何正斌 博士 國立屏東科技大學 工業管理研究所 副教授 製程失控判定原則 何正斌 博士 國立屏東科技大學 工業管理研究所 副教授

失控狀況 1 & 2 狀況1 狀況 2 當製程沒有問題卻發生狀況1的機率約為0.3% 連續9點都太小了 製程平均變小了 可能成因 要馬上行動 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1 當製程沒有問題卻發生狀況1的機率約為0.3% Common Cause 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 製程參數改變

? 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 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. 時間 製程失控(Out of Control) -製程有特殊因存在的情況

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

狀況 3 & 4 狀況 4 狀況3 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 UCL LCL A B C 狀況 4. 連續14點，一點大一點小 x UCL LCL A B C 狀況 3. 連續6點增加或減少 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 1, 5, 6相關，都代表可能有特殊因產生。 最常與狀況1併用 變異數變大(分配變肥) UCL LCL A B C 狀況 5. 3點中有兩點在A區或A區之外 x UCL LCL A B C 狀況 6. 5點中有4點在相同邊的B區或B區之外 x 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. 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 7 狀況 8 高興嗎？ 混合產品，混合管制圖 管太多 用錯管制界限 組內變異比組間變異大很多 狀況 7. 連續15點都在C區 狀況 8. 連續8點沒有一點在C區 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 X-bar s UCL LCL 狀況 #7 狀況#8

False Alarm 循序漸進的使用 全部8狀況都用 狀況 1→狀況 5→狀況 6 False Alarm機率 2.4% 50個點子約有一點Common Cause

Out-of-control 一點超出管制界線 三點中有兩點落在A區 連續8點在中心線同一側 五點中有四點落在B區或B區以外

Out-of-control 上昇趨勢 平均值跳動 週期性 週期性 系統性-不隨機 層別 混合變化

Example – Constructing Charts In Minitab, open sample worksheet CCVar.mtw From the menu select Stat > Control Charts > Xbar-R… Select data columns C1-C5 Minitab has routines for 18 different control charts. All of them are documented in the help system and in the Minitab manuals. In the next module, we will introduce charts for attribute data. In the previous module we introduced a flow chart to ease in selecting the appropriate charting system. Minitab has automated the tasks for constructing control charts

Perform Control Chart Tests Even though all eight tests are available, as discussed before, unless the special cause variation is subtle, start with tests 1 and 5. When those variations are eliminated, add further tests.

X-bar & R Chart – Minitab Output While Minitab provides a nice output for analysis and calculating, it doesn’t take the place of charts being filled in by the operators or by a real-time computer system. After-the fact analysis loses much of the power of control charts, that is, the power to act on the process as soon as the signal is received.

Recalculating Control Limits After identifying the cause for the out-of-control points they can be removed from the control limit calculations In the previous example points 9, 11, & 24 can be removed from the control limit calculations Press the Estimate button on the X-bar & R chart form and enter the offending data Do not exclude points when the cause of the OOC condition is not or cannot be identified. ? When would one NOT exclude OOC points from calculations?

Modified Minitab Output Notice the small changes in the control limits:

Existing Limits Minitab can also plot and evaluate the data if historical data is known and verified to be accurate Enter the historical data in the main form: This is useful when analyzing data for a process that has an established SPC system. The historical constants can be implemented for analysis of the most recent data.

Only recalculate the limits if the cause of the change is known Historical Data When analyzed with historical limits, notice the number of out of control points, now: Only recalculate the limits if the cause of the change is known