Time-series anomaly detection (TSAD) is an important task in many fields. There has been a growing trend in TSAD research toward methods built on pre-trained models or Transformer architectures. However, these methods often require substantial computational resources and large amounts of data. To address this, numerous recent studies have proposed alternative solutions using simpler architectures that offer lower computational costs while achieving competitive performance in terms of accuracy. Motivated by this direction, we propose a TSAD method called TriLinear (Tricube Smoothing Decomposition and Linear Forecasting for TSAD), which combines a linear model with time-series decomposition to deliver effective anomaly detection using a simple architecture. In this paper, we compare TriLinear with well-known TSAD methods on the standard benchmark datasets KDD and NAB. We also evaluate TSAD methods on a real-world astronomical dataset. These evaluations demonstrate the comprehensive performance and trade-offs of TSAD methods in terms of accuracy and robustness. We have published our source code publicly available at https://github.com/thanapol2/TriLinear/ .