Reliability Engineering I
Computer Exercise III
Spring 2013
The Final Analysis
Power Distribution Transformers at DP&L
Instructions:




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).
Data Collection:
Continue to use the data and results from Exercises #1 and #2 in addition to the data sets provided
below.
Analysis:
General Guidelines:

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.
1. Senior management at DPL finds the reliability of their power distribution transformers to be
unacceptable. They have asked their engineers for suggestions to improve the five year
reliability. The following changes are being considered:
Failure Mode A: In order to improve the reliability of those parts that deteriorate over time, a
preventive maintenance is performed replacing worn parts every two years which restore Failure
Mode A to as good as new. Find RA(10) under preventive maintenance.
Failure Mode B: In order to improve reliability during storms and other events that may trip the
transformer breakers, DPL is considering adding some standby redundancy circuitry to the
transformers. When activated, the standby circuitry will result in the same failure distribution
(i.e. Failure Mode B). Early testing has shown the new circuitry to have 0.005 failures per year in
standby and a switching failure probability of 0.03. Find RB(10) under standby redundancy.
Reliability Engineering I
Computer Exercise III
Spring 2013
Failure Mode C: Many transformers have been plagued with premature failures due to
substandard parts. A new parts supplier was found and the failure mode C parts were subjected to
accelerated life testing. Forty parts were put on test with the following failure times in years
(Type II testing). Based upon a chi-square test, determine the best fit distribution.
0.34
1.14
1.60
8.09
24.64
54.05
67.19
76.23
85.97
88.08
104.94
107.64
121.55
124.22
140.39
149.02
206.48
237.81
241.45
251.12
284.41
317.61
324.90
349.81
422.97
428.32
475.16
507.90
655.45
778.72
Best Fit Distribution MLE Parameter 1 MLE Parameter 2
In order to identify marginal performers and further enhance failure mode C reliability, any new
transformer will be operated in a (burn-in) testing environment for one year before being installed
in the field. Find RC(10|1) using the fitted distribution with a one year burn-in test period.
Complete the following table.
Reliability
RA(10)
Measurement
Before the
above changes
After the
above changes
RB(10)
RC(10)
RC(10|1)
Rsys(10)
2. In order to analyze the long term frequency of repair at a single BTS, the number of days
between failures was recorded as follows:
Days
Days
since
since
Date of
last
Date of
last
Failure
Failure
Failure
Failure
8/1/1998
387
3/2/2005
203
8/23/1999
261
9/21/2005
158
5/10/2000
288
2/26/2006
155
2/22/2001
243
7/31/2006
199
10/23/2001
198
2/15/2007
143
5/9/2002
220
7/8/2007
143
12/15/2002
204 11/28/2007
174
7/7/2003
226
5/20/2008
170
2/18/2004
178
11/6/2008
178
8/14/2004
200
5/3/2009
162
Days between consecutive failures (Type II data)
Date of
Failure
10/12/2009
3/15/2010
8/14/2010
1/20/2011
5/26/2011
10/11/2011
2/9/2012
6/8/2012
10/24/2012
2/20/2013
Days
since
last
Failure
154
152
159
126
138
121
120
138
119
121
Reliability Engineering I
Computer Exercise III
Spring 2013
Using the time between failures given in the above data set and assuming a minimal repair
process and Type II data, determine if the NHPP power law process is an acceptable model by
completing the following table. Unit of time should be in days.
Parameter a
Parameter b
Chi Sq stat for trend test
Cramer von Mises test
stat for NHPP
3. The replacement cost of a single PDT is $ 2,700 and the cost of a single failure has been
estimated at $ 350 which includes maintenance, travel, replacement parts, loss of transmission
time, and customer goodwill. Compute the following measures based upon the NHPP power law
model obtained in 2 and the repair distribution determined in exercise #2.
minimum cost replacement
time in years*
Probability of no failures
the first year
Expected number of
failures the first 15 years
inherent availability over
the first 10 (operating)
years
*assume 365 days a year
cost per day at the minimum
cost
Probability of more than one
failure the first year
(instantaneous) MTBF in
days at the end of the 2nd yr
inherent availability over
(operating) years 10 -20