The Principle of Mathematical Induction Applied to the Generalized Model for the Economic Design of X-Control Charts

Rahim and Banerjee [1] developed a general model for the optimal design of x-control charts. The model minimizes the expected cost per unit time. The heart of the model is a theorem that derives the expected total cost and the expected cycle length. In this paper an alternative simple proof for the theorem is provided based on mathematical induction.

Clinical usefulness of the baby vision test in young children and its correlation with the Snellen chart

AIM:To investigate the efficacy of a new visual acuity(VA)screening method,the baby vision test for young children.METHODS:A total 105 eyes of 65 children aged 2-8y were included in the study.Acuity testing was conducted using a standardized recognition acuity chart(Snellen visual chart:at 3 m)and the baby vision model assessment.The baby vision device includes a screen,a near infrared camera and a computer.Children were seated at a measured distance of 33-40 cm from a display for testing.VA was estimated according to the highest resolution the children could follow.Decimal VA data were converted to logarithm of the minimum angle of resolution(logMAR)for statistical analysis.The VA results for each child were recorded and analyzed for consistency.RESULTS:The mean VA measured using the Snellen visual chart was 0.62±0.32,and that assessed using the baby vision test was 0.66±0.27.The 95%limit of agreement was-0.609 to 0.695,with 95.2%(100/105)plots within the 95%limits of agreement.VA values of the baby vision test were significantly correlated with those of the Snellen chart(R=0.274,P=0.005).CONCLUSION:The baby vision test can be used as a relatively reliable method for estimating VA in young children.This new acuity assessment might be a valid predictor of optotype-measured acuity later in preverbal children.

Exploring Variability in Sea Level at a Tide Gauge Station through Control Charts

Monitoring temporal changes in sea level is important in assessing coastal risk.Sea level anomalies at a tide gauge station,if kinematically conceived,include systematic variations such as trend,acceleration,periodic oscillations,and random disturbances.Among them,the non-stationary nature of the random sea level variations of known or unknown origin at coastal regions has been long recognized by the sea level community.This study proposes the analyses of subgroups of random residual statistics of a rigorously formulated kinematic model solution of tide gauge variations using X-bar and S control charts.The approach is demonstrated using Key West,Florida tide gauge records.The mean and standard errors of 5-year-long subgroups of the residuals revealed that sea level changes at this location have been progressively intensifying from 1913 to the present.Increasing oscillations in sea level at this locality may be attributed partly to the thermal expansion of seawater with increasing temperatures causing larger buoyancy-related sea level fluctuations as well as the intensification of atmospheric events including wind patterns and the impact of changes in inverted barometer effects that will alter coastal risk assessments for the future.

Japanese candlestick charts for diabetes

Continuous glucose monitoring(CGM)is a popular technology among the diabetic population,especially in patients with type 1 diabetes and those with type 2 diabetes treated with insulin.The American Diabetes Association recommends standardization of CGM reports with visual cues,such as the ambulatory glucose profile.Nevertheless,interpreting this report requires training and time for CGM to be cost-efficient.In this work it has been proposed to incorporate Japanese candlestick charts in glucose monitoring.These graphs are used in price analysis in financial markets and are easier to view.Each candle provides extra information to make prudent decisions since it reports the opening,maximum,minimum and closing glucose levels of the chosen time frame,usually the daily one.The Japanese candlestick chart is an interesting tool to be considered in glucose control.This graphic representation allows identification of glucose trends easily through the colors of the candles and maximum and minimum glucose values.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

巧用Star Chart软件开展交互式可视化物理教学——以“行星的运动”为例

手机软件因其性能优良、携带方便等优点,是实现交互式可视化物理教学的得力助手。探讨了利用手机软件“Star Chart”开展交互式可视化物理教学的三个方法:模型与过程可视化、尺度与角度交互、信息共享交互,可为教师开展交互式可视化教学提供参考。

Effect of Measurement Error on the Multivariate CUSUM Control Chart for Compositional Data

