Large language model (LLM) agents have shown promise in automating complex data-analysis workflows, but their reliable deployment remains challenging in high-stakes industrial scenarios. Industrial anomaly detection (IAD) is essential for manufacturing quality, safety, and efficiency, yet existing LLM-based IAD agents mainly focus on execution while under-exploiting strategy formulation. Consequently, they struggle to handle heterogeneous modalities in a unified and cost-effective manner. Inspired by the DMAIC quality-management framework, we propose DMAIC-IAD (DMAIC-inspired Agentic Industrial Anomaly Detection), a "Plan First, Judge Later" multi-agent system that aligns LLM agents with structured industrial problem-solving. DMAIC-IAD distills heterogeneous references into standardized operating procedures (SOPs) before strategy generation, and introduces a pre-trained execution-free judge model to rank candidate strategies without costly runtime trials. Extensive experiments across four modalities show that DMAIC-IAD improves average detection performance over applicable agentic baselines by 37.76%.