【正文】 If the process mean can be easily adjusted by manipulating some process inputs, it may be helpful to shift the process mean to the desired value.216。 If we discard the point, no analytical justification other than assuming that the process has been out of control but will not now. Trial control limits after revision may cause more false alarms.216。FSGS M00 Rev B 59Designing an XR Chart This chart is for ? = % only.k,(1 b)FSGS M00 Rev B 60Sampling Interval Sample Size Procedure抽樣間隔和樣本大小選擇程序13. Instead of using above graph, following equation can be used to calculate n下列等式也可以計算 n值 :14. Alternatively, above formula isalso available in Minitab. Use:Stat Power and Sample Size 1sample Z這個公式也可以在 Minitab 中找到Designing an XR Chart FSGS M00 Rev B 61Example 1: Designing an XR ChartYour management has the following concerns with regards to implementing control charts at the shopfloor在推行控制圖時，管理層很關(guān)心下列問題 :1. False Alarm:錯誤報警Not more than 1 false alarm for every 500 hrs of production每500小時的生產(chǎn)不超過 1個錯誤報警 .2. Exposure:暴露Not more than 3 hrs exposure if process has shifted如果制程偏移，不超過 3小時暴露 .3. Allowable Shift允許偏移 :From historical data, Ppk ? .Min customer requirement, Ppk ? Design an appropriate XbarR chart to meet the above FSGS M00 Rev B 62After some time, the factory decides to switch to 14 hrs of production per ，工廠決定每天 14小時生產(chǎn)Tolerable false alarm:極限錯誤報警Average 1 false alarm per month (30 days)每月平均 1個錯誤報警What changes do you need to make to the charts you have designed in Example 1?照此條件，對所設(shè)計的例子 1的控制圖有何改變？Example 2: Designing an XR ChartFSGS M00 Rev B 63Where to Use SPC Charts? When a mistakeproofing device is not feasible當(dāng)過失防治設(shè)施不可行時? Identify processes with high RPNs from FMEA從 FMEA中識別高風(fēng)險度的制程216。 252。FSGS M00 Rev B 58Sampling Interval Sample Size Procedure抽樣間隔和樣本大小選擇程序9. Based on engineering judgment, define D = max. allowable process drift in m that must be detected根據(jù)工程判斷，決定 允許制程在 m內(nèi)漂移的最大值 D10. Establish process ?x from historical data, or if not available, collect some parts to get a rough estimate根據(jù)歷史數(shù)據(jù)建立制程，如果不可能，建立一個大概11. Alternatively, D/?x ratio (k) can be derived from process capability considerations using following equation:比例 k可以通過下列公式而得到k = D/?x = 3[ Ppkcurrent – Ppkmin ]12. With that, all parameters for puting n are found這樣，所有計算 n的參數(shù)已經(jīng)建立， n可以確定了 :n = f [? , b , D , ? ]Designing an XR Chart 252。 Exp. rate 7. From puted ARL1, establish the required b, or (1 – b), using ARL1 = 1/(1 – b)計算 b, or (1 – b), 8. At this juncture, sampling interval is already established some parameters already established for sample size calculation到現(xiàn)在已經(jīng)有了計算樣本大小的一些參數(shù) : n = f [? , b , D , ? ]Designing an XR Chart 252。3? limits, ? = % 222。 p ? 1/2 and n 10 implying np 5216。 It maximizes the chance of variability due to an assignable cause to appear between samples可以最大化異因在不同樣本內(nèi)出現(xiàn)的機(jī)會 .216。 Normal Distribution正態(tài)分布? Shewhart found that when the averages of subgroups from a constantcause system are plotted in the form of a histogram, the normal distribution appears修哈特發(fā)現(xiàn)當(dāng)把常量系統(tǒng)的子組平均值作成一個直方圖時，就出現(xiàn)了常態(tài)分布 . FSGS M00 Rev B 19Construction of XR Charts? The XR chart is the most versatile of control charts, and is used in most 用控制圖? Charting of averages and charting of ranges are used to check if a constantcause system exists均值圖和極差圖用于檢驗常量系統(tǒng)是否存在 . Xchart measures variability between samples均值圖測量 2個樣本間的差異Rchart measures variability within samples極差圖測量樣本內(nèi)的差異FSGS M00 Rev B 20The Center Line and Control Limits of a Xchart:The Center Line and Control Limits of a Rchart:Construction of XR ChartsFSGS M00 Rev B 21For sample size n 10, R loses its efficiency in estimating process sigma and Rchart may not be appropriate.樣本數(shù)大于 10時，極差不能用于估算制程標(biāo)準(zhǔn)差，極差圖不適用Construction of XR ChartsShewhart Constants修哈特常數(shù)FSGS M00 Rev B 22How do we begin to set up an XR chart from scratch?如何建立均值極差控制圖？Implementing the Control Chart控制圖的推行控制圖的推行FSGS M00 Rev B 23Implementing the Control Chart1) Preparation of Sampling抽樣準(zhǔn)備2) Data Collection數(shù)據(jù)收集3) Construct the Control Chart組建控制圖4) Analysis Interpretation分析5) Use the Control Chart as a Process Monitoring Tool使用控制圖作為制程監(jiān)控工具FSGS M00 Rev B 24Indicators of Instability制程不穩(wěn)定判斷Primary Indicators主要判斷依據(jù)? any point outside of a control limit任意點出界Secondary Indicators次要判斷依據(jù)? any nonrandom pattern of points on a control chart任意規(guī)律的點? shift or run交替性? Trend一定趨勢? Stratification分層? Mixture混合性? Periodicity周期性FSGS M00 Rev B 25MiniTab’s Tests for InstabilitySecondary IndicatorsPrimary IndicatorFSGS M00 Rev B 26Warning Limits警告線? The 3? control limits are also called action limits, . investigation and corrective action are required when a point plots outside of these limits/ 3?控制線又叫行動線，如果點在這些線以外，必須采取行動 .? Sometimes, 2? warning limits are marked on a control chart to increase the sensitivity of the control 2?警告線也標(biāo)示在圖上，以增加控制圖的敏銳性Lower Control LimitUpper Control LimitCenter LineSample Number or TimeSample Quality CharacteristicUpper Warning LimitLower Warning LimitSo what do you do if a point is above the Warning Limit?點在警告線以上如何辦？FSGS M00 Rev B 27? An important idea in control chart theory is the way we pull specimens to form a subgroup of data控制圖原理的一個重要概念是我們將樣本組成數(shù)據(jù)子組的方法 .? This should follow what Shewhart called the rational subgroup concept這必須依據(jù)修哈特的合理子組概念 .? The rational subgroup concept requires that parts are pulled consecutively from the process when forming a sub