Author : V.V.Singh, Dilip KumarRawal

International Journal of Scientific & Engineering Research Volume 2, Issue 10, October-2011

ISSN 2229-5518

Download Full Paper : PDF**Abstract: **This paper deals with the availability analysis of a complex system that consists of two subsystems namely subsystem 1 and subsystem 2.Subsystem 1 is working under k-out of –n good policy and subsystem 2 has two identical units in parallel configuration. Controller for proper functioning controls the subsystems 1. All failure rates are constant and follow exponential distribution but repairs follow general and Gumbel-Houggard family copula distribution. The system is analyze by supplementary technique by evaluating varies measures of reliability such as state transition probability, MTTF, etc. Some computations are taken as special cases by evaluating availability of system and profit analysis

**Keywords:**Controller, Gumbel-Hogaard family copula, human failure, MTTF, k-out of n policy, supplementary variable, profit function

**INTRODUCTION**Many author including [1,6,8] has discuss reliability of complex systems by taking varies failure and one repair policy. By thinking about present scenario and complexity of advance technology and modern demand of electronic equipments one need to study of a controller, which is used in, varies electronic devices and systems.

In this paper author has considered a complex system, which consists of two subsystems 1 and subsystem 2. The subsystem 1 follows (k- out of -n good) policy, the subsystem 2 has two identical units in parallel configuration. Both subsystems are connected in series. The subsystem1 controlled by a controller. The system can fail in following situations: (1) more than k units of subsystem 1 has failed but both units of subsystem 2 are in good working condition, (2) Human failure occur in system, (3) Controller of subsystem 1 fails, (4) Both units of subsystem 2 fail. The system will be in minor partial failure in following situations: (1) All units of subsystem 1 are good and one unit of subsystem 2 has failed, (2) At least k units of subsystem 1 are good and one unit of subsystem 2 has failed.

Many authors have considered reliability and MTTF of a complex system, with different types of failures and one type of repair. However, they did not consider one of the important

aspects of repair between two transitions states i.e. how system will be behaving when there are two different types of repair possible between two adjacent states, which seems to be possible in many engineering systems. When this possibility exists, reliability of the system can be analyzed with the help of copula [7]. The authors [10] have discussed the availability of a system having three units under preemptive resume repair policy using copula in deliberately failure state. Therefore, in contrast to the earlier models, here author has considered a model in which he tried to address the problem where two different repair facilities are available between adjacent states i.e. the initial state and complete failed states. All failure rates are assumed to follow negative exponential distribution. The repairs follow general and Gumbel-Hougaard family copula distributions. In present paper, S0 is state where the system is in good working condition. S1,S3,S4 are state where the system is in partial or degraded mode and states S2, S5, S6, S7,and S8 are states where the system is in completely failure mode. When the system is in degraded mode, the general repaired is employed but whenever the system is in completely failure mode, the system is repaired by Gumbel- Haugaard family copula [7]. The system is analyzed by supplementary variable technique and varies measures of reliability has been discussed and some particular cashes are also taken to highlight the result. The results are demonstrated by graphs and conclusions are drown by graphs.

Read More:

Click here...