One of the most challenging aspects of operating a large-scale web search engine is to accurately evaluate and monitor the search engine's result quality regardless of search types. From a business perspective, in the face of such challenges, it is important to establish a universal search quality metric that can be easily understood by the entire organisation. In this paper, we introduce a model-based quality metric using Explainable Boosting Machine as the classifier and online user behaviour signals as features to predict search quality. The proposed metric takes into account a variety of search types and has good interpretability. To examine the performance of the metric, we constructed a large dataset of user behaviour on search engine results pages (SERPs) with SERP quality ratings from professional annotators. We compared the performance of the model in our metric to those of other black-box machine learning models on the dataset. We also share a few experiences within our company for the org-wide adoption of this metric relevant to metric design.