Asian Journal of Mathematics & Statistics 1994-5418 2077-2068 Asian Network for Scientific Information 10.3923/ajms.2014.35.39 El Genidy Mohammed Mohammed 1 2014 7 1 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 T1. The continuous random variables T2 and T3 represented the time of the repairing stages which it were electrical and mechanical repairing respectively and the continuous random variable T4 represented a compile-time of the machine after repairing it. All the random variables had a normal distribution with different means and variances. The joint probability distribution function FT(t) was obtained as multiple linear regression form by calculating the probability density function f(Ti), 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 (1-FT(t)) can be computed and predicted its value easily by using the multiple linear regression form of FT(t) without performed many mathematical processes.

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