Statistical Methodologies for Quality Control: A Study on CNC Machine Tool Production at Merlo S.p.A.

In an industrial environment, quality control is critical for assuring that products comply with specifications and regulatory requirements. For precision machining operations, such as CNC turning at Merlo S.p.A., applying a sampling plan, rather than a full lot inspection, is an effective way to balance inspection needs with production costs and cycle times. However, the choice of the sampling plan directly impacts the risks tolerated by both producer and customer: on one side, the risk of rejecting good quality lots (producer’s risk α), and on the other, the risk of accepting bad quality ones (customer’s risk β). This thesis aims to compare different sampling plans, in particular, the company’s current plan (n=3, c=0), the ISO 2859 standard plans (single and double sampling), and a dynamic plan based on the process capability index Cpk, to identify the most effective strategy for reducing risks and ensuring outgoing quality. The methodology comparison combines two approaches. First, the plans were analysed through performance curves (OC, AOQ, ATI) derived from classical statistical formulations. Second, a Monte Carlo simulation over 1000 lots was performed under two conditions: a stable process (in-control state) and a deteriorated one (out-of-control state) to evaluate plan performance in realistic scenarios. The results show that the current plan provides no customer protection, with consumer’s risk β exceeding 95% and an unacceptable average outgoing quality (AOQL > 10%). ISO 2859 plans partially improve consumer protection but require very large sample sizes (up to 125 units) and are poorly suited to small lot sizes. In contrast, the dynamic Cpk-based plan consistently outperforms in in-control conditions, it reduces inspection effort by adapting to process capability, while in out-of-control conditions it drastically lowers consumer’s risk (≤ 5%), with a lower average number of inspected units compared to ISO plans. In conclusion, the study demonstrates that a Cpk-based dynamic plan is the most effective option for ensuring robust and flexible inspection efforts in CNC manufacturing. Its implementation would allow Merlo S.p.A. to combine high-quality control reliability with reduced inspection costs.