製程能力分析 何正斌 教授 國立屏東科技大學工業管理學系

Process Capability The ability of the process to produce parts that conform to the engineering specification. (spec) A good process should maintain a good statistical control conform to engineering spec A process might be in statistical control but not capable of meeting the spec because: the process is off-center for the nominal (規格中心) m=(LSL+USL)/2 –Lower Spec. Limit and Upper Spec. Limit 很穩定的差 當管制圖很久沒有out-of-control的情況(assignable cause)發生謂之穩定 the process variation is too large 很穩定的不穩定 both

品質特性數據為計量值時： Cp 當製程穩定時，品質特性數據為計量值且其分配呈常態分配或近似常態分配時， Cp 指標被用以說明一個製程符合規格之能力。 Cp 值愈高表示製程能力愈好，可接受的最小 Cp 值通常至少要1.33

Process Potential Capability-Cp Product Tolerance Example: A process mean is 325, standard deviation is 15, an upper spec. limit is 380 and lower spec. limit is 270 What is Cp? What is Cp if the mean is 355 but the standard deviation does not change? -3 +3 Process Tolerance

A Problem With Cp Which is the better process? What is the difference in Cp between the two processes? What can be done to make Cp more effective as a process capability statistic? If a process has a centering issue, Cp will not change. As the equation for Cp shows, it is only dependent on two things: the product tolerance and the process standard deviation. If the mean drifts in the long-term, the Cp will not change. Another statistic, Cpk, discussed next, includes variation of the mean from the target.

Cp值對應的不合格率及可用時機 不同的 Cp 值對應不同的不合格率及ppm值 Cp ＞1 即 USL  LSL＞6 則 P＜0.0027 Cp ＜1 即 USL  LSL＜6 則 P＞0.0027 Cp只能用於製程穩定，製程產出分配近似常態， ＝T (目標值)且 ＝m 的情形下 若  和 m 不相等，以 Cp 指標衡量製程能力是不正確的，因為這時Cp值會高估製程能力

Cpk 指標 以Cpk指標衡量製程能力時製程平均值並不一定要位於規格中心，即Cpk指標比Cp指標多說明了製程平均值偏離規格中心之情形，因此Cpk指標對製程能力的描述更準確 Cpk比Cp保守 (Cpk≦ Cp ，當＝m 時等號成立) Cpk值愈高表示製程能力愈好 望大特性的Cpk 望小特性的Cpk

Meet Cpk – Process Performance Example: A process mean is 355, standard deviation is 15, an upper spec. limit is 380 and lower spec. limit is 270 What is the Cpk?=0.56 What is the Cp?=1.2 This example highlights the relationship between Cpk and Cp. Each provides a unique piece of information regarding process capability. Cp reports the “could be’s” and Cpk reports the “what-it-is’s”

Ca指標 當製程穩定時，品質特性數據為計量值且其分配呈常態分配或近似常態分配時， Ca 指標被用以說明製程平均值  偏離規格中心 m 之程度。 ∣Ca∣值愈低表示製程能力愈好。

品質管理與實習 -抽樣與檢驗 何正斌 國立屏東科技大學工業管理學系

名詞釋意 Sampling(抽樣) 驗收抽樣(Acceptance Sampling) 工廠中QC部門可分為 品質不是靠檢驗得來的 從母體(Population)抽取其中的部份(樣本-sample)，希望樣本能代表母體的真實情況 驗收抽樣(Acceptance Sampling) 從一批產品中抽出一組樣本→檢查某些特定的品質特性 判定該批產品 允收、退貨、特採 工廠中QC部門可分為 IQC (input quality control)-駐廠檢驗 IPQC (in-process quality control)-紅衣隊伍 FQC (Final Quality Control)-來不及了，但可用來計算製程能力 品質不是靠檢驗得來的

計數值的逐批驗收抽樣計畫 單次抽樣計畫(Single sampling plan) d>c d≦c d>c A lot size N is submitted for inspection A single sampling plan is defined by The sample size n The acceptance number c Inspect a random sample of size n from a lot-(N) d=# of observed defectives Reject the lot d>c Accept the lot d≦c d>c

