??????? ????? ??? Cp, Cpk, Pp, Ppk

1
??????? ????? ??? Cp, Cpk, Pp, Ppk
2
IMPORTANT SPC RATIOS USED
This compares the requirement of the process
output vis-a-vis the inherent variability of the
process. Higher value than 1 implies that the
process has got the capability to give the
product within the set limits.
3
??????? ??? ???????SPC
?????? ????? ???? ???? ??????

??????? ????? ??????
??? ?????? ?? ??? ????? ?????? ???? ??????? ????
??????.????? ????? ?? ?? ?? ???? ??? ??? ??
?????? ?????? ????? ????? ?? ???? ?????? ?? ????.
vis-a-vis
4
PROCESS POTENTIAL INDEX (Cp)
The numerator is controlled by Design
Engineering

• Maximum Allowable Range of Characteristic
• Normal Variation of Process

Cp
The denominator is controlled by Process
Engineering
5
???? ?????? ?????? (Cp)
???? ?? ????? ?????? ???? ????? ?? ???

• ?????? ????? ???? ???? ??????
• ????? ????? ??????

Cp
???? ??? ?? ????? ?????? ?????? ????? ?? ???.
6

This gives us the positioning of the mean
vis-a-vis the USL and the relationship between
the two.
This gives us the positioning of the mean
vis-a-vis the LSL and the relationship between
the two.
Cpk - Process Performance Index. This is
important Cpk Minimum of (Cpu and Cpl)
for bilateral tolerances C pu for
unilateral tolerance on upper side i.e..
Cpl for unilateral tolerance on lower side
i.e..
7

??? ???? ??? ??????? ? USL ? ?????? ???? ?? ?? ??
?? ???
??? ???? ??? ??????? ? LSL ? ?????? ???? ?? ?? ??
?? ???
Cpk ???? ?????? ??????.??? ?? ???? ??? ???.
Cpk Minimum of (Cpu and Cpl) ???? ???????
?????? C pu ??????? ?????? ?? ??? ?????
????? Cpl ??????? ?????? ?? ??? ?????
??????
8

• These ratios help you in
• Predicting whether rejections will take place on
  the higher side or on the lower side.
• Taking centering decisions.
• Deciding whether to consider broadening of
  tolerances
• Taking Decisions on whether to go in for new
  m/cs.
• Deciding on the level of inspection required.

9

• ??? ?????? ?? ??? ??? ?? ??? ??
• ??? ???? ????? ??????? ?? ??? ????? ????? ?????
  ?? ???? ?? ??? ????? ?????.
• ????? ???? ?? ???? ??????? ??????
• ????? ???? ?? ???? ????? ??? ??????? ??????? ??
  ?? ??? ??????.
• ????? ???? ?? ???? ????? ??? ?? ????? m/cs????
  ?????
• ????? ???? ?? ???? ??? ?????? ???? ????.

10
SOME TYPES
Failure likely on lower side
CENTERING RELATED PROBLEMS
TOLERANCE OR NEW MACHINE DECISION
11
??? ??? ????
Failure likely on lower side
????? ??????? ?????? ?? ??????
??????? ?? ????? ???? ???? ?? ???? ????? ????
12
IMPORTANT SPC RATIOS USED

• Pp is based on same equation as Cp with one
  exception Pp employs the long term standard
  deviation (whereas Cp employs the short term
  standard deviation).
• Ppk is based on same equation as Cpk with one
  exception Ppk employs the long term standard
  deviation (whereas Cpk employs the short term
  standard deviation).

13
??????? ??? ??????? SPC

• Pp ????? Cp ?? ???? ???????? ?? ??? ?? ??? ?? ??
  ????? ??? ??? ??? ?? ??? ???? ?? ?????? ?????????
  ???? ????? ??????? ?? ???. ?? ?????? Cp ??????
  ????????? ????? ????? ?? ?? ??? ?? ????.
• Ppk ?? ???? ????????? ????? ??????? Cpk?? ??? ??
  ??? ?? ??? ????? ?? ??? ???? ?????? ?????????
  ???? ????? ?? ?? ??? ?? ???? ?? ?????? Cpk??????
  ????????? ????? ????? ?? ???? ?? ???.