How do I read this formula?

Question

It's been a long time since my college days, so I need some help for something that is likely pretty simple to most of you.

In the book Factory Physics, there is a formula for Service Level stated as follows:

$$Service Level = P\{CycleTime \le LeadTime\}$$

I'm not sure how to read or interpret the formula. Can you help me out in digesting it?

Thanks, in advance.

Answer 1

They define service level as a number between $0$ and $1$, indeed a probability. The service level equals the probability that your cycle time is less or equal to your lead time.

Somehow an interesting definition: one could imagine an ideal factory, where they deliver $1$ second earlier with probability $0.5$, or $1$ $\mathbf{year}$ later again with probability $0.5$.

Such factory would have the same service level metric of a competitor, delivering $1$ second earlier with probability $0.5$, or $1$ second later again with probability $0.5$.

I would still call the second one...

Answer 2

The "service level" is equal to the probability that the "cycle time" is less than or equal to the "lead time".