## 1 Introduction
### Reliability Research for Building Energy System  
The reliability analysis is very important in building an energy system design, which determines whether the system has sufficient capability to fulfill the requirements for both normal conditions (e.g., the design capacity is more than the operating duty) and abnormal conditions (e.g., the components' failure) [30; 31]. By considering the benefits of economic (i.e., the reduction of energy consumption and maintenance cost) and environmental management, the significance of reliability parameters was evaluated and emphasized by [PERSON] et al. [32]. The operation and maintenance characteristics of a HVAC system, which have an impact on the satisfaction of occupants, were studied by [PERSON] et al. [33]. A relationship between the satisfaction of occupants and the characteristics of a HVAC system was established based on questionnaire investigations. A regressed prediction model was also developed accordingly. [PERSON] et al. [34] developed a quantitative method according to the reliability analysis of air-conditioning systems, in order to estimate the optimum inspection period for condition-based maintenance in commercial buildings. Among these studies mentioned above, a very small number of studies have considered components' reliabilities by adopting quantitative methods in a HVAC system design process. In order to optimize the cooling water system configuration, [PERSON] et al. [35] developed a robust optimal design method by considering the system uncertainties and reliabilities. The results showed that the sized pumping system could have enough capability to supply the cooling and operate within its efficient region. In summary, most conventional and optimal chiller design methods are based on the annual cooling load under predefined conditions, which may ensure the designed systems operate at a satisfactory performance when the actual operating conditions are the same or close to the predefined conditions. However, in most occasions the actual conditions often deviate from the predefined conditions due to the inevitable uncertainties and equipment failures in the real world. In order to address the impact of uncertainties of design inputs and reliability of the components in operation, this study presents an optimal and robust design method for a chiller plant by considering both uncertainty and reliability simultaneously in quantitative ways. Different from previous studies that mainly addressed the cooling load distribution and its peak value in a typical year [36; 37; 38], in this paper, the distribution of the cooling load is calculated based on a large number of cooling load scenarios while considering a series of uncertainties. Monte Carlo simulation is employed to simulate these scenarios of cooling load for generating a more representative cooling load distribution. In contrast to the previous studies that mainly address the energy efficiency of a chiller plant, this study also considers the impacts of the reliability of chillers to justify whether the selected chiller plant has enough capacity to supply sufficient cooling for the users. Previous studies usually assumed that chillers have the same failure rates concerning the reliability (e.g., chillers with constant-speed or variable-speed drivers). In this paper, the failure rate difference between a constant-speed chiller and variable-speed chiller is considered and quantified. A steady probability distribution for various states of chiller plant is generated by the Markov method. In addition, compared with previous studies that selected the total chiller plant cooling capacity as a certain value, in this paper, the total chiller plant cooling capacity is selected within a searching range, which is determined corresponding to different unmet hours of the cooling load distribution. The optimal option for the chiller plant is selected among the optimal options of different total cooling capacities based on the total life-cycle cost. The organization of this study is summarized as follows.