Personally, I feel that there are two parts, which are important:
1. How large are the results (=bias and non-linearity) compared to the tolerance range
2. How large are the results compared to the standard deviation of the process.
In order to combine these two considerations I would calculate the C_g and C_gk value, which judges the bias. To judge the non-linearity, I would modify the formula to account for the non-linearity. Here an example: Say your specification limits are [450, 520], the product follow a normal distribution with mean 495 and standard deviation 5. Since the tolerance range is 70 the C_g value is C_g = k* 70/(6*5) = k* 2.333 and C_gk = k*(520-495)/(3*5) = k*0.83. Usually, k is taken to be in the range [0.1, 0.3]. In addition, you have to decide which C_pk-value your products needs, and use this as the lower limit for the C_gk value — note that the two only differ by the factor k.
Since the linearity of a gauge is a bias for a specific reference value, we can use the upper formula for C_gk and plug in the largest difference between reference value and measurement result. Of course, this is a C_gk only for the specific reference value — make sure that your notation reflects this, e.g. by using C_gk(target=…). Like this you use a single quantity (the C_pk-value of your product) to determine whether or not your gauge is sufficient — in addition with a predefined k-value.
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