质量管理旧七种方法之散布图

Click to edit the title text format,Click to edit the outline text format,Second Outline Level,Third Outline Level,Fourth Outline Level,Fifth Outline Level,Sixth Outline Level,Seventh Outline Level,Eighth Outline Level,Ninth Outline Level,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,散布图,小组成员：徐雪岩 杨烁,郭鹏宇 王凯,2011,年,9,月,散布图,一、概念,二、应用散布图的步,骤,骤,三、散布图的相关性,判,判断,四、散点图应用的发,展,展,五、散布图的应用示,例,例,一、概念,散布图,(scatter diagram),是研究成对出现,的,的两组相关数据,之,之间相关关系的,简,简单图示技术。,在,在散布图中，成,对,对的数据形成点,子,子云，研究点子,云,云的分布状态便,可,可推断成对数据,之,之间的相关程度,。,。,散布图可以,用,用来发现、显示,和,和确认两组相关,数,数据之间的相关,程,程度，并确定其,预,预期关系。,注意事项：,当需要强调的是,，,，在使用散布图,调,调查两个因素之,间,间的关系时，应,尽,尽可能固定对这两个因,素,素有影响的其他,因,因素，才能使通,过,过散布图得到的,结,结果比较准确。,六种典型的点子,云,云形状图,二、应用散布图,的,的步骤,选定对象。,收集成对数据（,X,，,Y,）（至少不得少,于,于,30,对,且数据是一一对,应,应的,）。,标明,X,轴和,Y,轴。,找出,X,和,Y,的最大值和最小,值,值，并用这两个,值,值标定横轴,X,和纵轴,Y,。,描点（当两组数,据,据值相等，即数,据,据点重合时，可,围,围绕数据点画同,心,心圆表示）。,判断（分析研究,点,点子云的分布状,况,况，确定相关关,系,系的类型）。,三、散布图的相,关,关性判断,对照典型图例判,断,断法,中值法（,象限判断法,）,相关系数判断法,实例钢的淬火,温,温度与硬度的相,关,关关系判断,54,880,26,52,840,11,49,840,30,46,820,15,50,860,29,45,830,14,52,860,28,51,830,13,46,830,27,53,870,12,50,840,25,53,820,0,57,880,24,42,810,9,54,880,23,51,860,8,53,850,22,50,870,7,44,810,21,59,890,6,44,820,20,54,850,5,49,830,19,45,840,4,55,870,18,48,850,3,55,860,17,56,890,2,48,820,16,47,810,1,硬度（,HRC,）,Y,淬火温度（,C,0,）,x,序号,硬度（,HRC,）,Y,淬火温度（,C,0,）,x,序号,对照典型图例判,断,断法,硬度（,HRC,）,淬火温度（,）,2.,中值,法,中值判断,法,法又叫象限判,断,断法、符号检,定,定判断法。使,用,用此法的步骤,如,如下：,在散布图上画,一,一条与,Y,轴平行的中值,线,线,f,，使,f,线的左、右两,边,边的点子数大,致,致相等；,在散布图上画,一,一条与,X,轴平行的中值,线,线,g,，使,g,线的上、下两,边,边的点子数大,致,致相等；,f,、,g,两条线把散布,图,图分成,4,个象限区域,I,、,II,、,III,、,IV,。分别统计落,入,入各象限区域,内,内的点子数；,分别计算对角,象,象限区内的点,子,子数；,判断规则；,若,n,I,n,III,n,II,n,IV,，则判为正相,关,关,若,n,I,n,III,n,II,n,IV,，则判为负相,关,关,中值,法,淬火温度（,）,3.,相关系数判断,法,法,相关系数判断,法,法的应用步骤,：,：,简化,X,、,Y,数据。,计算,X,2,，,Y,2,，,X Y,、（,X,Y,）和（,X,Y,）,2,。,计算,X,、,Y,、,X Y,、,X,2,、,Y,2,、,（,X,Y,）和,（,X,Y,）,2,。,计算,L,X X,、,L,Y Y,、,L,X Y,。,L,X X,=,X,2,（,X,）,2,N,L,X Y,=,Y,2,（,Y,）,2,N,L,X Y,=,X Y,（,X,）（,Y,）,N,判断,规,规则,计算,相,相关,系,系数,（,（,r,）。,r,L,XY,L,XX,L,YY,2.,查出,临,临界,相,相关,数,数据,（,（,）。,可根,据,据,N,2,和显,著,著性,水,水平,查表,求,求得,。,。