Linear Consecutive-k-out-of-n: G System Reliability Analysis

The concerned study pertains to the development of a new stochastic model for the reliability analysis of linear consecutive-k-out-of-n: G system, where k>n2. In the developed model, system may collapse as a result of common cause failure or hardware failure in its units. The system has exponentially distributed failure rates, and in case of breakdown, it is repaired with the copula method. The developed model has been examined through supplementary variable technique (SVT) along with Laplace transform. The current paper has specifically studied consecutive-(n-1)-out-of-n: G system. The performance of such system having ten components is explored and its various reliability measures have been obtained and discussed with the help of graphs. The originality of this work lies in incorporating common cause failure in conjunction with copula repair in the reliability modeling of consecutive systems through the SVT. The study confirms that an increase in failure rates and the number of components of the concerned system decreases mean time to failure (MTTF). The profit of linear consecutive-9-out-of-10: G system is examined with the help of a numerical example.