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 cos...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.展开更多
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 an...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.展开更多
Petrochemical industry plays an important role in the development of the national economy. Purified terephthalic acid(PTA) is one of the most important intermediate raw materials in the petrochemical and chemical fibe...Petrochemical industry plays an important role in the development of the national economy. Purified terephthalic acid(PTA) is one of the most important intermediate raw materials in the petrochemical and chemical fiber industries. PTA production has two parts:p-xylene(PX) oxidation process and crude terephthalic acid(CTA) hydropurification process. The CTA hydropurification process is used to reduce impurities, such as 4-carboxybenzaldehyde, which is produced by a side reaction in the PX oxidation process and is harmful to the polyester industry. From the safety and economic viewpoints, monitoring this process is necessary. Four main faults of this process are analyzed in this study. The common process monitoring methods always use T^2 and SPE statistic as control limits. However, the traditional methods do not fully consider the economic viewpoint. In this study, a new economic control chart design method based on the differential evolution(DE) algorithm is developed. The DE algorithm transforms the economic control chart design problem to an optimization problem and is an excellent solution to such problem. Case studies of the main faults of the hydropurification process indicate that the proposed method can achieve minimum profit loss.This method is useful in economic control chart design and can provide guidance for the petrochemical industry.展开更多
Validating a method of analysis goes through different steps, which aims at testing the normality of measurements distribution, estimating the uncertainty of the components of a measurement （i.e., accuracy and correc...Validating a method of analysis goes through different steps, which aims at testing the normality of measurements distribution, estimating the uncertainty of the components of a measurement （i.e., accuracy and correctness）, and finally, define the control tests of non degradation of the method performances. This paper outlines the steps for validating a biological method of analysis. It involves the construction of an experimental design, a statistical model, and the preparation of an interne laboratory reference material （pilot vaccine）. The latter is used to study the impact of deviation and variation factors, in order to, optimize the analytical method, to evaluate the bias （random error）, and to calculate the uncertainty of measurement, and make the control charts. This method is applied in the titration of live viral vaccines of Gumboro disease on chicken＇s embryos fibroblasts. The experimental results show that potential influence factors related to the titration method had no significant influence on the obtained results. Taking into account these results, an operating mode has been elaborated. The finalized method proved to be faithful to standard deviation of repeatability and reproducibility of 0.21 and 0.22, respectively, with a confidence level of 95%. The calculated uncertainty of measurement is equal to 0.2, which represents the average error level of a titer. A homogeneous stock of interne laboratory reference vaccine （MRIL）, with an average titer of 5.9 log DIT 50, was produced and the control chart set in away to provide the laboratory with an important tool of control and monitoring of the viral titers evolution in time, as well as, the mastery of the validated titration method performances.展开更多
提出了一种简单、有效的用以辅助设计单值控制图的方法.该方法综合考虑了样本容量、采样频率以及控制图控制限等3个参数，引入了平均生产产量APQ（average production quantity）作为衡量控制图性能的标准.基于APQ构建了一个数...提出了一种简单、有效的用以辅助设计单值控制图的方法.该方法综合考虑了样本容量、采样频率以及控制图控制限等3个参数，引入了平均生产产量APQ（average production quantity）作为衡量控制图性能的标准.基于APQ构建了一个数学模型，该数学模型以采样率和最大错判概率为已知输入来计算出最优的控制图设计参数，从而满足优化设计的目的.该方法包含了涉及控制图设计的所有关键元素，但是它比控制图的经济和半经济设计模型简单易用.展开更多
针对输出质量特性服从正态分布的随机偏移单部件可修系统,研究了可变样本容量和控制线(Variable Sampling Size and Control Limits,VSSCL)均值控制图和预防维修策略联合经济设计问题。首先,构建了VSSCL均值控制图和预防维修策略联合经...针对输出质量特性服从正态分布的随机偏移单部件可修系统,研究了可变样本容量和控制线(Variable Sampling Size and Control Limits,VSSCL)均值控制图和预防维修策略联合经济设计问题。首先,构建了VSSCL均值控制图和预防维修策略联合经济设计的集成框架,揭示控制图和预防维修策略运行的耦合机制;然后,基于VSSCL均值控制图和系统状态特征参数,针对给出的集成框架确定了可能形成系统更新的四个维修事件的发生概率,并进一步利用更新过程理论和全概率公式,建立了VSSCL均值控制图和预防维修策略联合经济设计的平均单位时间成本最小决策模型;同时,针对具体实例,将构建的联合设计决策模型和独立设计决策模型进行比较分析,结果表明联合设计决策模型具有明显的经济优势;最后,利用回归正交试验设计方法对模型参数的灵敏度进行了分析。展开更多
针对在统计过程控制(Statistical Process Control,SPC)中人力资源分配的问题,研究了采用均值-极差(-R)控制图监控过程时,人力资源分配对-R控制图经济设计的影响。首先,构建带有人力资源分配的X-R控制图经济费用函数模型;其次,采用...针对在统计过程控制(Statistical Process Control,SPC)中人力资源分配的问题,研究了采用均值-极差(-R)控制图监控过程时,人力资源分配对-R控制图经济设计的影响。首先,构建带有人力资源分配的X-R控制图经济费用函数模型;其次,采用模式搜索算法对模型进行寻优,获得控制图设计参数的综合最优解、最小费用以及最优的人力资源分配;最后,进行了算例说明和参数的灵敏度分析,结果表明在-R控制图的监控活动中,合理的人力资源分配可以明显的减小过程处于失控状态的时间以及监控过程的费用。展开更多
文摘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.
