## Why & How Cpm came into existence? Weren’t Cp & Cpk enough to trouble us?

Amrendra Roy

In the earlier post (see earlier post “what is Taguchi Loss function?”) we end up the discussion stating that Cp need to be penalized for the deviation of the process mean from the specification mean.

If you are producing goods near to LSL or USL hence, the chances of rejection increases which in turn increases the chances of reprocessing and rework thereby increasing the cost. Even if you manage to pass the quality on borderline then your customer has to adjust his process accordingly to accommodate your product thereby, increasing his set-up time and cost involved in readjusting his process. Moreover, the variance from your product and the variance from the customer’s process just get adds up to given final product with more variance (remember! Variance has an additive property).

It’s fine that we need to produce goods and services at the center of the specification, which means that we should know the position of process mean with respect to the center of the customer’s specifications. Hence another index was created called as Cpm was introduced which compensates for the deviation of process mean from the specification mean.

For calculating Cpm, the Cp formula is modified where the total variance of the system becomes

Where μ = process mean & T = specification mean or target specification

Hence, Cp formula

is modified to

This is necessary because if I can keep the process mean and the specification mean near to each other, the chances of touching the specification limits would be less which in turn would reduce the chances of reprocessing and we can control the process in a better way.

If μ = T, then Cpm = Cpk = Cp

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