# Phased System Reliability Modeling and Assessment for Construction of Lunar Scientific Base
## 1 Introduction  
As lunar exploration continues to advance, major space powers such as the United States, Russia, Europe, and China have proposed numerous lunar exploration schemes and development plans, with lunar base construction being a critical objective [1; 2; 3]. The lunar scientific base (LSB), as the preliminary stage of the lunar base, is of great significance to the long-term exploration and exploitation of lunar resources [4; 5; 6]. The LSB generally includes multiple pieces of lunar surface detection equipment, such as landers, rovers, energy stations, robots, and scientific exploration instruments [7]. It is impossible to send such a large amount of equipment to the moon in just one launch due to the limited carrying capacity. Therefore, the complex systematic project of the LSB construction must be completed through a progressive method of \"multiple launches and lunar surface assembly\" [8]. The LSB construction requires substantial investment, a long construction period, and high technical risk. Thus, an accurate reliability assessment of the LSB construction is critical for successful mission implementation. As a common method to quantify the failure risk in complex aerospace systems, reliability assessment involves uncertainties affecting their behavior and helps engineers make more informed decisions during the design phase [9]. In order to ensure the smooth completion of the LSB construction, the industrial sector explicitly called for a quantitative reliability assessment of the whole construction process and put forward high-reliability index requirements. An accurate reliability assessment depends on reasonable reliability modeling. According to the basic concept of step-by-step LSB construction [7], the overall construction is divided into three main processes: lunar surface fixed-point delivery of equipment, lunar surface transport of equipment, and lunar surface docking assembly of equipment. The-phased reliability model proposed in this paper regards the overall construction as a series system composed of the three phases described above, considering that the failure of any one phase will lead to the failure of the whole LSB construction. This novel model makes the reliability confidence limits of each phase independent, thus avoiding correlation and simplifying the calculation. The confidence limits assessment for series system reliability has always been challenging in reliability engineering [10; 11; 12; 13]. In particular, the LSB construction process may face the problem of small sample tests and zero-failure data. For example, aerospace equipment is usually expensive and the production batch is not large, so only small sample tests can be conducted [14; 15; 16; 17]. Besides, such products end up being highly reliable and having a long life. Due to the limitations of development cycles and test costs, it is unaffordable to conduct prolonged testing. The limited test time makes it difficult to appear failure data in reliability test results; in other words, zero-failure data is often obtained [18; 19; 20]. The Lindstrom-Madden (LM) method [21] and the modified maximum likelihood (MML) method [22] are the main methods used in engineering to assess the lower confidence limit (LCL) for series system reliability. The core idea behind them is to reduce the test results to a set of binomial (pass/fail) tests with a pseudo-test number \(n\) and a pseudo-success number \(s\) (i.e., the system is considered to have passed \(s\) out of \(n\) tests). Furthermore, the theory of confidence intervals for binomial distribution reliability is used [23]. However, the traditional methods are based on the theory of maximum likelihood estimation and therefore have large errors in small sample cases [24]. In addition, these two methods are not applicable when there are zero-failure subsystems in a series system [25; 26]. In recent years, the Bayesian and Bootstrap methods have been developed for estimating the confidence limits of series system reliability.