Control charts(CCs)are one of the main tools in Statistical Process Control that have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous decades.Measurement errors(M.E’s)are involved in the quality characteristic of interest,which can effect the CC’s performance.The authors explored the impact of a linearmodel with additive covariate M.E on the multivariate cumulative sum(CUSUM)CC for a specific kind of data known as compositional data(CoDa).The average run length(ARL)is used to assess the performance of the proposed chart.The results indicate that M.E’s significantly affects themultivariate CUSUM-CoDaCCs.The authors haveused theMarkov chainmethod to study the impact of different involved parameters using six different cases for the variance-covariance matrix(VCM)(i.e.,uncorrelated with equal variances,uncorrelated with unequal variances,positively correlated with equal variances,positively correlated with unequal variances,negatively correlatedwith equal variances and negatively correlated with unequal variances).The authors concluded that the error VCM has a negative impact on the performance of themultivariate CUSUM-CoDa CC,as the ARL increases with an increase in the value of the error VCM.The subgroup size m and powering operator b positively impact the proposed CC,as the ARL decreases with an increase in m or b.The number of variables p also has a negative impact on the performance of the proposed CC,as the values of ARL increase with an increase in p.For the implementation of the proposal,two illustrated examples have been reported formultivariate CUSUM-CoDaCCs inthe presence ofM.E’s.Onedealswith themanufacturingprocessof uncoated aspirin tablets,and the other is based on monitoring the machines involved in the muesli manufacturing process.

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

Nonparametric(distribution-free)control charts have been introduced in recent years when quality characteristics do not follow a specific distribution.When the sample selection is prohibitively expensive,we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts.In this study,we proposed a nonparametric homogeneously weighted moving average based on theWilcoxon signed-rank test with ranked set sampling(NPHWMARSS)control chart for detecting shifts in the process location of a continuous and symmetric distribution.Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed NPHWMARSS control chart.The proposed NPHWMARSS control chart’s performance is compared to that of parametric and nonparametric control charts.These control charts include the exponentially weighted moving average(EWMA)control chart,Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart,the nonparametric EWMA sign control chart,Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart,and the homogeneously weighted moving average control charts.The findings show that the proposed NPHWMARSS control chart performs better than its competitors,particularly for the small shifts.Finally,an example is presented to demonstrate how the proposed scheme can be implemented practically.

Memory-Type Control Charts Through the Lens of Cost Parameters

A memory-type control chart utilizes previous information for chart construction.An example of a memory-type chart is an exponentially-weighted moving average(EWMA)control chart.The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts.Meanwhile,the EWMA median chart is robust against outliers.In light of this,the economic model of the EWMA and EWMA median control charts are commonly considered.This study aims to investigate the effect of cost parameters on the out-of-control average run lengthðARL_(1)Þin implementing EWMA and EWMA median control charts.The economic model was used to compute the ARL_(1) parameter.The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis.When the input parameters change based on a predetermined percentage,the ARL_(1) is affected.According to the results of the EWMA chart,nine input parameters had an effect andfive input parameters had no effect on the ARL_(1) parameter.Further,only seven of the 14 input parameters had an effect on the ARL_(1) of the EWMA median chart.However,the effect of each input parameter on the ARL_(1) was different.Moreover,the ARL_(1) for the EWMA median chart was smaller than the EWMA chart.This analysis is crucial to observe and determine the input parameters that have a significant impact on the ARL_(1) of the EMWA and EWMA median control charts.Hence,practitioners can obtain an overview of the influence of the input parameters on the ARL_(1) when implementing the EWMA and EWMA median control charts.

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.

Contributions of annual and semiannual tidal constituents to chart datum in the China seas and adjacent waters

Global uniform chart datum(CD)surface construction is the basic upon which to realize various vertical datums transformation,and is of great importance for geospatial data expression under the same vertical datum.Generally,the CD level is computed by developing the function between tidal constituents’harmonic constants and time,i.e.,the lowest astronomical tide is taken as the lowest predicted tide level by adopting the major constituents over a 19-a period.The CD surface prescribed in China is the theoretical lowest tide(TLT)and is calculated using 13 tidal constituents,i.e.,short-period(Q_(1),O_(1),P_(1),K_(1),N_(2),M_(2),S_(2),K_(2),M_(4),MS_(4)and M_(6))and long-period(Sa and Ssa)tidal constituents.Although the accuracy in determining short-period tidal constituents has improved gradually,the long-period tide has not been studied thoroughly owing to nonstationary and temporal variations.Previous studies have intended to evaluate the effect of Sa and Ssa tides in the determination of the TLT level for the purpose of determining a more accurate CD surface for the China seas and adjacent waters.Here,the parameters of long-period tidal correction and long-period tidal correction rate were treated as the effect of both Sa and Ssa on the TLT,and the TOPEX/Poseidon and Jason series satellite altimetry data ranged from October 1992 to April 2022 were adopted to analyze the contribution of long-period tidal constituents.Results showed that the average long-period correction value is 10.10 cm(range from 8.57 cm to 14.98 cm),and that the average long-period tidal contribution rate is 14.56%(range from 9.09%to 23.97%)in the China seas and adjacent waters.Finally,data from 82 tide gauge station with at least a 1-a record of hourly observations were compared with satellite-derived result.We concluded that the long-period tidal contribution should not be neglected in TLT construction.Furthermore,to reduce tidal datum uncertainty,accurate extraction of long-period tidal constituents should receive closer attentions.

