For any construction work we characterize the double design by

(a) Show that the double of an equal (arrangement) framework is an arrangement (equal) framework.

(b) Show that the double of a double construction is the first design.

(c) What is the double of a k-out-of-n structure?

(d) Show that a negligible way (cut) set of the double framework is an insignificant cut (way) set of the first

structure.

question 30

Segment I is supposed to be relevantto the framework if for some state vector x,

Othenvise, it is supposed to be unessential.

(a) Explain in words what it implies peak a part to be insignificant.

(b) Let A1,

Similar to the insignificant way sets ota framework, and let S signify the arrangement of segments.

Show that S = l_Ji_ Ai if and just fall segments are applicable.

Ck mean the insignificant cut sets. Show that Ci if and just assuming all

(c) Let Cl,

parts are important.

question 31

Register the upper and lower limits ot r(p) utilizing the two strategies for the

(a) two-out-of-three framework and

(b) two-out-of-visit framework.

(c) Compare these limits witn the specific dependability when

05

(ii) p,

(iii) p,

= 0.8

= 0.2

question 32

Show that it every (autonomous) part ot an arrangement framework has an IFR conveyance, at that point the

framework lifetime is itself IFR by

(a) snowing that

iF(t) = E Xi (t)

Where F(t) is the disappointment rate work ot the framework; and i(t) the disappointment rate work ot the

lifetime ot segment

(b) utilizing the definition ot IFR given in Exercise 22