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
LSL
Cpl
3 st USL
Cpu
3 st
Example:
A process mean is 355, standard deviation is 15, an upper spec. limit is 380 and lower spec. limit is 270
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?
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
ˆ R in X R chart
Cp

USL LSL
6
d2
ˆ S in X S chart
C4
Process Potential Capability-Cp
m
Ca (USL LSL) 2
Ca

2(x m) USL LSL
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
What is Cp?
-5 -4 -3 -2 -1 0 1 2 3 4 5 What is Cp if the mean is 355 but
-3
+3
Process Tolerance
the standard deviation does not change?
A Problem With Cp
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
What is the Cpk?=0.56
What is the Cp?=1.2
-4 -3 -2 -1 0 1 2 3 4 5
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。
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
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
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
若 Cp = 1 即 不良率 p = 0.0027
Cp ＞1 即 USL LSL＞6 則 P＜0.0027 Cp ＜1 即 USL LSL＜6 則 P＞0.0027
Product Tolerance USL LSL


Process Tolerance
6 st
Product Tolerance
Example:
A process mean is 325, standard deviation is 15, an upper spec. limit is 380 and lower spec. limit is 270
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
C pk

min



LSL，USL
3
3

望大特性的Cpk 望小特性的Cpk
Meet Cpk – Process Performance
Cpk min{Cpl,Cpu}