$2.$ Process Capability

From the lecture we learned that natural process variability is the variability that we expect to face in our normal production environment. This natural variability is defined as $+/-3\backslash$sigma from the mean, which is equivalent to $99\mathrm{.}73\%$ of the production $($property of a normally distributed variable$).$Comparing this natural process variability $($represented by $+/-3\backslash$sigma to the specification limits gives us a measure for our $$Process Capability.$$

$2$b$.$ A food producer is bottling vinegar.

The amount of acid in this vinegar is allowed to be between $12$ mg $2$ mg$.$

Currently the process is running with a mean $(\backslash$mu $)$ of $12\mathrm{.}7$ mg and a standard deviation $(\backslash$sigma $)$ of $0\mathrm{.}3$ mg$.$

What is the CPK value for the amount of acid in the vinegar for this process?

$+/-3\backslash$sigma to the specification limits gives us a measure for our $$Process Capability.$$