation during commercial manufacturing. CPV ensures that the process continues to remain within a validated state. CPV requires the collection and analysis of data related to critical quality attributes, critical material attributes, and critical process parameters on a minimum basis. Data is then used to elucidate process control regarding the capability to meet predefined specifications and stability via statistical process control (SPC) tools. In SPC, the control charts and Nelson rules are commonly used throughout the industry to monitor and trend data to ensure that a process remains in control. However, basic control charts are susceptible to false alarms and nuisance alarms. Therefore, it is imperative to understand the assumptions behind control charts and the inherent false alarm rates for different Nelson rules. In this article, the authors have detailed the assumptions behind the usage of control charts, the rate of false alarms for different Nelson rules, the impact of skewness and kurtosis of a data distribution on the false alarm rate, and methods for optimizing control chart design by reducing false alarm rates and nuisance signals.
美国食品和药物管理局 2011 年《工艺验证指南》和国际协调理事会《质量准则》建议将持续工艺验证 (CPV) 作为制药、生物制药和其他受监管行业的一项强制性要求。作为产品生命周期管理的一部分,在第一阶段的工艺特征描述和第二阶段的工艺鉴定和验证之后,CPV 作为第三阶段的验证在商业生产过程中执行。CPV 可确保工艺继续保持在验证状态。CPV 要求至少收集和分析与关键质量属性、关键材料属性和关键工艺参数有关的数据。然后,通过统计过程控制(SPC)工具,利用数据阐明与满足预定规格和稳定性的能力有关的过程控制。在 SPC 中,控制图和纳尔逊规则在整个行业中被普遍用于监测和趋势分析数据,以确保过程始终处于控制之中。然而,基本控制图容易出现误报和骚扰报警。因此,必须了解控制图背后的假设以及不同纳尔逊规则固有的误报率。在本文中,作者详细介绍了使用控制图背后的假设、不同纳尔逊规则的误报率、数据分布的偏度和峰度对误报率的影响,以及通过降低误报率和干扰信号来优化控制图设计的方法。
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引用次数: 0
Optimization of the Non-Linear Diffussion Equations 非线性扩散方程的优化
Pub Date : 2024-04-02 DOI: 10.11648/j.sjams.20241201.12
Rukia Fwamba, Isaac Chepkwony, W. Fwamba
Partial Differential Equations are used in smoothening of images. Under partial differential equations an image is termed as a function; f(x, y), XÎR2. The pixel flux is referred to as an edge stopping function since it ensures that diffusion occurs within the image region but zero at the boundaries; ux(0, y, t) = ux(p, y, t) = uy(x, 0, t) = uy(x, q, t). Nonlinear PDEs tend to adjust the quality of the image, thus giving images desirable outlooks. In the digital world there is need for images to be smoothened for broadcast purposes, medical display of internal organs i.e MRI (Magnetic Resonance Imaging), study of the galaxy, CCTV (Closed Circuit Television) among others. This model inputs optimization in the smoothening of images. The solutions of the diffusion equations were obtained using iterative algorithms i.e. Alternating Direction Implicit (ADI) method, Two-point Explicit Group Successive Over-Relaxation (2-EGSOR) and a successive implementation of these two approaches. These schemes were executed in MATLAB (Matrix Laboratory) subject to an initial condition of a noisy images characterized by pepper noise, Gaussian noise, Brownian noise, Poisson noise etc. As the algorithms were implemented in MATLAB, the smoothing effect reduced at places with possibilities of being boundaries, the parameters Cv (pixel flux), Cf (coefficient of the forcing term), b (the threshold parameter) alongside time t were estimated through optimization. Parameter b maintained the highest value, while Cv exhibited the lowest value implying that diffusion of pixels within the various images i.e. CCTV, MRI & Galaxy was limited to enhance smoothening. On the other hand the threshold parameter (b) took an escalated value across the images translating to a high level of the force responsible for smoothening.
