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。