Establishment of auto-sampling frequency using a two-state Markov chain model

- Robotic samplers employed in high volume production processes are studied.
- Sampling frequency for robotic/auto-samplers can be small and effective.
- A two-state Markov chain model formulation is formulated.
- Consumer protection is highlighted for the design.
- A detailed cost analysis of statistical sampling is done.

Modern bulk material production processes are high volume and high quality processes. The manual grab sampling of bulk material is known to be biased and unrepresentative. Auto-samplers, which are robotic samplers of bulk material in small increments, provide for better representative samples of the production process. The amount and sampling frequency for an auto-sampler can be varied depending on the product type and quality characteristic of interest. This article presents a statistical methodology for determining the sampling frequency for auto-samplers using a two-state Markov chain model for detecting the foreign matter contamination in the production.