

Joint Probability Distribution Function of the Repairing Time for the Defective
Machines in the Multiple Queues System 
Mohammed Mohammed El Genidy 
Abstract:
This study dealt with the queues system in one of the industrial workshops
which it was composed of four queues, the first and the fourth queues were connected
in series, while the second and the third queues were connected in parallel
to repair defective machines such that the repairing process included two parts,
it were electric and mechanic parts. The first stage was the dismantling of
the machine into two parts with the time represented by a continuous random
variable T_{1}. The continuous random variables T_{2} and T_{3}
represented the time of the repairing stages which it were electrical and mechanical
repairing respectively and the continuous random variable T_{4} represented
a compiletime of the machine after repairing it. All the random variables had
a normal distribution with different means and variances. The joint probability
distribution function F_{T}(t) was obtained as multiple linear regression
form by calculating the probability density function f(T_{i}), i = 1,
2, 3, 4 where T is a continuous random variable represented the whole time repairs
in the system and t represented a maximum value of T. On the other hand the
probability that the system will be failure or defective at T>t is equal
to (1F_{T}(t)) can be computed and predicted its value easily by using
the multiple linear regression form of F_{T}(t) without performed many
mathematical processes.


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How to cite this article:
Mohammed Mohammed El Genidy , 2014. Joint Probability Distribution Function of the Repairing Time for the Defective
Machines in the Multiple Queues System. Asian Journal of Mathematics & Statistics, 7: 3539. DOI: 10.3923/ajms.2014.35.39 URL: https://scialert.net/abstract/?doi=ajms.2014.35.39




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