基金funded by the Universiti Kebangsaan Malaysia,Geran Galakan Penyelidikan,GGP-2020-040.
文摘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.
基金supported by the National Natural Science Foundation of China (61422303, 21376077)Fundamental Research Funds for Central Universities
文摘Petrochemical industry plays an important role in the development of the national economy. Purified terephthalic acid(PTA) is one of the most important intermediate raw materials in the petrochemical and chemical fiber industries. PTA production has two parts:p-xylene(PX) oxidation process and crude terephthalic acid(CTA) hydropurification process. The CTA hydropurification process is used to reduce impurities, such as 4-carboxybenzaldehyde, which is produced by a side reaction in the PX oxidation process and is harmful to the polyester industry. From the safety and economic viewpoints, monitoring this process is necessary. Four main faults of this process are analyzed in this study. The common process monitoring methods always use T^2 and SPE statistic as control limits. However, the traditional methods do not fully consider the economic viewpoint. In this study, a new economic control chart design method based on the differential evolution(DE) algorithm is developed. The DE algorithm transforms the economic control chart design problem to an optimization problem and is an excellent solution to such problem. Case studies of the main faults of the hydropurification process indicate that the proposed method can achieve minimum profit loss.This method is useful in economic control chart design and can provide guidance for the petrochemical industry.
文摘Validating a method of analysis goes through different steps, which aims at testing the normality of measurements distribution, estimating the uncertainty of the components of a measurement （i.e., accuracy and correctness）, and finally, define the control tests of non degradation of the method performances. This paper outlines the steps for validating a biological method of analysis. It involves the construction of an experimental design, a statistical model, and the preparation of an interne laboratory reference material （pilot vaccine）. The latter is used to study the impact of deviation and variation factors, in order to, optimize the analytical method, to evaluate the bias （random error）, and to calculate the uncertainty of measurement, and make the control charts. This method is applied in the titration of live viral vaccines of Gumboro disease on chicken＇s embryos fibroblasts. The experimental results show that potential influence factors related to the titration method had no significant influence on the obtained results. Taking into account these results, an operating mode has been elaborated. The finalized method proved to be faithful to standard deviation of repeatability and reproducibility of 0.21 and 0.22, respectively, with a confidence level of 95%. The calculated uncertainty of measurement is equal to 0.2, which represents the average error level of a titer. A homogeneous stock of interne laboratory reference vaccine （MRIL）, with an average titer of 5.9 log DIT 50, was produced and the control chart set in away to provide the laboratory with an important tool of control and monitoring of the viral titers evolution in time, as well as, the mastery of the validated titration method performances.
文摘提出了一种简单、有效的用以辅助设计单值控制图的方法.该方法综合考虑了样本容量、采样频率以及控制图控制限等3个参数，引入了平均生产产量APQ（average production quantity）作为衡量控制图性能的标准.基于APQ构建了一个数学模型，该数学模型以采样率和最大错判概率为已知输入来计算出最优的控制图设计参数，从而满足优化设计的目的.该方法包含了涉及控制图设计的所有关键元素，但是它比控制图的经济和半经济设计模型简单易用.
文摘针对输出质量特性服从正态分布的随机偏移单部件可修系统,研究了可变样本容量和控制线(Variable Sampling Size and Control Limits,VSSCL)均值控制图和预防维修策略联合经济设计问题。首先,构建了VSSCL均值控制图和预防维修策略联合经济设计的集成框架,揭示控制图和预防维修策略运行的耦合机制;然后,基于VSSCL均值控制图和系统状态特征参数,针对给出的集成框架确定了可能形成系统更新的四个维修事件的发生概率,并进一步利用更新过程理论和全概率公式,建立了VSSCL均值控制图和预防维修策略联合经济设计的平均单位时间成本最小决策模型;同时,针对具体实例,将构建的联合设计决策模型和独立设计决策模型进行比较分析,结果表明联合设计决策模型具有明显的经济优势;最后,利用回归正交试验设计方法对模型参数的灵敏度进行了分析。
文摘针对在统计过程控制(Statistical Process Control,SPC)中人力资源分配的问题,研究了采用均值-极差(-R)控制图监控过程时,人力资源分配对-R控制图经济设计的影响。首先,构建带有人力资源分配的X-R控制图经济费用函数模型;其次,采用模式搜索算法对模型进行寻优,获得控制图设计参数的综合最优解、最小费用以及最优的人力资源分配;最后,进行了算例说明和参数的灵敏度分析,结果表明在-R控制图的监控活动中,合理的人力资源分配可以明显的减小过程处于失控状态的时间以及监控过程的费用。
