Permutation Test as a Novel Robust Statistical Approach for Gauging a Change in the Rate of Stochastic Preignition

<div>Multiple statistical methods were evaluated to determine the most suitable approach to gauge whether a gasoline deposit control additive (DCA) causes a statistically significant increase in rate of stochastic preignition (SPI) in a direct injection, turbocharged, spark ignition (SI) engine. SPI is an abnormal combustion phenomenon observed at highly boosted conditions in turbocharged SI engines. The high in-cylinder pressures observed during an SPI event have the potential to cause physical damage to the engine.</div> <div>The SPI rate is a function of engine operating conditions as well as fuel and oil properties. DCAs are commonly used in commercial gasoline at very low concentrations (20–200 ppm m/m) to prevent the buildup of carbon deposits in the combustion chambers and fuel systems. Since the effect of DCAs on SPI rate can be subtle and the data inherently stochastic, a controlled engine test methodology with robust statistical analysis is required to conclusively determine whether a gasoline detergent increases or mitigates the rate of SPI occurrence. Therefore, the TOP TIER™ Standardized Dynamometer Test Method to Evaluate Additized Detergent Gasoline for Stochastic Pre-Ignition (hereafter referred to as the TOP TIER™ Additive SPI Test Protocol) described herein is designed to gauge whether a gasoline additive causes a statistically significant change in the SPI rate at a controlled operating condition as compared to unadditized gasoline.</div> <div>This study focuses on the statistical analysis portion of the test protocol. Multiple statistical approaches were evaluated using data from the TOP TIER™ Additive SPI Test Protocol to determine the most appropriate and robust approach for detecting a statistically significant difference in SPI rates. The analysis included the two-sample (unpaired) t-test, linear mixed-effects models (LMMs), the Mann–Whitney U test, and the permutation test. The results indicated a combination of permutation paired with Wilkinson’s method as the most suitable approach.</div>