This paper presents the development and use of benchmarking grey-box models for the detection and diagnosis of multiple-dependent faults (MDFDD) of a water-cooled centrifugal chiller. Models are developed using data recorded by a Building Automation System (BAS) from a central cooling plant of an institutional building. The forward residual-based fault detection model identifies a fault symptom, when the difference between the measured value of target variable and benchmarking value exceeds the corresponding threshold. For the fault diagnosis, most publications start from a known single fault and establish the impact on following variables in the system. This paper presents a rule-based backward approach. The proposed method identifies if (i) the fault symptom is correct (i.e., a variable has abnormal values), or (ii) the fault symptom is incorrect (i.e., the symptom of target variable is caused by impacts generated by other faulty variables due to the dependency between variables), or (iii) both target and regressor variables are abnormal. For testing the proposed MDFDD model, some artificial faults are inserted into the measurement data file, and results are discussed about the method potential for the application.