New plans orthogonal through the block factor

TL;DR

This paper introduces methods for constructing plans orthogonal through the block factor (POTBs), enabling the design of larger, more complex experiments with multiple factors and levels, including symmetrical and two-level factor plans.

Contribution

It presents new procedures for expanding initial plans into larger POTBs, specifically for symmetrical experiments with multi-level factors and inter-class orthogonal plans for two-level factors.

Findings

Constructed POTBs for symmetrical experiments with three or more levels.

Developed plans inter-class orthogonal through the block factor for two-level factors.

Provided systematic procedures for adding blocks and factors to initial plans.

Abstract

In the present paper we construct plans orthogonal through the block factor (POTBs). We describe procedures for adding blocks as well as factors to an initial plan and thus generate a bigger plan. Using these procedures we construct POTBs for symmetrical experiments with factors having three or more levels. We also construct a series of plans inter-class orthogonal through the block factor for two-level factors.