Reliability Engineering I
Computer Exercise II – theoretical distributions
Spring 2013
Power Distribution Transformers at DP&L
Continued
Instructions:
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You are to solve the following problem by completing the tables in the Analysis section.
You must do your own work and submit your own solution although you may discuss the
problem with your classmates.
You may use any textbook as a reference, and you may use any computer application;
however, the reliability software provided with the textbook along with MS Excel is
sufficient to work the problem.
You should submit your solution over the Web by completing the form on the Web
Submission page.
Background:
Continue to analyze the Power Distribution Transformers (PDT). Management is still
concerned about the reliability and maintainability of these transformers. However, the Chief
Engineer believes that a more accurate assessment can be made if they fit theoretical distributions
to the reliability and maintainability data that has been collected.1
Data Collection:
Continue to use the data from Exercise #1.
Analysis:
General Guidelines:
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1
Consider only the exponential, Weibull, minimum extreme value, normal,
lognormal, and gamma distributions.
When using the chi-square goodness-of-fit test, select the distribution having the
smallest Chi-square statistic that is less than the critical value at the 15 percent
level of significance (this is the “best fit” distribution). Use Sturges Rule with equal
expected cell counts. If no distribution passes the test, then repeat with unequal
cell counts.
When using the method of least squares, use the product limit estimator and the
mean plotting position. Select the distribution having the largest R-squared value
(this is the “best fit” distribution). However, if the best fit distribution is Weibull
where 0.95 <  < 1.05, then select the exponential in place of the Weibull.
The Chief Engineer is a recent graduate of the Engineering Management program and knows his stuff.
Reliability Engineering I
Computer Exercise II – theoretical distributions
Spring 2013
1. Reliability and Maintainability Model: Find the “best fit” failure and repair distributions
for the overall system using the entire set of failure and repair data based upon the chi-square
goodness-of-fit test. Then complete the table below.
Best Fit
Distribution
MLE Parameter Estimates
Failure distribution
Repair distribution
2. System Performance: Using the result from 1, complete the following table.
Measurement
R(1 yr)
R(2 yr)
MTTF
Median
90% design
life
H(2 hr)
H(4 hr)
MTTR
Median
90th percentile
Reliability
Measurement
Maintainability
(in hours)
3. Failure Mode Analysis: Compute separate failure distributions for each failure mode.
Complete the following table using the method of least-squares to determine the best failure
distribution.
Failure Mode
“Best” Failure
Distribution
Least-square
Parameter Estimates
MLE Parameter
Estimates
Failure Mode A:
Failure Mode B:
Failure Mode C:
4. Using the distributions in #3 and the MLE parameters, complete the following table:
Measurement
R(1 yr)
R(2 yr)
MTTF
Median
90% design
life
Failure Mode A:
Failure Mode B:
Failure Mode C:
5. System Performance: Complete the following table using #3, #4, and the MLE estimates.
Measurement
System
Reliability
R(1 yr)
R(2 yr)
Median
90% design life