偏微分方程用于平滑图像。在偏微分方程中,图像被称为函数;f(x, y), XÎR2。像素通量被称为边缘停止函数,因为它确保扩散发生在图像区域内,而在边界为零;ux(0, y, t) = ux(p, y, t) = uy(x, 0, t) = uy(x, q, t)。非线性 PDE 往往会调整图像的质量,从而使图像呈现出理想的外观。在数字世界中,需要对图像进行平滑处理,以用于广播目的、内部器官的医学显示(即 MRI(磁共振成像))、星系研究、闭路电视(CCTV)等。该模型为图像平滑化提供了优化方案。利用迭代算法,即交替方向隐含法(ADI)、两点显式组连续超松弛法(2-EGSOR)以及这两种方法的连续实施,获得了扩散方程的解。这些方案是在 MATLAB(矩阵实验室)中执行的,初始条件是以胡椒噪声、高斯噪声、布朗噪声、泊松噪声等为特征的噪声图像。由于算法在 MATLAB 中执行,平滑效果在有可能成为边界的地方有所降低,参数 Cv(像素通量)、Cf(强制项系数)、b(阈值参数)和时间 t 都是通过优化估算出来的。参数 b 保持最高值,而 Cv 显示最低值,这意味着 CCTV、MRI 和 Galaxy 等不同图像中像素的扩散受到限制,从而增强了平滑化效果。另一方面,阈值参数(b)在所有图像中的值都在上升,这意味着平滑化的作用力很大。
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引用次数: 0
On Different Extraction Methods of Factor Analysis 论因子分析的不同提取方法
Pub Date : 2023-11-21 DOI: 10.11648/j.sjams.20231103.12
Awogbemi, Clement Adeyeye, Koyejo Samuel Olusegun, Olowu Abiodun Rafiu
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引用次数: 0
Improvement of the Raabe-Duhamel Convergence Criterion Generalized 拉贝-杜哈梅尔收敛标准的改进 广义
Pub Date : 2023-11-16 DOI: 10.11648/j.sjams.20231103.11
El Hadji Abdoulaye Thiam, Papa Moussa Niang
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引用次数: 0
Volatility Modelling of Stock Returns of Selected Nigerian Oil and Gas Companies 尼日利亚石油和天然气公司股票收益的波动模型
Pub Date : 2023-08-15 DOI: 10.11648/j.sjams.20231102.11
Maruf Ariyo Raheem, Regina Domingo Mbeke, Elisha John Inyang
: Modelling volatility asset returns is a well-researched concept in financial statistics, given its significance to investment analysts, economists, risk-averse investors, policymakers and other relevant stakeholders to underpin the market and the general economic performance and resilience to shocks, domestically and internationally. Thus, this study fits an appropriate ARCH/GARCH family model to daily stock returns volatility of each of the selected five most traded assets of the oil and gas marketing companies on the Nigerian stock exchange (NSE), using daily closing prices from January 1, 2005, to December 31, 2020. First-order symmetric and asymmetric volatility models with the Normal, Student’s t, Skewed Student’s t and generalized error distributions (GED) were fitted to select the best model with the most appropriate error distribution using appropriate model selection criteri EGARCH (1,1) with GEDs was found to be the best-fitted models based on the Akaike Information Criterion (AIC). The results indicated the presence of a leverage effect in the series and how the volatility reacts to good news as against bad news implying that positive shock has a higher impact on the returns of the respective companies. Based on the findings it is recommended that, for enhanced precision, GARCH family models with appropriate error distribution be applied in underpinning assets volatility, which in turn would help to better understand the nature of inherent shocks characterizing asset volatility of the respective companies. With such knowledge, appropriate investment decisions are made to guide risk-averse investors in their investments.
