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3. Production Process Characterization
3.1. Introduction to Production Process Characterization
3.1.3. Terminology/Concepts

Populations and Sampling

We take samples from a target population and make inferences In survey sampling, if you want to know what everyone thinks about a particular topic, you can just ask everyone and record their answers. Depending on how you define the term, everyone (all the adults in a town, all the males in the USA, etc.), it may be impossible or impractical to survey everyone.  The other option is to survey a small group (Sample) of the people whose opinions you are interested in (Target Population) , record their opinions and use that information to make inferences about what everyone thinks. Opinion pollsters have developed a whole body of tools for doing just that and many of those tools apply to manufacturing as well.  We can use these sampling techniques to take a few measurements from a process and make statements about the behavior of that process.
Facts about a sample are not necessarily facts about a population If it weren't for process variation we could just take one sample and everything would be known about the target population.  Unfortunately this is never the case.  We cannot take facts about the sample to be facts about the population.  Our job is to reach appropriate conclusions about the population despite this variation.  The more observations we take from a population, the more our sample data resembles the population. When we have reached the point at which facts about the sample are reasonable approximations of facts about the population, then we say the sample is adequate.
Four attributes of samples Adequacy of a sample depends on the following four attributes:
  • Representativeness of the sample (is it random?)
  • Size of the sample
  • Variability in the population
  • Desired precision of the estimates
We will learn about choosing representative samples of adequate size in the section on  defining sampling plans.
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