QC七大手法之管制图

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,管理图,QC,手法之六,目 录,名称、定义,原理,种类,基本形状,X,图与,R,图,XR,S,图,P,图,Pn,图,C,缺陷图,U,图,管理状态的判断,管理图的使用,注意事项,2024/11/30,2,什么是管理图？,又名-控制图,它是用于分析和判断工序是否处于稳定状态所使用的带有管理界限的图,1926年休哈特（美）博士根据统计学原理提出管理图绘制方法,根据使用侧重点不同，可分为分析用管理图和控制用管理图,2024/11/30,3,原 理,3,原理管理图上下限是根据正态分布中 3,范围内概率原理制定的（小概率事件）,能判断是否出现异常,基本不能把非异常判断为异常（误判概率较小）,质量波动原因-偶然原因（随机、不可避免、正常）；异常原因（系统、有规律、可避免）,稳定状态-仅受偶然原因影响的状态,2024/11/30,4,管理图种类-,两大类九种,计量值管理图（5种）,平均值管理图（,X,图）,单值管理图（,X,图）,中位数管理图（,X,图）,极差管理图（,S,图）,移动极差管理图（,R,S,图）,计数值管理图（两小类4种）,计件值管理图（2种）,不良品率管理图（,P,图,不良品管理图（,Pn,图,计点值管理图（2种）,缺陷数管理图（,C,图）,单位缺陷数管理图（,U,图）,又可分为两种-,分析用管理图 通过分层或改变分群方法探讨偏差原因,控制用管理图-通过每日数据打点查明工序是否异常,2024/11/30,5,管理图,计量值管理图,计数值管理图,X,图,X,图,X,图,R,图,R,S,图,计件值管理图,计点值管理图,P,图,Pn,图,C,图,U,图,2024/11/30,6,时间或样本序号,上管理限,UCL,下管理限,LCL,中心线,CL,特性值,管理图形状,2024/11/30,7,基本制作方法,从工序按时间顺序定时抽样，每次抽样的样本容量应相同。如样本容量为5，每班按时间顺序抽取20 个样本，共100个数据,计算中心线、上下管理限,按时间顺序或样本序号将数据用点子描在图上并连线,根据点子所在位置判断工序质量状况。,2024/11/30,8,X-R,图,X,图-观察工序平均值变动情况,R,图-观察工序离散情况,适用于计量值质量特性的管理，如长度、电阻值、抗拉强度、纯度等,为什么用,R,图代替,S,图？,S,计算复杂，不便使用；,R,在一定程度上反映了数据离散情况,S=AR,系数,A,随样本容量而变,2024/11/30,9,制图步骤,收集数据-,N=100（1）,近期数据（2）数据与工序今后状态一致,数据分群-20-25个，每群一般4-6个数据，最多不超10个,分群方法-条件大致相同群内不含不同性质的数据，保证群内仅有偶然因素影响，一般按时间顺序或采用随机数表法,填入数据记录表，计算,X、R,计算总平均,X=X/K（K-,群数）,X,比测量值多两位,计算,R=R/K（,位数多一位）,计算管理界限,X,图-,CL=X,UCL=XA,2,R,LCL=X,A,2,R,R,图-,CL=R,UCL=D,4,R,LCL=D,3,R,2024/11/30,10,绘图-管理图绘制在直角坐标纸上，背景线条应细而浅,选择纵坐标考虑-上下限间隔30,MM,；,界限外有充分余地,选择横坐标-点间2-3,MM,使图美观，易用,中心线用实线；上下限用虚线或点划线,记入标点-区别清楚；界限外的点特殊标记；分层用颜色表示；点间依序用细实线相连,复核-使管理图界限符合实际-点子是否都在界限内；若有异常点应采取纠正措施并剔除之再次计算绘制、在复核、直至所有点均正常为止。多次修正后的管理界限就可用来工序控制了,档案记录-数据个数,N；,样本容量；抽取方式；数据来源；控制项目；取样时间；质量特性；分析处理意见；测量者；仪器及精度；绘图者、日期；其他现场观察事项。,2024/11/30,11,系数表,n,A,2,D,4,D,3,2,1.880,3.267,0,3,1.023,2.575,0,4,0.729,2.282,0,5,0.577,2.115,0,6,0.483,2.004,0,7,0.419,1.924,0.076,8,0.373,1.864,0.136,9,0.337,1.816,0.184,10,0.308,1.777,0.223,2024/11/30,12,数据记录表-晶体管直流放大倍数 (*表示异常）,序号,X,1,X,2,X,3,X,4,X,5,Xmax,Xmin,X,R,1,0.023,0.015,0.375,0.240,0.077,0.375,0.015,0.146,0.360,2,0.410,0.044,0.015,0.028,0.019,0.410,0.015,0.103,0.395,3,0.600*,0.015,0.028,0.140,0.019,0.600,0.015,0.160,0.585,4,0.013,0.380,0.200,0.022,0.070,0.380,0.013,0.137,0.367,5*,-0.056,-0.200,0,-0.088,-0.078,0,-0.200,-0.084,0.200,6,0,-0.145,0,-0.060,0,0,-0.145,-0.041,0.145,7*,-0.113,-0.170,-0.090,-0.224,-0.111,-0.090,-0.224,-0.142,0.134,8,0,-0.088,-0.060,0,0,0,-0.088,-0.030,0.088,9,0.118,0.121,0.163,0.303,0.088,0.303,0.088,0.159,0.215,10,0.148,0.531*,0.141,0,-0.055,0.531,-0.055,0.153,0.586,11,0.158,0.188,0.260,0.063,0.222,0.260,0.063,0.178,0.197,12,0.065,0.154,0.149,0.062,0.149,0.154,0.062,0.116,0.092,13,0.130,0.071,0.250,0,0.080,0.250,0,0.106,0.250,14,0.150,0.200,0.051,0.083,-0.063,0.200,-0.063,0.084,0.263,15,0.094,0.074,0.149,0.167,0.123,0.167,0.074,0.121,0.093,2024/11/30,13,数据记录表-晶体管直流放大倍数 (*表示异常）,序号,X,1,X,2,X,3,X,4,X,5,Xmax,Xmin,X,R,16,0.180,0.083,0.180,0.091,0.091,0.180,0.083,0.125,0.097,17,0.220,0.083,0.157,0.049,0.250,0.250,0.049,0.109,0.201,18,0.160,0.049,0.099,0.148,0.036,0.160,0.036,0.098,0.124,19,0.099,0.073,0.093,0.087,0.117,0.117,0.073,0.094,0.044,20,-0.740*,0.042,0.031,0.063,-0.032,0.063,-0.740,-0.127,0.803,21,0.135,0.104,0.227,0.175,0.053,0.227,0.053,0.139,0.174,22,0.338,0.141,0.190,0.129,0.036,0.338,0.036,0.167,0.302,23,0.340,0.108,0.211,0.181,0.200,0.340,0.108,0.208,0.232,24,0.181,0.053,0.133,0.125,0.054,0.181,0.053,0.109,0.128,25,0,0.030,0.026,0.053,0.162,0.162,0,0.054,0.162,26,0.097,0,0.107,0.037,0.020,0.107,0,0.052,0.107,27,0,0.035,0,0.612*,0.262,0.612,0,0.182,0.612,28,0.037,0.171,0.038,0.117,0.125,0.171,0.037,0.098,0.134,X,0.08836,R,0.2532,2024/11/30,14,X-R,图示例,N=140;n=5;k=28,X,图-,CL=0.08836,UCL=0.23446,LCL=-0.05774,R,图-,CL=0.2532,UCL=0.5355,LCL=0,剔除8组异常数据(35678102027)计算,X,图-,CL*=0.12015,UCL*=0.23373,LCL*=0.00657,R,图-,CL*=0.19658,UCL*=0.41634,LCL*=0,2024/11/30,15,CL,CL*,CL,CL*,UCL,UCL*,UCL,UCL*,LCL,LCL*,LCL,LCL*,A,图,R,图,2024/11/30,16,X-R,S,管理图,计量值管理图,应用场合-希望尽快发现、消除异常；工序只能获一个数据（日电耗）；工序内部均匀，不需多个测定值；费用、时间关系只能得一个测定值；,优点-无烦琐计算，数据直接打点；从测定到判定时间短,缺点-不易发现工序分布平均的变化,移动极差,R,S,-,顺序观测值,X,1,、X,2,X,N,相邻观测值之差,R,S,=（R,S1,+R,S2,+R,SK-1,）/K-1,X,图-,UCL=X+2.66R,S,CL=X,LCL=X2.66R,S,R,S,图-,UCL=3.27R,S,CL=R,S,LCL,不考虑,2024/11/30,17,P,图,计数值管理图,通过观察产品不良率管理质量,样本容量50且数量一致,使二项分布接近正态分布,计算,P,P=,Pn/n(Pn,-,样本中不良品数,n-,样本容量),计算,P,P=,Pn/n,计算管理限,UCL=P+3P(1P)/n,CL=P,LCL=P3P(1P)/n,当,LCL,得负数时表示不考虑下限,2024/11/30,18,Pn,图,Pn,图用于不良品数管理,样本容量一定且大些(,n,50),计算不良品平均个数,Pn,=,Pn/k(k,),计算管理限,UCL=Pn+3Pn(1P),CL=,Pn,(P=,Pn,/n),LCL=Pn3Pn(1P),(LCL0,不考虑),2024/11/30,19,C,图,计点管理图,一定单位中缺陷数管理,服从泊松分布,C5,时近似正态分布,平均缺陷数,C,C=C/K(K-,群数),计算管理限,UCL=C+3C,CL=C,LCL=C3C,(LCL0,不考虑),2024/11/30,20,U,图,计点管理图,观察样本中单位缺陷数管理,单位缺陷数,U=C/n,平均单位缺陷数,U,U=C/n,计算管理限,UCL=U+3U/n,CL=U,LCL=U3U/n,2024/11/30,21,绘制管理图目的,目的-从中发现有关质量、工程作业等管理状态情况,找出异常原因并消除之,使用时应清楚-点怎样随工序变动,找出工程分布变化趋势对于工序某种变化,点应怎样变动,当工序处稳定状态,质量特性呈正态分布,不随时间变化,点都在界限内,无缺陷排列.,2024/11/30,22,判定工序处稳定状态条件,工序稳定,应同时满足两个条件-没有超出界限的点;点排列分布无缺陷.,休哈特做定量解释-只有满足以下条件之一才算工序稳定,(1)连续25点以上处于界限内,(2)连续35点仅有1个点超出界限,(3)连续100点有不多于2点超出界限,2024/11/30,23,点的缺陷排列,1、连,2、点多,在同侧,3点连,7点连,5点连,11点有10点在上侧,2024/11/30,24,点的缺陷排列,3、趋势,4、周期,性变化,6点连续升,7