Engineering Reliability

Problem  1                   Problem  2  

                       

   

 

   

     

       

Problem 1 (30%): In the attached sheet are data collected from a survival test of an electronic component in a specific thermal environment. Use these data in the following. As part of the quality control, 25 components were subjected to test until failure. The data presented (one set for each team) gives the time, in seconds, at which they failed.

Using the approach covered in class (show probability plots; usage of 'canned' programs for fitting distribution will be penalized) fit a Weibul distribution to this data. a. Determine the two parameters of the pdf. b. Determine its mean and the standard deviation. (denote the mean by W ) c. If the target life and the Lower Specification Limit (LSL) are as provided in

the table (specific for each team), determine % yield.

Problem 2 (30%): A circuit-board is assembled using four identical components (numbered 1 through 4) in their youth phase (ie. constant failure rate) with MTTF , W .( W determined above.) The overall life of the board is reflected by the reliability diagram given below, (Note: components 1 and 2 occur at two places).

a. Write down its structure function (x) explicitly in terms of the states xi. b. Determine all of its path sets. c. Identify the minimal path sets. (Hint: there will be 3) d. Redraw the diagram as a parallel structure of the minimum path series structures,

and generate its structure function. e. Determine the reliability function R(t) for each minimal path set.

Problem 1 (30%): In the attached sheet are data collected from a survival test of an electronic component in a specific thermal environment. Use these data in the following. As part of the quality control, 25 components were subjected to test until failure. The data presented (one set for each team) gives the time, in seconds, at which they failed.

Using the approach covered in class (show probability plots; usage of 'canned' programs for fitting distribution will be penalized) fit a Weibul distribution to this data. a. Determine the two parameters of the pdf. b. Determine its mean and the standard deviation. (denote the mean by W ) c. If the target life and the Lower Specification Limit (LSL) are as provided in

the table (specific for each team), determine % yield.

Problem 2 (30%): A circuit-board is assembled using four identical components (numbered 1 through 4) in their youth phase (ie. constant failure rate) with MTTF , W .( W determined above.) The overall life of the board is reflected by the reliability diagram given below, (Note: components 1 and 2 occur at two places).

a. Write down its structure function (x) explicitly in terms of the states xi. b. Determine all of its path sets. c. Identify the minimal path sets. (Hint: there will be 3) d. Redraw the diagram as a parallel structure of the minimum path series structures,

and generate its structure function. e. Determine the reliability function R(t) for each minimal path set.

f. Using (e) above, determine the R(t) of the circuit-board, and determine its reliability at 30 seconds.

g. If the MTTF of each component in the highest reliable path set is increased by

for this question) h. Determine all of its cut sets. i. Identify the minimal cut sets. j. Redraw the diagram as a series structure of the minimum cut parallel structures,

and generate its structure function.

Problem 3. (30%)

C nits a, b, and c. 1. Using the numerical value for , determine the MTTF of each unit. 2. Ignore the unit with the least reliability (a judgment call may be involved here).

You now have an active parallel system with two units. Assume that both these units can be repaired as and when they occur with a constant repair rate of

1.5 / . i. Draw the state transition diagram for this system.

ii. Determine the transition matrix M in P MP . iii. Determine numerically the steady-state probability state vector

iv. Determine the steady-

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Problem  3    

 

                Data  

1.5884E+01

2.2748E+01

2.0435E+01

1.5528E+01

1.6978E+01

2.2020E+01

1.8425E+01

1.6250E+01

1.6611E+01

1.1202E+01

1.4635E+01

1.5114E+01

1.8043E+01

2.1401E+01

1.2765E+01

2.5028E+01

2.0877E+01

1.9616E+01

1.3991E+01

2.0021E+01

1.9215E+01

1.8815E+01

2.3701E+01

1.7693E+01

1.7327E+01

Target1.7500E+01

LSL1.5000E+01

 

f. Using (e) above, determine the R(t) of the circuit-board, and determine its reliability at 30 seconds.

g. If the MTTF of each component in the highest reliable path set is increased by

for this question) h. Determine all of its cut sets. i. Identify the minimal cut sets. j. Redraw the diagram as a series structure of the minimum cut parallel structures,

and generate its structure function.

Problem 3. (30%)

C nits a, b, and c. 1. Using the numerical value for , determine the MTTF of each unit. 2. Ignore the unit with the least reliability (a judgment call may be involved here).

You now have an active parallel system with two units. Assume that both these units can be repaired as and when they occur with a constant repair rate of

1.5 / . i. Draw the state transition diagram for this system.

ii. Determine the transition matrix M in P MP . iii. Determine numerically the steady-state probability state vector

iv. Determine the steady-

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