在金融统计中,波动性资产回报建模是一个得到充分研究的概念,因为它对投资分析师、经济学家、厌恶风险的投资者、政策制定者和其他相关利益相关者具有重要意义,可以支撑市场和总体经济表现以及对国内和国际冲击的抵御能力。因此,本研究使用2005年1月1日至2020年12月31日的每日收盘价,将适当的ARCH/GARCH家族模型拟合到尼日利亚证券交易所(NSE)石油和天然气营销公司选定的五种交易最多的资产中的每一种的每日股票回报波动率。对具有正态、学生t、偏态学生t和广义误差分布(GED)的一阶对称和非对称波动率模型进行拟合,利用合适的模型选择准则选择误差分布最合适的模型,其中基于赤池信息准则(AIC)发现具有广义误差分布的EGARCH(1,1)是最合适的模型。结果表明,杠杆效应的存在,以及波动率对好消息的反应,而不是对坏消息的反应,这意味着积极的冲击对各自公司的回报有更高的影响。根据研究结果,建议采用具有适当误差分布的GARCH家族模型来支持资产波动,以提高精度,这反过来将有助于更好地理解表征各自公司资产波动的固有冲击的性质。有了这些知识,就可以做出适当的投资决策,以指导规避风险的投资者进行投资。
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引用次数: 0
Determination of the Utilization and Effort Level of Mackerel Scad (Decapterus spp) in the North Bolaangmongondow Waters North Sulawesi 确定北苏拉威西岛北 Bolaangmongondow 水域鲭鱼(Decapterus spp)的利用率和努力程度
Pub Date : 2023-06-09 DOI: 10.11648/j.sjams.20231101.12
John Socrates Kekenusa, Sendy Beatrix Rondonuwu, Marline Sofiana Paendong
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引用次数: 0
On Statistical Analysis of Eight Sexually Transmitted Diseases Using Categorical Analysis of Variance: A Case Study of the University of Nigeria Teaching Hospital 用分类方差分析对8种性传播疾病的统计分析——以尼日利亚大学教学医院为例
Pub Date : 2023-01-13 DOI: 10.11648/j.sjams.20231101.11
Nnaemeka Martin Eze, Chimeremeze Davidson Sibigem, Oluchukwu Chukwuemeka Asogwa, Chinonso Michael Eze, Samson Offorma Ugwu, Felix Obi Ohanuba
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引用次数: 0
Carleman Estimate for a Singulary Perturbed Degenerated Parabolic Equation 一类奇异摄动退化抛物方程的Carleman估计
Pub Date : 2021-10-29 DOI: 10.11648/J.SJAMS.20210905.11
Zeine Sid Elemine, I. Faye, Alassane Sy, D. Seck
In this paper, we are concerned with the the internal control of an elliptic singularly perturbed degenerated parabolic equation. This parabolic equation models sand transport problem near the coast in areas subjected to the tide. We study first the null controllability result of the parabolic equation modeling sand transport equation.The limit problem obtained by homogenization problem is also considered. We use distributed and bounded controls supported on a small open set of the initial domain. We prove the null controllability of the system at any time by using observability inequality for both problem. For this purpose, a specific carleman estimate for the solutions of degenerate adjoint limit problem is also proved.
本文研究了一类椭圆型奇摄动退化抛物方程的内控制问题。该抛物方程模拟了受潮汐影响地区海岸附近的输沙问题。首先研究了抛物方程模拟输沙方程的零可控性结果。同时考虑了由均匀化问题得到的极限问题。我们在初始域的一个小开放集上使用支持的分布式和有界控件。利用可观测不等式证明了系统在任意时刻的零可控性。为此,还证明了退化伴随极限问题解的一个特殊的carleman估计。
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引用次数: 0
On the Restricted Poisson Ridge Regression Estimator 关于受限泊松岭回归估计量
Pub Date : 2021-08-26 DOI: 10.11648/J.SJAMS.20210904.12
E. Yehia
For modeling count data, the Poisson regression model is widely used in which the response variable takes non-negative integer values. However, the presence of strong correlation between the explanatory variables causes the problem of multicollinearity. Due to multicollinearity, the variance of the maximum likelihood estimator (MLE) will be inflated causing the parameters estimation to become unstable. Multicollinearity can be tackled by using biased estimators such as the ridge estimator in order to minimize the estimated variance of the regression coefficients. An alternative approach is to specify exact linear restrictions on the parameters in addition to regression model. In this paper, the restricted Poisson ridge regression estimator (RPRRE) is suggested to handle multicollinearity in Poisson regression model with exact linear restrictions on the parameters. In addition, the conditions of superiority of the suggested estimator in comparison to some existing estimators are discussed based on the mean squared error (MSE) matrix criterion. Moreover, a simulation study and a real data application are provided to illustrate the theoretical results. The results indicate that the suggested estimator, RPRRE, outperforms the other existing estimators in terms of scalar mean squared error (SMSE). Therefore, it is recommended to use the RPRRE for the Poisson regression model when the problem of multicollinearity is present.
