Sampling of One-Dimensional Lots The Continuous Model

This chapter should reinforce the important information that we presented in Chapter 7 and place it in its proper context and also expands on the various components of the Overall Estimation Error OEE already introduced in Chapter 4. The continuous model of a one-dimensional lot has very important industrial applications. The model applies to material moving on conveyor belts, pipes, ducts, streams, rivers, olive oil generated in a plant after the crushers, glass bottle thickness in a beer bottle factory, consistency of fragment size distribution in bags filled with cat litter material, etc. It also applies to stationary, elongated piles, whose cross-section is relatively constant. It is an extremely versatile approach with only our imagination for limits. To this model of the lot corresponds a sampling model consisting of a given number of increments. Each of these increments are selected at random systematic, stratified random, or strict random intervals. The continuous model of sampling studied in this chapter is applicable to all objects that can be transformed into a one-dimensional model, regardless of their physical state, origin, or composition. The problem is approached exactly in the same manner for all the various components of interest, but it should be clearly understood that each of these components carries its own heterogeneity; therefore, each component needs its own solutions, then the most challenging component may ultimately rule the selected sampling protocol.