Ch4 Methods and Philosophy of SPC

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1 Ch4 Methods and Philosophy of SPC
Statistical Process Control（SPC）： 1. Powerful collection of problem-solving tools. 2. Reduce variability to achieve process stability& improve capability. 3. Build an environment in which all individuals in an organization desire continuous improvement in quality and productivity. Seven major tools（The magnificent seven）： 1. Histogram or stem-and-leaf display Check sheet. 3. Pareto chart Cause and effect diagram. 5. Defect concentration diagram Scatter diagram. 7. Control chart.

2 In any production process, regardless of how well designed
or carefully maintained it is, a certain amount of inherent or natural variability will always exist. This natural variability or “background noise” is the cumulative effect of many small, essential unavoidable causes. A process that is operating with only chance cause of variation present is said to be in statistical control. A process that is operating in the presence of assignable cause is said to be out of control. e.g. improperly adjusted or controlled machines,operator errors, or defective raw material.

3 SPC的主要功能：Elimination of variability in the process.
1. 及早發現 assignable causes of process shift. 2. 其中Control chart為一個on-line process-control technique，除了可detect process shift，亦可用來 估計生產過程的參數來決定process capability，及 提供可改進過程的有用資訊。

4 Control chart Shewhart control charts：
：A sample statistic that measures some quality characteristic of interest ：The mean of ：The standard deviation of （upper control limit） Center line = （lower control limit）

5 Typical control chart Points plot within the control limits & no nonrandom pattern : process is in control, no action is necessary. A point plots outside of the control limits or random pattern exists : process is out of control, investigation and correction action are required to eliminate the assignable cause.

6 A point plotting within the control limits is equivalent to
failing to reject the hypothesis of statistical control. A point plotting outside the control limits is equivalent to rejecting the hypothesis of statistical control. Type I error of the control chart : the process is out of control when it is really in control. Type II error of the control chart : the process is in control when it is really out of control. Operating-characteristic cure : an indication of the ability of the control chart to detect process shifts of different magnitudes.

7 E.g. Piston-ring的直徑 Process average = 74 mm（ ） Process standard deviation = 0.01 mm（ ） Sample size = 5 （n） Sampling frequency = every hour Assume ～ Normality distributed About of the sample diameters will fall between

8 3-sigma control limits 如附圖。 Control limits的寬度與 成正比。 若假設 為已知，則 決定control limits等價於 決定右列檢定的拒絕區域

9 Control chart 的最主要作用 Improve the process 通常
大部分的系統皆不是在 control state之下操作。 Routine且attentive的使用control chart可找出 assignable causes，藉由除去 causes 來減少 variability且improve process。 Control chart僅能detect assignable causes， management、operator and engineering action才能eliminate這些causes。 如附圖。

10 Control chart 可分為下列兩類 （1）Variable control charts：
( i ) measure of central tendency ( ii) measure of variability 來描述品質的特徵。 e.g Chart, S chart, R chart （2）Attributes control charts： attribute：品質的特徵無法以數字來表示，只能將其區分為 ( i ) conforming（non-defective） ( ii) non-conforming（defective） e.g. P chart（control chart for fraction non- conforming）, c chart, u chart.

11 Design of the control chart
（1）Selection of the sample size Statistical consideration e.g. n增加，prob. of type II error下降。 （control limit 變窄有助於detect out of control） （2）Control limits （3）Frequency of sampling 近來的研究則會加入economic的考量 e.g. 1. Cost of sampling 2. Losses from allowing excessive amounts of defective product to be produced

12 Choice of control limits
LCL Center line UCL （1）k增加  Type I error下降 Type II error增加 （2）k=3, 3-sigma control limit（U.S.A.通常使用此標準.） prob. of type I error = , if normality is assumed.  An incorrect out of control signal will be generated in only 27 out of 10,000 points. （3） 稱為0.001probability limits (Western Europe通常使用此標準) 當統計量的分布是未知時，則無法求probability limit的值 比較 及 （如附圖）

13 Warning limits = （4） （若使用0.001 limits，則warning limits為0.025limits） 若有多點落在Warning limits及control limits之間，則 懷疑process可能是out of control. Solution  當發現有上述情況產生可即時 增加sampling frequency再做研判。 ＊ 3-sigma limit亦稱為action limits，因為有點落在 3-sigma之外，則立即找出assignable cause，如有 必要則立即採取corrective action。 如附圖。

