基于VBA编程的尧敦图绘制方法及其在能力验证中的应用

基于霍特林T²检验推导了ISO 13528标准的能力验证尧敦(Youden)椭圆数学模型,并推导了尧敦椭圆的画法。通过细分Z_X坐标轴的方式把该数学模型转化为Excel的计算模型,采用VBA编程绘制出z值为坐标轴的尧敦图,通过坐标转换可以绘制以测量结果为坐标轴的尧敦椭圆。在1个尧敦图中同时绘制出置信水平为95%和99%的置信椭圆,直观地显示出满意结果、存疑结果和不满意结果。结合尧敦图可以分析实验室结果偏离原因,指导实验室的整改。即使不采用VBA编程,在Excel 平台上直接采用细分坐标轴的方法绘制尧敦图,也能够减少大量的计算工作,提高了绘图的效率,可以促进尧敦图在能力验证数据统计分析中的应用。应用绘制方法绘制了不锈钢化学成分分析能力验证中磷元素的尧敦图,根据绘制的尧敦图并结合能力验证数据分析了不满意或有问题结果产生的原因。

Drawing method for Youden plot by VBA programming and its application in proficiency testing

The mathematical model of Youden ellipse for proficiency testing of ISO 13528 standard was derived base on Hotelling′s T² test. Meanwhile, the drawing method of Youden ellipse was also proposed. This mathematical model was changed to the calculation model of Excel by subdividing Z_X axis. The Youden plot with axis of z-score was drew using VBA programming. Meanwhile, the Youden plot with axis of testing results was obtained by axis transformation. In the same Youden plot, the confidence ellipse with confidence levels of 95% and 99% were drawn out respectively to give a visual display of satisfactory results, questionable results and unsatisfactory results. The reasons for result deviation in laboratory could be analyzed by combining Youden plot to guide the remediation of laboratory. Even without VBA programming, the subdivided axis drawing method could be used to draw out Youden pot directly in Excel, which could reduce the calculation amount and improve the plotting efficiency. The method could facilitate the use of Youden plot in proficiency testing. The Youden ellipse of phosphorus in the proficiency testing of stainless steel chemical composition analysis was drawn by the proposed method. The reasons of unsatisfactory or problematic results were analyzed according to the Youden ellipse and results of proficiency testing.