國立屏東科技大學工業管理系教授 何正斌 博士 管制圖概述 國立屏東科技大學工業管理系教授 何正斌 博士

工作站與管制圖 工作站 X’s(因-可控制) Y’s(果) N’s(亂因-不可控) Y’s(果) 持續且有系統記錄Y，Y一但有變異(OOC-怎麼可能！)，就趕緊去找原因(OCAPs)，使得Y可以恢復正常。

持續且有系統記錄Y 持續？ 系統化？ 穩定的製程要持續監控 抽樣的樣本能代表母體特性 每批抽6個量測金線拉力 每批全都量 發現因X控制不好所造成Y的變異 發現特殊因(Special Cause) 系統化？ 抽樣的樣本能代表母體特性 每批抽6個量測金線拉力 拉力平均( xbar ) 拉力全距( R ) 每批全都量

管制圖範例 持續 有 系 統 結果有兩種 In Control 反應哈哈笑 Out of Control 趕緊調整X 結果能迅速反應 UCL 結果能迅速反應 CL LCL 最快能多快 Real Time? 知空間，搶時間 OCAPs

Out of Control Action Plans 製程失控行動計畫

? 在控 Vs 失控 製程在控(In Control) 製程失控(Out of Control) 製程有特殊因存在的情況 Y有變異 時間 預測 Predictability does not necessarily mean good. The process could predictably produce 50% bad product if the natural process limits are much wider than the specification requirements. Some special cause variation may also not be bad. Tool wear is an example. A chart of a machining operation will usually show out of control trends as the tool wears. The chart is then used to replace the tool when it reaches a specific point of wear, based on the control chart values. Using control charts without knowledge of the process will be of little value. 製程失控(Out of Control) 製程有特殊因存在的情況 Y有變異 時間

失控狀況 1 & 2 狀況1 要馬上行動 可能成因 狀況 2 連續9點都太小了 製程平均變小了 可能成因 狀況 1. 一點超出A區 UCL LCL A B C 狀況 1. 一點超出A區 x 狀況 2.連續9點都在中心線的同側 UCL LCL A B C x 狀況 2 連續9點都太小了 製程平均變小了 可能成因 製程參數改變 狀況1 要馬上行動 可能成因

Prob(All 9 Xi<Mean)=0.59=0.001953 圖解失控狀況1及 2 Prob(All 9 Xi<Mean)=0.59=0.001953 Prob(Z>3)=0.00135 s X-bar UCL LCL 狀況 #2 狀況 #1

狀況 3 & 4 狀況 4 狀況3 可能成因 可能成因 夜班差，日班好 機台1好，機台2糟 工程師一直在調整製程參數 UCL LCL A B C 狀況 3. 連續6點增加或減少 x UCL LCL A B C 狀況 4. 連續14點，一點大一點小 x The number of 狀況s can be increased as the stability of the process increases. When there are no longer any points outside the three sigma limits, it is time to use some more subtle 狀況s. When the process varies outside the upper and lower control limit often, it is of little value to look for the fourteen alternating points in a row 狀況. The Black Belt has bigger fish to fry. 狀況 4 可能成因 夜班差，日班好 機台1好，機台2糟 工程師一直在調整製程參數 當製程極少發生狀況1時考慮 狀況3 可能成因 刀具磨損 化學配方濃度改變 污染程度慢慢增加

圖解狀況 3 X-bar s UCL LCL 狀況 #3

圖解狀況 4 X-bar s UCL LCL 狀況#4

狀況 5 & 6 狀況 6 狀況 5 狀況 5. 3點中有兩點在A區或A區之外 狀況 6. 5點中有4點在相同邊的B區或B區之外 UCL LCL A B C 狀況 5. 3點中有兩點在A區或A區之外 x 狀況 6. 5點中有4點在相同邊的B區或B區之外 UCL Sometimes 狀況 5 is included with 狀況 1 for evaluation. Sometimes even 狀況 6. The idea is to look for process excursions far out from the middle. The problem with adding 狀況s is that the chance of having a false positive increases ~ 0.3% with each added 狀況. If all eight 狀況s are used, the rate is 2.4%, or approximately 1 out of 50. Be judicious in your selection of 狀況s. False positives are often interpreted as true positives without an assignable cause. This can be a very frustrating experience. A x B C C B x A LCL 狀況 6 狀況 1, 5, 6相關，都代表可能有特殊因產生。 不合群的那一點可能是因為嚴格管控 狀況 5 最常與狀況1併用 變異數變大(分配變肥) 懷疑有特殊因

圖解狀況 5 & 6 X-bar UCL LCL 狀況 #6 狀況 #5 s s s s

狀況 7 & 8 狀況 8 R Chart很寬 組抽樣原則錯誤 狀況 7 狀況 7. 連續15點都在C區 高興嗎？ 混合產品，混合管制圖 UCL LCL A B C UCL LCL A B C x 狀況 7 can be caused by control limits that need recalculation or by a very high range chart, that is, the within group variation is larger then the between variation. Check the range chart to help differentiate. High variation in the Range chart and low variation in the X-bar chart usually indicates an irrational basis for selecting subgroups. Reformulate the subgroup selection to answer the desired questions. x 狀況 7 高興嗎？ 用錯管制界限 組內變異比組間變異大很多 R Chart很寬 組抽樣原則錯誤 狀況 8 混合產品，混合管制圖 管太多