Top-down法评定EDTA络合滴定法测定海洋沉积物中碳酸钙含量的不确定度

依据Top-down技术中的质控图法对EDTA络合滴定法测定海洋沉积物中碳酸钙含量的不确定度进行评定。利用2021年质控样标准物质GBW 07333、GBW 07314和GBW 07316中CaCO_(3)测定值的时序数据进行评定,3组时序数据正态统计量A^(2*)(s)和独立性统计量A^(2*)(RM)均小于1,CaCO_(3)测定值、A_(EWMi)和移动极差控制图没有失控点,3组时序数据处于受控状态。当CaCO_(3)质量分数分别为2.05%、6.20%和38.56%时,计算得其扩展不确定度分别为0.08%、0.07%和0.20%。将测量不确定度与对应含量值进行线性拟合建立了不确定度预测模型,GBW 07309和GBW 07334中CaCO_(3)的测量不确定度预测值分别为0.09%和0.18%,预测值与Top-down技术获取的评定结果较为吻合。

Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

CO_(2)分注井气嘴节流特性及矿场应用

为了解决CO_(2)分注井节流压差建立困难,气嘴易冲蚀的技术难题,通过构建CO_(2)物性变化的流动-传热耦合模型,揭示2级和3级节流气嘴的流场演化机制,优化设计气嘴结构、建立了绕流气嘴节流图版并开展现场应用。结果表明:流量为10 m3/d时,2级嘴径1.4 mm和3级嘴径1.6 mm的绕流气嘴分别能产生将近6 MPa和8 MPa的节流压差,证明绕流气嘴结构合理、性能可靠、能够达到调整层间压差的技术要求;参照气嘴图版优选的节流气嘴,现场应用20口井,节流压差可达4 MPa左右,调整后注入压力上升2.4 MPa,加强层相对吸气比例由9.7%上升至50.7%,有效调整了层间差异,解决了分注井小层吸气不均的问题。研究结果指导现场测调,为CO_(2)分注规模化应用提供技术支撑。

叙事病历可行性探讨:从概念到临床实践

基于病历反思功能的学理思考、缓和医疗领域病历书写实践的重要发现、对叙事医学工具的概念辨析等内容,结合实证调查材料与分析,聚焦于病历书写实践展开思考与研究。主要内容包括:对叙事病历概念进行界定,即叙事病历是应用于临床,融入叙事性内容的病历;明晰其不同层次的特征与功能;探索其运用于临床的实践路径。在对北京协和医学院叙事医学实践独特性深入发掘的基础上,强调以叙事思维来书写病历的必要性;具体落脚于以叙事的思维与形式助力推动现行病历书写的改善,进一步寻求叙事医学临床路径的一般性框架和多种可能性。

控制图在车用催化器中贵金属测定中的应用

研究建立一种应用于催化器中贵金属测定过程监控的均值-标准差质控图,以确保实验室日常分析结果的准确、可靠。采用标准HJ 509-2009中电感耦合等离子体质谱法测定催化转化器中的铑、钯、铂等3种贵金属元素的含量,收集近两年的质控样的60组数据,进行了正态分布检验,计算了各元素含量结果的平均值、标准偏差,绘制了均值控制图和标准差控制图。结果表明,质控样中铑、钯、铂贵金属元素的数据结果均在均值控制图、标准差控制图的上下限范围内,表明实验室在该段期间内利用电感耦合等离子体质谱法对催化转化器样品中的铑、钯、铂的测定结果的准确可靠。均值-标准差控制图可以有效地观察整个贵金属元素测定过程中的数据变化趋势,有助于判断检测过程是否受控,以保证日常的报告检测结果符合实验室报出的要求,确保结果的准确可靠。

嵌套帕累托图及鱼骨图分析测氡仪检定中不合格项及原因

测氡仪检定合格率相对其他放射性测量仪器来说,偏低一些。为探索各类测氡仪共性的不合格项及影响因素,进而为仪器生产厂家改进和用户使用保养提供建议,最终提高测氡仪检定的合格率,本文从计量机构的优势出发,对近5年的检定数据进行统计,采用统计分析中的嵌套帕累托图,分析影响测氡仪检定合格率的主要项目,针对主要项目深入剖析,分析主要项目中的关键因素,结合上述分析结果及鱼骨图,指出造成测氡仪检定合格率低的关键因素及对策措施。从分析结果可以得出,瞬时测氡仪检定的最主要不合格项是外观和标识,其主要影响因素是土壤采样罐漏气,而连续测氡仪检定的主要不合格项是体积活度响应,主要影响因素是体积活度响应年偏离量偏大,对于测氡仪检定不合格项可从加强人员培训、技术改进及提高零部件质量3个方面进行改善。通过本次统计分析,找出测氡仪检定中不合格项的主要因素并给出合理改进建议,有助于仪器生产厂家、计量技术机构及仪器用户三方协作,从而提高测氡仪检定的合格率,对测氡仪的改进与发展起到积极促进作用。

