# Cpk for Contaminant Mass - Washing Parts

U

#### Uchiha

Hi all,

I am trying to figure out something: we have a machine that washes parts. After the washing, we weigh the remaining contamination level in the part to assess the efficiency of the washing operation done by the machine. We have a specification (contamination must be less than 10 mg).

My question is: does it make sense to talk about process capability in this case? (Cpk)
If yes, then how would we calculate it?

Cheers

S

#### sitapaty

Process capability is applicable to all processes theoritically But it is practically applicable to mass production processes.In the case of cleaning if the batch quantity is large you can apply SPC and calculate CPK using the standard formulae and correct method of collecting data.On the otherhand if the batch quantity is small say less than 10/day you may need to collect data for about 10 days to get sufficient data.In that case the process input conditions are required to be kept uniform on all days.
Therefore CPK is rarely specified for claning operation

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
why do you need to calculate Cpk?
process capability is really a much more involved thing than calculating some index.

*I* would plot the results over time with the spec limit and look at the data. that will tell you much more about the process capability than any pseudo - or real - statistic ever could.

#### bobdoering

Trusted Information Resource
Even if you did some type of capability, Cpk would not be it. It is for normally distributed distributions, bi-lateral specifications with the target in the center. You have a unilateral tolerance with a target at 0, physically limited to zero (can not go below.) That would make the distribution non-normal - probably a beta type distribution. You would need to transform, etc., to even come up with anywhere near meaningful value.

Cpk is designed specifically to do two things: 1) determine the probablilty that your distribution falls within tolerance AND 2) whether the distribution is centered. You do not have a centering function for your process, specification or distribution - making Cpk nonsensical.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
You do not have a centering function for your process, specification or distribution - making Cpk nonsensical.
is there ever a time when Cpk is logical?

#### bobdoering

Trusted Information Resource
is there ever a time when Cpk is logical?
Only as a 20,000 ft overview of a process. It surely has no prediction power whatsoever. Yet, in automotive - and any industry they have polluted - they still hang their hat from this mess like it does. SMH.

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