單次抽樣計畫範例

計數值的逐批驗收抽樣計畫 雙次抽樣計畫(double sampling plan) n1=sample size of the first sample c1 and c2=acceptance number of the first sample n2=sample size of the second sample c3=acceptance number both samples inspect a random sample of n1 from the lot d1=number of defectives accept d1≦c1 d1>c2 reject c1<d1<=c2 inspect a random sample of n2 from the lot d2=number of defectives accept d1+d2 ≦ c3 d1+d2>c3 reject

雙次抽樣計畫範例

抽樣計畫-MIL-STD-105E 計數值檢驗 單次抽樣、雙次抽樣、多次抽樣 檢驗水準I,II,III 樣本大小英文字母 送驗批大小 平均品質水準(Acceptable Quality Level) 可被接受的最大製程(產品)不合格率 生產前段AQL比較小 抽樣條件 正常(normal) 寬鬆(reduced) 嚴格(tightened)

MIL-STD-105E使用程序

Examples Ex1 Ex2-減量 or 加嚴 Ex3 查Code Letter N=5000+檢驗水準II ，則得L 單次抽樣計畫+正常抽樣條件，則查單次正常 AQL=2.5 n=200, Ac=10, Re=11 Ex2-減量 or 加嚴 單次減量 單次加嚴 轉換法則 Ex3 N=5000+檢驗水準II ，則得L 雙次抽樣計畫+正常抽樣條件 n1=125, n2=125, c1=5, c2=9,c3=12

多種缺點 品質管理●六標準差式-劉漢容，陳文魁 設某種螺栓包含有五項缺失屬於主要的，十一項缺失屬於次要A及八項缺失為次要B。指定主要、次要A及次要B之AQL值分別為1.0%、4.0%及6.5%。此種螺栓採用105E標準之正常檢驗的雙次抽樣計畫，其檢驗水準為Ⅱ級且N = 10000。試用105-表查取雙次抽樣計畫。 缺失級別 裘蘭博士 貝爾電話 通用公司 嚴重缺失 － － － 主要缺失 100 100 50 次要A缺失 75 50 25 次要B缺失 25 10 10 輕微缺失 5 1 5

OC Curve-Operating Characteristic Curve Ideal OC curve - p269 fig. 9.1 當執行全檢時才會有ideal oc curve Typical OC curve – p268 fig.9.2 p, N, n, C Assumption? Hypergeometric. Binomial, or Poisson Distributions 計算允收機率，即可繪圖 Example

OC-curve 生產者風險(producer’s risk) 消費者風險(consumer’s risk) 生產者生產出好產品但被拒收 消費者接受壞產品 example 以下有關作業特性曲線(operating characteristic curve) 的敘述何者不正確？ (A)此曲線表示所使用的抽樣計畫其受驗批在各種不良率下能被允收的機率，(B)受驗批在允收品質內被拒絕之機率稱為生產者風險率或型I誤差(type I error) 率，(C)作業特性曲線愈平緩，抽樣計畫辨別好批與壞批的能力愈佳，(D)作業特性曲線適用於計量值抽樣計畫，也適用於計數值抽樣計畫。(93碩士甄試)

The End

Ideal OC curve Back

Typical OC curve Back

Producer’s Risk Vs Consumer’s Risk from OC Curve Back

Review: Populations vs. Samples Sample – the group of objects from which one actually gathers data The purpose of a hypothesis test is to determine the characteristics of the population from sample data. Sample data is noisy. Population – the entire group of objects about which one wishes to draw an inference Sample Statistics Sample Mean – Estimate for Standard Deviation – s Population Statistics Mean – m Standard Deviation – s Back

Code Letter 較小樣本 較大抽樣風險

單次-正常

單次-加嚴

單次-減量

轉換法則 ≦5→Accepted and remain reduced ≧8→Rejected and turn to Normal =6,and 7 →Accepted and to Normal