中国大气田烷烃气碳同位素组成的若干特征

勘探开发大气田是一个国家快速发展天然气工业的重要途径。1991年至2020年,中国新探明大气田68个,促进2020年产气1925×10^(8)m^(3),成为世界第4产气大国。基于中国70个大气田的1696个气样组分和烷烃气碳同位素组成数据,获得中国大气田烷烃气碳同位素组成特征:①δ^(13)C_(1)、δ^(13)C_(2)、δ^(13)C_(3)和δ^(13)C_(4)的最轻值和平均值,随分子中碳数逐增而变重,而δ^(13)C_(1)、δ^(13)C_(2)、δ^(13)C_(3)和δ^(13)C_(4)的最重值,随分子中碳数逐增而变轻。②中国大气田δ^(13)C_(1)值的分布区间为−71.2‰~−11.4‰,其中生物气δ^(13)C_(1)值的分布区间为−71.2‰~−56.4‰;油型气δ^(13)C_(1)值的分布区间为−54.4‰~−21.6‰;煤成气δ^(13)C_(1)值的分布区间为−49.3‰~−18.9‰;无机成因气δ^(13)C_(1)值的分布区间为−35.6‰~−11.4‰;根据这些数据编制了中国大气田的δ^(13)C_(1)值尺图。③中国天然气δ^(13)C_(1)值的分布区间为−107.1‰~−8.9‰,其中生物气δ^(13)C_(1)值为−107.1‰~−55.1‰;油型气δ^(13)C^(1)值为−54.4‰~−21.6‰;煤成气δ^(13)C_(1)值为−49.3‰~−13.3‰;无机成因气δ13C1值为−36.2‰~−8.9‰;根据上述数据编制了中国天然气的δ^(13)C_(1)值尺图。

基于危险因素评估白内障患者术后角膜水肿发生风险的预测模型构建与验证

目的:构建基于危险因素评估白内障患者术后角膜水肿发生风险的预测模型并验证。方法:选取2021年7月—2023年7月本院收治的339例白内障患者(339眼),将入选者以7∶3比例(按随机数字表法)随机分为建模组(237例)与验证组(102例),根据术后是否发生角膜水肿将患者分为角膜水肿组和非角膜水肿组;构建列线图模型(R软件),评估模型预测效能。结果:本研究237例患者中有68例在术后发生角膜水肿,发生率为28.69%。角膜水肿组和非角膜水肿组在年龄、糖尿病史、晶状体核硬度、手术切口靠前、术前前房深度、后弹力层撕脱方面比较有统计学差异(P<0.05)。多因素Logistic回归分析结果显示,年龄、糖尿病史、晶状体核硬度、手术切口靠前、术前前房深度和后弹力层撕脱是白内障患者术后发生角膜水肿的危险因素(P<0.05)。建模组ROC曲线下面积(AUC)为0.950,区分度较好,H-L检验为χ^(2)=7.364,P=0.681,一致性良好。外部验证的AUC为0.966,区分度较好,H-L检验为χ^(2)=7.517,P=0.702,一致性良好。结论:年龄、糖尿病史、晶状体核硬度、手术切口靠前、术前前房深度和后弹力层撕脱是白内障患者术后发生角膜水肿的危险因素,构建的列线图模型区分度与一致性良好,能直观预测白内障患者术后发生角膜水肿的风险。

极区横向坐标系的极球面投影特性及使用方法

根据极区横向坐标系与航海图配合使用需要,研究了极球面投影极区航海图上横向坐标系的投影特性及使用方法。首先,根据横向坐标系定义和极球面投影公式,推导了极球面投影海图上横向坐标系经纬线和子午线收敛角的投影公式;然后,结合极区航海图的图幅规格、类型和航海绘算要求,对单幅海图上横向经纬线格网形态和横向子午线收敛角分布特性进行了定量分析,给出了图上横向坐标系格网及横向子午线收敛角的使用方法;最后,根据极球面投影航海图上各航向基准的几何关系,得到基于横向子午线收敛角的横向航向、真航向和地理航向的相互转换关系,形成了横向坐标系在极球面投影极区航海图上的初步使用方案,可为后续极区航海图编制使用、电子海图显示及信息系统研制提供参考依据。