14 Sample size and sampling frequency
（1）Larger samples easier to detect small shift in the process. e.g. operating-characteristic curve for , 如附圖。 （2）從detecting shifts的觀點 --- large sample very frequently 但卻不是economically feasible. Small samples at short intervals（current industry favor） Large samples at longer intervals. 特別是在high volume manufacturing process及多類 assignable causes會發生的情況，企業界較喜歡採用 “small samples at short intervals”的方式取樣。

15 目前由於Automatic sensing及measurement technology
（e.g. microcomputers）的發展  使得每個被製造的unit 終究都可以被tested！ 見附圖，The probability of detecting a shift from mm to mm increases as the sample size n increases. 我們欲檢測的“the size of the shift”將影響到n的選取。 即為在 之下會accept 的機率 （犯type II error的機率）

16 （3）另一個可以協助決定sample size 及sampling frequency
的量是--- Average run length（ARL） = the average number of points that must be plotted before a point indicate an out of control condition. E.g. Shewhart control chart中 Sampling frequency （Average time to signal） 其中 p = 任何點會超出Control limit的機率 ∴對 with 3-sigma limits

17 即就算整個process是在control之下，平均每370個樣本
仍會出現一個“out of control”的訊號。 若sampling frequency為每小時，則表示平均每370個小 時會有一個false alarm. 假設n=5，且process的mean已shift到74.015mm（i.e. process 已out of control），則從前面之O.C. curve知  平均而言，從發生shift到detect出shift需要2小時。

18 若想improve發現shift的時間可
1. 增加sample size n. e.g. n=10時，由O.C. curve知， p = 0.9 ∴ ARL=1.11，ATS=1.11 hours 2. Sampling more frequency e.g. 每半個小時取一次樣本，則平均約1小時即可detect. 因此若在shift發生後1小時，即必須要能detect出該shift， 可採取下面兩種Design的方法： Design 1 Sample size = n = 5 Sampling frequency：every half hour Design 2 Sample size = n = 10 Sampling frequency：every hour

19 Rational subgroups選取的兩項原則
Using chart to detect changes in the process mean 當Assignable causes發生時 （1）使differences between subgroups的機會達到最大。 （2）使由assignable cause造成difference within a subgroup 的機會達到最小。

20 Rational subgroups選取的方法
(1）Each sample consists of units that were produced at the same time （or as chosely as possible）（snapshot）. ---主要用於detect process shift（此法可minimize within sample variability且maximize between sample variability 且可得到一個較佳的standard deviation的估計值） （2）Each sample consists of units of product that are representive of all units that have been product since the last sample was taken. 亦即 each subgroup is a random sample of all process output over the sampling interval. ---當control chart 是用來決定是否接受 All units of product that have been product since the last sample.

21 注意事項 1. 若process shift to an out of control state and then
back in control between samples，則使用方法（1） 較難發現此種shift，此時建議採用方法（2）。 2. 方法（2）中，若process mean drifts between several levels during the interval between sample，此將造成 ，而造成process是in statistical control的假象！ 3. Several machines that pool their output into a common stream or different heads on the same machine … -----Apply control chart to the output for each individal machine. 4. Rational subgroup consist of a single observation! E.g. chemical process... chart 的control limits變大

22 approach to rational subgroups
The “snapshot” approach to rational subgroups （a）Behavior of the process mean. （b）Corresponding and R control charts. 每次取5個 連續樣本  Shift in process mean. R chart  Process variability is stable.

23 approach to rational subgroups
The random sample approach to rational subgroups （a）Behavior of the process mean. （b）Corresponding and R control charts. 此種抽樣方法易造成within sample 的range過大，而使 chart的limit 過寬，造成in control的假象！

24 Patterns on Control Charts
Defn：A run is defined as a sequence of the same type, the number of the sequence is called its length. e.g. A sequence of increasing （decreasing）points is called a run up（down）. 通常A run of length 8 or more points has a very low probability of occurrence in a random sample of points.  被視為out of control的情況。

25 右圖的週期型態可能是由 operator fatigue, raw material deliveries, heat, or stress build up and so forth，雖然process並未真正的out of control，仍可由消除或減少其原因來改進生產的variability，見下圖。 An chart with a cyclic pattern （a）Variability with the cyclic pattern. （b）Variability with the cyclic pattern eliminated.

