International Journal of Engineering & Technology IJET-IJENS Vol:10 No:01 59 108501-6464 IJET-IJENS © February 2010 IJENS I J E N S Abstract— Effective maintenance management is essential to reduce the adverse effect of equipment failure to operation. This is accomplished by accurately predicting the equipment failure such that appropriate actions can be planned and taken in order to minimize the impact of equipment failure to operation. This paper presents a development of model based on Markov process for a degraded multi-state system to evaluate the system performance. The system degradation was quantified by five distinct level of system’s production output ranging from perfect functioning state to complete failure with zero output. At any point in time, the system can experience Poisson failure from any state upon which an imperfect repair will be performed while imperfect preventive maintenance will be performed at the last acceptable state as indicated by minimum acceptable production output. This research explored a method of estimating of transition matrix for the five state Markov process by utilizing production output data. The results indicate the applicability of Markov where comparison with traditionally binary model is presented. Index Term— Multi-State system reliability, Markov process, imperfect repair. I. INTRODUCTION Effective maintenance management is essential and critical as a way to reduce the adverse effect of equipment failures and to maximize equipment availability. The increase in equipment availability means higher productivity and thus higher profitability provided that the maintenance optimization does include the cost factor. This has lead to increase research interest in the subject of optimizing maintenance management. It is estimated that 15% to 45% of total production cost are attributed to maintenance cost with 30% of total manpower involvement [1]. This is significant; however, the consequence of an inefficient maintenance management is far beyond the direct cost of maintenance although not easily quantifiable. The maintenance’s high cost and low efficiency is one of the last cost saving frontier for companies to improve profitability [11] The current research will be focusing on the development of performance evaluation model for repairable equipment subjected to degradation which, in time, reduces the ability of the system to perform its intended function. A repairable system is defined as a system which can be restored to satisfactory working All authors are with Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia *Corresponding author. Tel.: 605-368 7058; fax: 605-365 6461 (email: masdimuhammad@ petronas.com.my). condition by repairing or replacing the damaged components that caused the failure to occur other than replacing the whole system [20]. Performance model would include the evaluation of system reliability as well as system availability with respect to time. The degradation process, if left unattended, will often lead to degradation failure [14]. The degradation can be caused by a myriad of factors including variable operating environment, fatigue, failures of non-essential components and random shocks on the system [16] II. BACKGROUND Traditionally, reliability analysis of repairable system depends upon the assumption that the system can be in a binary state; either fully working conditions or complete failures. With the assumption, numerous approaches, methodologies and models have emerged to predict the reliability of repairable systems corresponding to different repair assumptions. The models include variations of perfect renewals process which assumes perfect repair and non-homogenous Poisson process (NHPP) for minimal repair assumption as discussed in literatures including [8], [12] and [4]. Still, another model called generalized renewal process (GRP) with the assumption that the repair process is in between perfect repair and minimal repair as proposed by [6] and further researched by Yanez, Joglar and Modarres in [21], V. Krivtsov [7] and Weckman et al in [19] to name a few. However, there are cases as mentioned by researchers such as Soro, Nourelfath and Ait-Kadi [16], Donat, et al.[3] and Ramirez-Marquez and Coit [15] that binary assumption failed to characterize actual system reliability behavior. In these cases, analysis using multi-state system (MSS) assumption is found to be more appropriate. MSS is defined as system that can have a finite number of performance rates with various distinguished level of efficiency [9]. Typical systems where MSS has been applied successfully are in the area of water distribution [13], telecommunication, oil and gas supply system and power generation and transmission [15]. This is due to the fact that there are distinct degradation phases for the system prior to complete failure which is evident from different levels of production outputs. Common methods in accessing the performance of MSS are based on four different approaches: Extension of Boolean models to the multi-valued case, the stochastic process (Markov and semi-Markov), the universal generating function and the Monte-Carlo simulation techniques [9]. Each approach has advantages and disadvantages depending on the system understudy. Reliability Evaluation for a Multi-State System Subject to Imperfect Repair and Maintenance Masdi Muhammad*, M Amin Abd Majid , Ainul Akmar Mokhtar Mechanical Engineering Department, Universiti Teknologi PETRONAS