A mathematical method that employs probability theory* for inferring the properties of a population parameter from which the sample is taken is known as inferential statistics. Inferential statistics is a set of methods used to make generalizations, estimations, or predictions. Example: If determining the statistical capability of a process, we would take periodic samples of parts from a process and from these samples we would make inferences about the performance of the whole population of parts produced by the process.*

Use: Let’s say that we want to determine the statistical capability of a process. And, let’s say that 28 machines are producing a particular part. This process has 14 operators that run the parts. The operators use their own measurement devices. There are three sources of raw material that feed into the process. The process runs two shifts per day five days a week.

**Scenario one:** To determine process capability, the team measures the parts from machine number 16 over a period of one day I’m just one shift using just one measurement device and one operator. The *inference space *is limited to one machine, with one person, with one measurement device, over a period of time of eight consecutive hours. This is a very tight inference space.

**Scenario two:** To determine process capability, the team measures a sampling of parts from each of the 28 machines produced by 14 operators using 14 measurement devices over two shifts over a period of one month. This is a very loose inference space, but in this scenario, the team will have a much better insight into the true capability of the process.

It is best to have as loose of an inference space as possible. Understand that the looser the inference space, the more money it will cost to gather the data. The bottom line is, “What risk is the team willing to live with of being incorrect in their assessment of the true process capability?”