圖解狀況 7 & 8 back X-bar s UCL LCL 狀況 #7 狀況#8

Y一但有變異 Y是對的嗎？ OOC的判定 永遠沒有OOC???的管制圖 抽樣計畫 量測系統分析(Measurement System Analysis) OOC的判定 管制圖上點子超出管制界限 管制界限是算出來的，規格界限是客戶給的 兩者沒有關係 管制圖上的點子不隨機 沒事不代表不會OOC 只是發生的機率很低 永遠沒有OOC???的管制圖

Xbar-R管制圖公式 R管制圖： Xbar管制圖： UCL = CL = LCL = UCL = CL = LCL =

Rbar太大

Rbar太小-混料(A&B)

Xbar-S管制圖公式 S管制圖： Xbar管制圖： UCLS = CLS = LCLS = UCL = CL = LCL =

管制圖範例1 管制圖程式 為何5個？ 如何抽樣？ 管制界限如何算出來？ R管制圖沒有管制界限？ OOC Action?

管制圖範例2

不穩定製程管制圖範例

BP-Xbar R管制圖 用錯PPS

TSMC-Control Chart OCAPs (Out of Control Action Plans) OSAPs(Out of Spec. Action Plans)

I-MR管制圖 n=1 I-individual MR-moving range MRi=Ixi-xi-1I 有一點OOC STAT→ Control Charts →Variable Charts for Individuals →I-MR

Attribute Control Chart 不連續管制圖

不連續管制圖分類 Defective Data p and np charts Defect Data Package does/does not leak Lamp does/does not light Go/no-go gauge data p and np charts 樣本數相同-p or np chart都可以 樣本數不同-只能用p chart Defect Data Bubbles in a windshield Paint flaws on a casing Errors on an invoice Bad die on a wafer C chart(缺點數管制圖) & u chart(單位缺點數管制圖) 樣本數相同-c or u chart都可以 樣本數不同-只能用u chart

p 管制圖 Subgroup size Subgroups are usually quite large (50 to 200 or more!) Ideally, each subgroup should have at least 5 non-conforming units Minimum: 90% of the subgroups must have at least one non-conforming unit Subgroup sizes need not be constant, but should be within ± 25% of the mean subgroup size The lower the number of non-conforming units, the larger the required subgroup size In general, attribute charts need much larger subgroup sizes than the equivalent variable charts

p 管制圖 LCL When the mean proportion defective is small, the LCL can be a negative number. In this case there is no LCL and p=0 is still within the control limits It is advantageous to pick a subgroup size that establishes a lower control limit. This way improvements can also be detected

p 管制圖-example A plastic molding plant manufactures two-liter plastic bottles for the soft drink industry A common failure mode of the molding process is pinholes in the bottles that will cause long-term seepage. The bottles can be pressure tested for leakage. The test is destructive. A number of bottles from each lot of plastic are tested for leaks and the number of rejects are recorded Construct a p-chart of the defective bottles and evaluate whether the process is in control.

c chart- example Each month, 100 invoices are audited and the total number of mistakes is recorded. In a molding process, there is a problem with pinholes in plastic bottles. Each day, a number of bottles are examined and the number of pinholes are recorded.

黃金四法則 餓了就吃 吃你『想吃』而非『該吃』的東西 有意識地吃，用心享受每一口食物 感覺飽就不再吃

SPC-Charts For All Occasions Variable Data? % Defective or Defects? No Defects There are many types of control charts available. The ones in this flow chart are the most common and the most familiar. They were developed to be used local to the process. The mathematics for these charts is easy to learn and to teach and does not require more than a simple calculator. The variable charts are for variable-type inputs or outputs. The attribute charts are usually reserved for outputs. Remember, the goal is to have zero defects in the outputs by controlling the inputs. Try to use variable charts on inputs instead of attribute charts on outputs. Yes % Defective Rational Subgroups? No Constant Sample Size? Constant Sample Size? I & MR chart No No Yes Yes Yes p-chart u-chart Subgroup Size >8? Easy to Compute sigma? Yes np- or p-chart c- or u-chart No Yes No X-bar & R chart X-bar & S chart

Demerit Control Chart When several less severe or minor defects can occur, we may need some system for classifying nonconformities or defects according to severity; or to weigh various types of defects in some reasonable manner.

Demerit Systems Class A Defects - very serious Class B Defects - serious Class C Defects - Moderately serious Class D Defects - Minor Let ciA, ciB, ciC, and ciD represent the number of units in each of the four classes.

Demerit Systems The following weights are fairly popular in practice: Class A-100, Class B - 50, Class C – 10, Class D – 1 di = 100ciA + 50ciB + 10ciC + ciD di - the number of demerits in an inspection unit

~THE END~ ~To Be Continued~