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Keywords:
Controller Failure, Deliberate Failure, Gumbel-Hougaard Family Copula, MTTF, Natural Calamity, Strike, Supplementary Variables.Abstract
This paper deals with the reliability and profit analysis of an N-unit plant with two types of failure i.e. Partial failure and complete failure. The plant has N- units and at least k units are required to be in operational mode to fulfill the satisfactory needs of customer demand. Till the time k units are in good operational condition, i.e. at most (k-1) units fail, the plant can fulfill the needs of market demands and failure of more than k units it cannot satisfy customer requirements. Other types of failures like human failure and deliberate failure can also affect the functioning of plant. An important aspect of system failure, which is usually observed in industry, the strike of employees is also considered for study of mathematical model. The natural calamities such as earthquake, tsunami and sudden catching of fire that can fail the system completely, have also been considered in study of the model. The system has been studied by supplementary variable technique and various measures of reliability, such as availability, state transition probabilities, MTTF and profit function have been discussed. Some particular cases have also been discussed by taking different values of failure rates.
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