对于计数数据的建模,广泛采用泊松回归模型,该模型的响应变量为非负整数值。然而,由于解释变量之间存在很强的相关性,导致了多重共线性问题。由于多重共线性,极大似然估计量(MLE)的方差会膨胀,导致参数估计变得不稳定。多重共线性可以通过使用脊估计等有偏估计来解决,以最小化回归系数的估计方差。除了回归模型外,另一种方法是对参数指定精确的线性限制。本文提出用受限泊松脊回归估计(RPRRE)来处理参数有精确线性限制的泊松回归模型中的多重共线性问题。此外,基于均方误差(MSE)矩阵准则,讨论了该估计量与现有估计量相比具有优越性的条件。最后,通过仿真研究和实际数据应用验证了理论结果。结果表明,RPRRE估计器在标量均方误差(SMSE)方面优于其他现有估计器。因此,当存在多重共线性问题时,建议对泊松回归模型使用RPRRE。
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引用次数: 5
Corporate Strategy, Pay Gap and Employee Turnover Rate: Based on Mediation Model
Pub Date : 2021-07-24 DOI: 10.11648/J.SJAMS.20210903.12
Xiangyi Zhu
The characteristics of prospector are to constantly find new market opportunities, carry out technological innovation, and obtain growth opportunities by moving to high value-added fields. Defender often choose a relatively stable market area and take effective actions, such as setting competitive prices or providing high-quality products and services, to actively prevent subsequent competitors from entering this industry. Although different strategic types of enterprises have different business preference, they cannot do without the active cooperation of employees in the process of strategy implementation, because they are the closest to the production and customers. If the incentive mechanism conflicts with employees' interests, employees may respond by leaving. Based on the sample of China's A-share listed companies from 2007 to 2019, this paper uses the fixed effect model to examine the impact of strategy on employee incentive mechanism and turnover rate. The empirical results show that, compared with defender, the pay gap of prospector is higher, and the above phenomenon is more significant in enterprises with lower labor intensity. In addition, prospector will also push up the turnover rate of employees, in which the pay gap plays a mediating role. This conclusion not only enriches the research of strategic theory and compensation contract, but also has some enlightenment for the relevant government departments to develop vocational training to improve employees' skills.
探矿者的特点是不断寻找新的市场机会,进行技术创新,通过向高附加值领域转移来获得增长机会。捍卫者往往选择一个相对稳定的市场领域,采取有效的行动,如制定有竞争力的价格或提供高质量的产品和服务,积极阻止后续竞争者进入该行业。虽然不同战略类型的企业有不同的经营偏好,但在战略实施的过程中,都离不开员工的积极配合,因为员工是最接近生产和客户的。如果激励机制与员工利益冲突,员工可能会以离职作为回应。本文以2007 - 2019年中国a股上市公司为样本,运用固定效应模型考察了战略对员工激励机制和离职率的影响。实证结果表明,与防守者相比,探矿者的薪酬差距更大,且上述现象在劳动强度较低的企业中更为显著。此外,勘探者也会推高员工的离职率,其中薪酬差距起到中介作用。这一结论不仅丰富了战略理论和薪酬契约的研究内容,而且对政府相关部门开展职业培训,提高员工技能具有一定的启示意义。
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引用次数: 0
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Science Journal of Applied Mathematics and Statistics
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