---

Home |  Assignments |  Lectures | Resources

---

Assignments

Assignment 1:

This assignment consists of five problems, problems 5, 6, 7 and 8 are from the ``blue book''.

Problem # 1:
Show the result that was proved in Example 1.14 in Page 34, using the SDP.

Note: Some students are not clear about the difference between inclusion-exclusion and SDP. Refer to (Rd) on page 15 is inclusion-exclusion and (Re) on page 16 is SDP.

Problem # 5:
Seven lamps are shown as shown in figure 1.P.3. Each lamp can fail with probability q, independently of all the others. The system is operational if no two adjacent lamps fail. Obtain an expression for system reliability.

Problem # 6:
Consider a base repeater in a cellular communication system with two control channels and three voice channels. Assume that the system is up so long as atleast one control  channel and atleast one voice channel is functioning. Draw a realiability block diagram for this problem and write down an expression for system reliability. Next, draw a fault tree model for this system. Note that this fault tree has no repeated events and hence can be solved  in a way similar to that for a series-parallel reliability block diagram.

Problem # 7:
Modify the base repeater problem so that a control can also function as a voice channel. Draw a fault tree model for the modified problem. Notice that the fault tree has repeated events. Derive the reliability expression using the SDP method.

Problem # 8:
Return to Example 1.13 but now permitting a shared link B-C as shown in figure 1.P.4. Draw the fault tree for modeling the reliability for the communication network. Note that due to the shared link, the fault tree will have a shared or repeated event. Derive an expression for system reliability using the SDP method as in Example 1.14.
 

Assignment 2:

This assignment consists of 6 problems. problems 1, 3, 7 are from page numbers 56, 57. Problem 4 from page number 58. Problems 7, 8 from page 59.

Problem #1:
Consider the following program segment:
                                 if B then
                                        repeat S1 until B1
                                 else
                                        repeat S2 until B2

Assume that P(B = true) = p, P(B1= true) = 3/5, and P(B2 = true) = 2/5. Exactly one statement is common to statement groups S1 and S2: Write ("good day"). After many repeated executions of the proceeding program segment, it has been estimated that the probability of printing exactly three "good day" messages is 3/25. Derive the value of p.

Problem #3:
In order to increase the probability of correct transmission of a message over a noisy channel, a repetition code is often used. Assume that the "message" consists of a single bit, and that the probability of a correct transmission on a single trial is p. With a repetition code of rate 1/n, the message is transmitted a fixed number (n) of times and a majority voter at the receiving end is used for decoding. Assuming n = 2k + 1, k = 0, 1, 2, ..., determine the error probability Pe of a repetition code as a function of K.

Problem #7:
Plot the reliabilities of an m out of n system as a function of the simplex reliability
R(0 <= R <= 1) using n = 3 and k = 1, 2, 3 [parallel redundency, TMR(triple modular redundancy) and a series system, respectively].

Problem #4:
Assume that the probability of successful trnasmission of a single bit over a binary communication channel is p. We desire to trnasmit a 4-bit word over the channel. To increase the probability of successfule word trnasmission, we may use 7-bit Hamming code(4 data bits + 3 check bits). Such a code is known to be able to crrect single-bit errors[HAMM 1980]. Derive the probabilities of successfule word transmission under the two schemes and derive the condition under which the use of Hamming code will improve performance.

Proble #7:
For the fault tree shown in Figure 1.P.8
      (1) Write down the structure function.
      (2) Derive reliability expressions by
                  (a) State enumeration method
                  (b) Method of inclusion-exclusion
                  (c) Sum of disjoin products method
                  (d) Conditioning on the shared event (E2bar).

Problem #8:
For the BTS sector/transmitter of Example 1.21, draw the equivalent fault tree, and derive reliability expressions by means of state enumeration, inclusion-exclusion, and SDP methods.

Assignment 3:

This assignment consists of 6 problems. problems 1, 2 from 129 page number. Problem 6 of 148 page and problems 5, 6, 7 of 153 page.
assignment03.ps

Assignment 4:

This assignment consists of 5 problems. Problem 3 from 165 page. Problems 4, 8 of 166 page and problem 4 of page 197. Problem 5 from 207 page.
assignment04.ps

Assignment 5:

This assignment consists of 7 problems. Problems 3, 4, 6, 9, 10, 12, 13 from 235-237 pages.
assignment05.ps

Assignment 6:

This assignment consists of 6 problems. problem 1 from 254-255 page, problems 1, 2 from 262, problem 4 from 287 and problems 1, 2 from 294 page.
assignment06.ps

Assignment 7:

This assignment consists of 7 problems. Problems 1, 7 from 420 - 421 pages, problems 1, 2 from 425 - 426 pages and problems 1, 3, 4 from 435 - 436 pages.
assignment07.ps

Assignment 8:

This assignment consists of 6 problems. Problems 6, 7 and 9 are from 436 - 437 pages, problem 3 from 451 page and problems 5, 6 from 475 pages.
assignment08.ps

Assignment 9:

This assignment consists of 6 problems. Problems  7, 8 and 9 are from 475 - 476 pages, and problems 1, 2 and 3 from 482 - 483 pages.
assignment09.ps

Assignment 10:

This assignment consists of 6 problems. Problems  2, 3, 9, 10, 11 and 12 from 518 - 519 pages.
assignment10.ps

*  All assignments are due every tuesday before the class.

---

Home |  Assignments |  Lectures | Resources

---