This paper analyzes the effect of subgroup size on the x-bar chart characteristics using sample influx (SIF) into forensic science laboratory (FSL). The characteristics studied include changes in out-or-control points...This paper analyzes the effect of subgroup size on the x-bar chart characteristics using sample influx (SIF) into forensic science laboratory (FSL). The characteristics studied include changes in out-or-control points (OCP), upper control limit UCLx, and zonal demarcations. Multi-rules were used to identify the number of out-of-control-points, Nocp as violations using five control chart rules applied separately. A sensitivity analysis on the Nocp was applied for subgroup size, k, and number of sigma above the mean value to determine the upper control limit, UCLx. A computer code was implemented using a FORTRAN code to create x-bar control-charts and capture OCP and other control-chart characteristics with increasing k from 2 to 25. For each value of k, a complete series of average values, Q(p), of specific length, Nsg, was created from which statistical analysis was conducted and compared to the original SIF data, S(t). The variation of number of out-of-control points or violations, Nocp, for different control-charts rules with increasing k was determined to follow a decaying exponential function, Nocp = Ae–α, for which, the goodness of fit was established, and the R2 value approached unity for Rule #4 and #5 only. The goodness of fit was established to be the new criteria for rational subgroup-size range, for Rules #5 and #4 only, which involve a count of 6 consecutive points decreasing and 8 consecutive points above the selected control limit (σ/3 above the grand mean), respectively. Using this criterion, the rational subgroup range was established to be 4 ≤ k ≤ 20 for the two x-bar control chart rules.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
文摘This paper analyzes the effect of subgroup size on the x-bar chart characteristics using sample influx (SIF) into forensic science laboratory (FSL). The characteristics studied include changes in out-or-control points (OCP), upper control limit UCLx, and zonal demarcations. Multi-rules were used to identify the number of out-of-control-points, Nocp as violations using five control chart rules applied separately. A sensitivity analysis on the Nocp was applied for subgroup size, k, and number of sigma above the mean value to determine the upper control limit, UCLx. A computer code was implemented using a FORTRAN code to create x-bar control-charts and capture OCP and other control-chart characteristics with increasing k from 2 to 25. For each value of k, a complete series of average values, Q(p), of specific length, Nsg, was created from which statistical analysis was conducted and compared to the original SIF data, S(t). The variation of number of out-of-control points or violations, Nocp, for different control-charts rules with increasing k was determined to follow a decaying exponential function, Nocp = Ae–α, for which, the goodness of fit was established, and the R2 value approached unity for Rule #4 and #5 only. The goodness of fit was established to be the new criteria for rational subgroup-size range, for Rules #5 and #4 only, which involve a count of 6 consecutive points decreasing and 8 consecutive points above the selected control limit (σ/3 above the grand mean), respectively. Using this criterion, the rational subgroup range was established to be 4 ≤ k ≤ 20 for the two x-bar control chart rules.
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。