26 The Western Electric Handbook（1956）suggests a set of
decision rules for detecting nonrandom patterns on control charts. Specifically, it suggests concluding that the process is out of control if either 1. One point plots outside the 3-sigma control limits. 2. Two out of three consecutive points plot beyond the 2-sigma warning limits. 3. Four out of five consecutive points plot at a distance of 1-sigma or beyond from the center line. 4. Eight consecutive points plot on one side of the center line. ＊ These rules apply to one side of the center line at a time. Sensitizing rules 5. An unusual or nonrandom pattern in the data. 6. One or more points near a warning or control limit.

27 Example：A Western Electric zone rules
（又稱為zone rules for control charts） 如右圖 ∵最後4點均超過 1-sigma limit. ∴根據Western Electric zone rules，此為 nonrandom的pattern， 即process is out of control.

28 假設analyst使用上述的k個criteria，且其中第i個criteria的
Type I error 機率為 ，且若此k個criteria為互相獨立的， 則其overall Type I error（or false-alarm probability）for the decision based on all k tests為： 假設 = reject using i-th criterion. e.g. Type I error 變大

29 The rest of the “Magnificent Seven”
1. Histogram 2. Check sheet 3. Pareto chart 4. Cause and effect diagram 5. Defect concentration diagram 6. Scatter diagram 7. Control chart

30 A check sheet to record defects on tank use in an aerospace
application 由於每個月僅生產數個tank， 因此可summarizing the data monthly！ Time-oriented summary可用於 檢驗其是否有trend or patterns. 可利用trial run確認the check sheet layout and design.

31 The Pareto chart does not identify the most important defects,
but only these that occur most frequently. Pareto chart of the tank defect data Frequency distribution (histogram) of attribute data arranged by category

32 Example of Pareto charts： Electronic assembly process
Stacked Pareto chart Supplier A provides a disproportionally large share of the defection components Locate the device on the printed circuit board

33 Non-manufacturing applications of
quality-improvement method. e.g. 採購機構所畫的Pareto charts

34 Cause and effect diagram for the tank defect problem

35 Cause and effect diagram
1. Define the problem or effect to be analyzed. 2. Form the team to perform the analysis. Often the team will uncover potential causes through brainstorming. 3. Draw the effect box and the center line. 4. Specify the major potential cause categories and join them as boxes connected to the center line. 5. Identify the possible causes and classify them into the categories in steps 4. Create new categories,it necessary. 6. Rank order the causes to identify those that seem most likely to impact the problem. 7. Take corrective action.

36 Defect concentration diagram 的例子
1. Surface-finish defects on a refrigerator.

37 2. Defect concentration diagram for the tank.

38 A scatter diagram Identify potential relationship. Not necessary imply causality!

39 4-6 SPC的實例（製造業） 製造印刷電路板工廠中鍍銅的過程中，常因為下列三種原 因，製造出不符合規格的產品：
1. brittle copper (易碎的銅) 2. copper voids (銅的空隙) 3. Long flow time （其中以此項最麻煩，因為容易造 成過多的工作積壓，並影響工作進度。） 由下列成元員形成一個Improvement Team 1. Plating Tank Operator 2. 負責生產過程的工程師 3. Quality engineer

40 先上課學習“Magnificent seven” 。
第一次小組會議即發現改進品質的最大障礙在於 miss delivery target ，故決定首要目標是減少生產過程中的flow time. 基於operator的經驗，此小組很快的認定造成過長flow time的主因來自於鍍槽中控制銅濃度的調節器的故障時間（downtime）過多。 使用Cause and Effect Analysis 1. 由腦力激盪找出造成Controller downtime的11個主因。 2. 設計一張Check sheet加在工作日誌（logbook）中，機 器每次故障即有一名組員來負責填寫該Check sheet。 3. 收集4-6星期的資料（共收集了6星期）。

41 Pareto analysis 由Pareto analysis中，該小組認為“重建colorimeter”為改進 品質的重要步驟。 在收集資的過程該小組並採用Control charts來monitor Copper concentration，其採樣法為：每日以人工測量三次 的Copper concentration，取其平均。見 、 chart R chart （maximum-minimum）Jan. 3. 、 Tolerance Diagram （以線段連接每日極大與極小值，在 Tolerance Diagram的上下界為specification limits而非control limits，故當observation超過此界限，將造成當機!）由該圖可 見在Jan. 3.假日開機後，當機的次數顯著增加。

42 2月初，由manufacturing engineering重造colorimeter及
controller ，希望藉此可以恢復cooper concentration的 variation到pre-shutdown的level。 結果：將controller的downtime從60%降到少於20%，至 此process已可達到要求的production rate。 下一步該小組決定要降低生產過程的不良律，已知defect 的兩大主類為：1.brittle copper；2.copper voids.