,3.,判断,规,规则,：,：,若,r,，则,X,与,Y,相关,若,r,，则,X,与,Y,不相,关,关,64,8,12,36,4,6,2,15,64,8,15,25,9,5,3,14,196,14,33,121,9,11,3,13,400,20,91,169,49,13,7,12,256,16,48,144,16,12,4,11,225,15,26,169,4,13,2,10,9,3,2,4,1,2,1,9,289,17,66,121,36,11,6,8,289,17,70,100,49,10,7,7,784,28,171,361,81,19,9,6,361,19,70,196,25,14,5,5,81,9,20,25,16,5,4,4,169,13,40,64,25,8,5,3,625,25,144,256,81,16,9,2,64,8,7,49,1,7,1,1,（,X,Y,）,2,X,Y,XY,Y,2,X,2,Y,X,N,O,169,13,36,81,16,9,4,30,8049,453,1716,3778,839,312,141,合计,256,16,60,100,36,10,6,29,324,18,72,144,36,12,6,28,81,9,18,36,9,6,3,27,484,22,112,196,64,14,8,26,196,14,40,100,16,10,4,25,625,25,136,289,64,17,8,24,484,22,112,196,64,14,8,23,324,18,65,169,25,13,5,22,25,5,4,16,1,4,1,21,36,6,8,16,4,4,2,20,144,12,27,81,9,9,3,19,484,22,105,225,49,15,7,18,441,21,90,225,36,15,6,17,100,10,16,64,4,8,2,16,（,X,Y,）,2,X,Y,XY,Y,2,X,2,Y,X,N,O,相关,系,系数,判,判断,法,法,注：,表中,X,值是,（,（,X,800,）,1/10,的简,化,化值,；,；,Y,值是,（,（,Y,40,）,1,的简,化,化值,。,。,表中,X,Y,、（,X,Y,）,2,栏是,校,校对,栏,栏，,以,以免,X,、,Y,、,X,2,、,Y,2,、,XY,各栏,计,计算,错,错误,，,，导,致,致相,关,关性,结,结论,错,错误,。,。校,核,核公,式,式是,：,：,（,X,Y,）,X,Y,（,X,Y,）,2,X,2,2,（,X,Y,）,Y,2,计算,L,XX,、,L,YY,、,L,XY,。,L,XX,=,X,2,（,X,）,2,N,L,YY,=,Y,2,（,Y,）,2,N,L,XY,=,XY,（,X,）（,Y,）,839,（,141,）,2,30,176.3,3778,（,312,）,2,30,533.2,1716,30,249.6,141,312,N,相关,系,系数,判,判断,法,法,计算,相,相关,系,系数,（,（,r,）。,r,L,XY,L,X,X,L,Y,Y,176.3,533.2,249.6,0.814,3.,判,断,断,规,规,则,则,：,：,2.,查,出,出,临,临,界,界,相,相,关,关,数,数,据,据,（,（,）,。,。,根,据,据,N,2,和,显,显,著,著,性,性,水,水,平,平,查,表,表,求,求,得,得,0.361,（,0.05,）,r,0.814,0.361,，,所,所,以,以,钢,钢,的,的,硬,硬,度,度,与,与,淬,淬,火,火,温,温,度,度,呈,呈,强,强,正,正,相,相,关,关,。,。,后,附,附,相,相,关,关,系,系,数,数,检,检,查,查,表,表,以,上,上,三,三,种,种,判,判,断,断,方,方,法,法,对,对,同,同,一,一,实,实,例,例,进,进,行,行,分,分,析,析,判,判,断,断,的,的,结,结,论,论,是,是,一,一,致,致,的,的,。,。,相,关,关,系,系,数,数,检,检,查,查,表,表,0.537,0.423,20,0.708,0.675,10,0.549,0.433,19,0.735,0.602,9,0.561,0.444,18,0.765,0.632,8,0.575,0.456,17,0.798,0.666,7,0.590,0.468,16,0.834,0.707,6,0.606,0.482,15,0.874,0.754,5,0.623,0.497,14,0.917,0.811,4,0.641,0.514,13,0.959,0.878,3,0.661,0.532,12,0.990,0.950,2,0.684,0.553,11,1.000,0.997,1,0.01,0.05,0.01,0.05,N,2,N,2,相关系,数,数检查,表,表,0.181,0.138,200,0.449,0.349,30,0.254,0.195,100,0.456,0.355,29,0.267,0.205,90,0.463,0.361,28,0.283,0.217,80,0.470,0.367,27,0.302,0.232,70,0.478,0.374,26,0.325,0.250,60,0.487,0.381,25,0.354,0.273,50,0.496,0.388,24,0.372,0.288,45,0.505,0.396,23,0.393,0.304,40,0.515,0.404,22,0.418,0.325,35,0.526,0.413,21,0.01,0.05,0.01,0.05,N,2,N,2,散点图,应,应用的,发,发展,用散布,图,图进行,预,预测和,控,控制的,方,方法,确定两,变,变量的,线,线性关,系,系后，,画,画出变,量,量,X,、,Y,的回归,直,直线。,当,当回归,直,直线与,实,实际情,况,况拟合,较,较好时,，,，可以,进,进行预,测,测或控,制,制变量,的,的取值,范,范围。,相关关,系,系与回,归,归分析,相关分析与回归分析,对变量间,统计依赖关系,的考察主要是通过,相关分析,(correlation analysis),或,回归分析,(regression analysis),来完成的：,统计关,系,系与回,归,归分析,1.,在