Page 8 - SUBHARADEV SEN AND AHMED

SEN AND AFIFY

(ii) When the two components in the parallel system are dependent in
positive sense, mean times to failure are less than those for the IID
case as the values of α increase towards +1. Whereas, completely
reversed scenario is observed when the two components in the
parallel system are dependent in negative sense and α decreases
towards 1.

(iii) For dependent standby system, the mean times of system failure are
less than those in the IID case when α is positive. However,
completely reversed picture is observed when α is negative.

4. SYSTEM RELIABILITIES

The probability that a system survives up to a time t (> 0), is called the
reliability of the system at time t. Reliabilities for the series, parallel and
standby systems are obtained as

1 1 , (15)

1 2 1 1 (16)

and

1 1 , , 2 2 , 2 ,

(17)
respectively.
Now, we proceed to compare the reliabilities of the three different systems.
For this purpose, we consider α = -1.00, -0.75, -0.50, 0.00, 0.25, 0.50, 0.75
and 1.00; and the range parameter θ = 5.00. We take p as 0.5 (< 1) and 1.5
(> 1) to calculate the values of R 1(t), R 2(t) and R 3(t) at mission times t =
0.25, 0.50, 0.75, 1.00, 1.50, 2.00, 2.50 and 3.00. Statistical software R
(version 3.5.1) is utilized for calculations. The results are presented in Table
2 and Table 3.
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