## 1 Introduction  
The Mahalanobis-Taguchi system (MTS) is a powerful tool for studying multidimensional systems developed by [PERSON] [1; 2; 3]. MD and Taguchi robust engineering are effectively integrated and applied to the diagnosis and prediction of multivariate data. Due to its effectiveness and easy operation without any underlying statistical assumptions, this method has been widely used in various applications such as product quality testing systems, mechanical fault diagnoses, financial early-warnings, medical diagnoses, and other fields [4; 5; 6; 7].  
MTS is a pattern recognition system that employs the concepts of orthogonal arrays (OAs) and signal-to-noise ratios (SNRs) to screen useful features. The feature selection process, however, is seen as not optimal by several scholars [8; 9; 10]. Therefore, some scholars have carried out in-depth and extensive research and have achieved promising results, making important contributions to the development of MTS [11; 12; 13; 14; 15; 16; 17]. The majority of those methodologies are based on metaheuristic algorithms such as the genetic algorithm (GA), binary particle swarm optimization (BPSO), binary ant colony optimization (BACO), and the binary gravitational search algorithm (BGSA), effectively improving the feature selection strategy.  
Another challenge to implementing MTS in practice is the determination of a suitable threshold for distinguishing between normal and abnormal observations. [PERSON] [18] proposed a quadratic loss function (QLF) to determine the classification threshold, but this is unrealistic because it is difficult to estimate the relative cost or loss in reality. A simpler and more practical approach using the Chebyshev theorem, called the \"probability threshold method\", has been proposed [19]. There is also a substantial body of qualitative research in developing threshold determination methods [20; 21; 22].  
A novel two-stage Mahalanobis classification system (MCS), as well as its integrated version (IMCS), has been recently proposed by the current authors [16; 17]. IMCS integrates the decision boundary searching process, which is based on the particle swarm optimizer algorithm, directly into the feature selection phase (based on BPSO or BGSA) for constructing the MD space. Compared to classical MTS, both MCS and IMCS showed improved classification performance for sorting (i.e., good/bad structural quality) complex metal parts based on their vibrational response [17].  
The primary objective of this paper is to investigate the influence of the reference MD space on the classification performance of the recently proposed IMCS classifier [17]. The reference MD space is constructed by considering (i) normal samples, (ii) abnormal samples, and (iii) both normal and abnormal samples. In addition, the impact of an imbalanced dataset on classification accuracy is also discussed. This paper is organized into five sections. Section 2 presents the concept of multidimensional MD space. The procedure of IMCS with three different reference MD spaces is demonstrated in Section 3, followed by an experimental case study on complex-shaped metallic turbine blades and a numerical study on dogbone cylinders in Section 4. Section 5 gives the conclusions of this paper.