# Multi-parameter One-Sided Monitoring Test

## TL;DR

This paper introduces a new, more powerful statistical test for monitoring multiple quality indices in forestry products, improving upon traditional likelihood ratio tests by balancing size control and power.

## Contribution

A novel testing method that slightly relaxes size control to achieve significantly higher power in multi-parameter one-sided hypothesis testing.

## Key findings

- New test maintains good size control
- Significantly more powerful than likelihood ratio test
- Performs well in monitoring multiple quality indices

## Abstract

Multi-parameter one-sided hypothesis test problems arise naturally in many applications. We are particularly interested in effective tests for monitoring multiple quality indices in forestry products. Our search reveals that there are many effective statistical methods in the literature for normal data, and that they can easily be adapted for non-normal data. We find that the beautiful likelihood ratio test is unsatisfactory, because in order to control the size, it must cope with the least favorable distributions at the cost of power. In this paper, we find a novel way to slightly ease the size control, obtaining a much more powerful test. Simulation confirms that the new test retains good control of the type I error and is markedly more powerful than the likelihood ratio test as well as many competitors based on normal data. The new method performs well in the context of monitoring multiple quality indices.