The length of time that a machine operates without failure is denoted by $Y_1$ and the length of time to repair a failure is denoted by $Y_2.$ After a repair is made, the machine is assumed to operate like a new machine. $Y_1$ and $Y_2$ are independent and each has the same density function

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Let $U_1=\frac{Y_1}{Y_1+Y_2},$ the proportion $of$ time that machine $1isin$ operation during any one operation$-$repair cycle and $U_2=Y_1+Y_2$ the length $of$ the cycle.

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