## 1 Introduction  
Various factors are considered in system design, such as efficiency, costs, safety, and environmental effect. Availability is also one of the important issues in the system design. The definition of the availability from BS4778-3.1 (British standards, quality vocabulary, availability, reliability, and maintainability terms.) Guide to concepts and related definitions is the ability of an item under the combined aspects of reliability, maintainability, and maintenance support to perform its required function at a specified instant or for a specified period [1]. The availability indicates that how much a system approaches ideal operation without production loss caused by equipment failures or undesired external events. Availability estimation is frequently performed in the oil and gas, chemical, and power plant industries to find the optimum design option, to predict the production level, and to evaluate maintenance and operating policies. Many previous studies conducted the availability estimation for various systems to improve their designs. [PERSON] and [PERSON] [2] estimated the availability of production and electrical systems using the developed numerical method. They considered failure and repair rates following the non-exponential distribution. [PERSON] and [PERSON] [3] conducted the availability estimation for two similar chlorine production plants which were located in different environmental conditions (Iraq and Switzerland). They employed the concept of \"delayed time\" to take into account the additional time required to reach full production rate. [PERSON] [4] estimated the availability of a natural gas compressor plant to investigate its unavailability. Since the plant had no backup systems, the unavailability estimation was crucial. They concluded that the availability analysis provided useful information to determine the optimum number of spares. [PERSON] [5] indicated the methodologies for the availability estimation of oil/gas production and transport systems. He described not only an analytical approach but also a simulation method for the availability estimation. [PERSON] and [PERSON] [6] conducted the availability estimation for an ammonia plant using both analytical and simulation method. They concluded that the performance of the plant could be improved by changing the overhaul strategy and plant configuration. [PERSON] and [PERSON] [7] analyzed the availability of a reverse osmosis (RO) plant for producing potable water from seawater through desalination. They employed failure mode effect analysis (FMEA) and fault tree analysis (FTA) techniques to investigate the downtime pattern and failure. [PERSON] et al. [8] assessed the availability of an offshore installation using Monte Carlo simulation. [PERSON] et al. [9] suggested a general approach for the reliability and availability assessment of complex systems by employing Monte Carlo simulation. They validated the proposed approach by performing a case study for cogeneration plants. [PERSON] and [PERSON] [10] estimated the availability of a gas re-injection plant for the oil and gas production. They utilized reliability block diagram (RBD) techniques in conjunction with Monte Carlo simulation. They also considered the leak because the plant should be stopped when the leak was detected. [PERSON] et al. [11] estimated the availability of conventional and novel propulsion systems with a BOG handling system of an LNG carrier. They estimated the availability depending on the required function to prevent rough evaluation: design propulsion load, emergency propulsion load, and BOG utilization. [PERSON] and [PERSON] [12] suggested a new modeling approach for predicting the availability of a production system. They considered not only machine failures but also the material supply, management, and set-up in the proposed method. They also investigated the uncertainties caused by the various production environment using a fuzzy Bayesian method. [PERSON] et al.