43 決定以實驗設計的方法來迅速的identify controllable input variables into the process.
1. 目的---Minimize 鍍銅時的缺失。 2. 採用Table 4-1的16runs， 考慮5個主要factors：Copper concentration、Sodium hydroxide concentration、Formaldehyde concentration、 Temperature、Oxygen。 3.由統計分析來決定主因及是否存在交互作用。 4.經由調整主因子到一個新的level之後，不良率降為原來 的1/10。 該組利用SPC的方法，有效的改進製造的流程時間，並利 用實驗設計的方法，使其生產過程toward一個near-zero- defect的capability。

44 4-7 SPC的實例（非製造業） 製造業與非製造業應用SPC工具的差異主要有下列兩項： 1. 非製造業中，缺乏定義品質的一個測量系統
2. 非製造業中，需要improve的system不易觀察 例如：1. 製造業---PC assembly line的performance 2.非製造業---finance organization的運作， marketing，material and procurement， customer support，field service，engineering development and design，software development and programming。

45 非製造業要應用SPC之前，主要必須先能 1. 充分的定義要改進的系統 2. 能採用一個明確的測量系統 通常可採用 1. Flow charts---可用來identify在process中value-added 及non-value-added的activities. 2. Operation process charts 來協助定義並了解非製造業的process。 非製造業可採取10種方法來消除non-value-added的activities. e.g. 不需要的步驟瓶頸。

46 planning organization主要負責製造每 項工作的plans及documents，並送到 工廠。
實例：在一個大的太空製造業公司中的一個 planning organization主要負責製造每 項工作的plans及documents，並送到 工廠。 通常這些plans都很大，需要印製數百頁，若出錯時， 將造成factory floor各種問題。 e.g. rework, scrap, overtime, lost production time, missed delivery schedule. 見high-level flow chart，但此flow chart太籠統，無法 適度的找出non-value-added activities。

47 可採用step-down的approach。
e.g. 對每個block（如：planner, check…）再加以細分其 工作項目。. 該planning organization的經理決定以“減少planning errors”為其改進品質的目標。 由下列人員組成一個小組： managers, planners, and checkers。

48 在上述的planning process的例子中，很多被identify的原因
與個別planner的經驗、訓練及supervision有關，及與設計 與發展工程師的poor input information亦相關，當這些 causes被有系統的移除、消去後，此組織在長期使用SPC的 方法之後，使其planning errors降到少於one planning error per 1000 operations。 取樣方法：每星期隨機取3個plans，並找出其所有的errors。 Check sheet（用於每個plan） Summary check sheet（每個月的資料）

49 Pareto analysis：65%的planning error來自於operations
section。 Pareto analysis：omitted operations及process specification 為operation section error的主因。 結論：造成planning errors的主因有兩點。 1. Planner不是充分的了解工廠的製造過程。 2. Planner不清楚目前在使用的process specification。 行動：執行一個program來使planner熟悉上述兩點，並要 求planner要對所發生的planning errors提供更多的 feedback。

50 結果：由run chart of planning errors中可見
planning errors / per operation的個數在前半段已明 顯下降，其原因可能是由於對Planner的 1. Increased training；2. Supervision activities；及 提供他們更多關於過去造成planning error的相關資 訊。 此小組建議應以組成一個team的方式來負責策畫一個plan， 取代由一個人來負責一個plan，這樣方能促成factory與 planning兩部門運作的交流。

51 一旦SPC的觀念可被這些planner所接受，他們即可將之
運用在其他的應用，如run chart of planning errors中若 再加入cater line及上下界，即為一個有用的control chart。 Control chart最大的作用在於其能有效的identify assignable cause。 一旦存在assignable causes，則系統製造錯誤的比例將高於 系統中只存在chance cause！ 系統內 Chance cause Assignable cause 系統外

52 一旦assignable cause存在，則必須將之找出，並清除其root
causes。 然chance cause則是屬於系統本身的一種特性，僅能由改進 工作方法、步驟、人員訓練、更換機器、原料等地方著手， 而這些皆為Management的職責。

53 Operating-characteristic curves for an chart
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