R&T 2007 - Replacement Interval Calculations - Elder.pdf

Pressure Relief Valve
Pressure Relief Valve
Pop Test Data
Pop Test Data
Statistical
Statistical
Replacement Interval Calculation
Replacement Interval Calculation
by
by
Frederick T. Elder
Frederick T. Elder
IRC Research and Technology Forum
IRC Research and Technology Forum
February 9, 2007
February 9, 2007
(c) Frederick T. Elder
(c) Frederick T. Elder

When to Replace per IIAR 110
When to Replace per IIAR 110
„
„ After a known relief, and within a reasonable time,
After a known relief, and within a reasonable time,
spring
spring-
-loaded relief valves shall be replaced by new
loaded relief valves shall be replaced by new
or remanufactured certified valves. If re
or remanufactured certified valves. If re-
-seating is
seating is
not complete, replacement shall be immediate.
not complete, replacement shall be immediate.
„
„ When a component reliability program is in place to
When a component reliability program is in place to
verify relief valve functionality and longevity by
verify relief valve functionality and longevity by
history, testing, disassembly and inspection, and
history, testing, disassembly and inspection, and
periodic statistical review of these activities, relief
periodic statistical review of these activities, relief
valves may be replaced at any interval justified by
valves may be replaced at any interval justified by
the findings of such a program. In the absence of
the findings of such a program. In the absence of
such a program, each relief valve shall be replaced
such a program, each relief valve shall be replaced
at the frequency recommended by the relief valve
at the frequency recommended by the relief valve
manufacturer. In the absence of both a component
manufacturer. In the absence of both a component
reliability program and manufacturers’
reliability program and manufacturers’
recommendations, relief valves shall be replaced
recommendations, relief valves shall be replaced
every five years if not indicated earlier at annual
every five years if not indicated earlier at annual
inspection.
inspection.

Why Test?
Why Test?
„
„ Properly assess health of NH3
Properly assess health of NH3
refrigeration safety system
refrigeration safety system
„
„ OSHA has required it in prior
OSHA has required it in prior
settlement agreements
settlement agreements
„
„ It may save $$$
It may save $$$
„
„ It may answer a PHA question
It may answer a PHA question

Maintenance Guidance
Maintenance Guidance
„
„ http://www.valve
http://www.valve-
-world.net/srv/ShowPage.aspx?pageID=640
world.net/srv/ShowPage.aspx?pageID=640

Outline
Outline
„
„ Background and
Background and
Advantages of Weibull
Advantages of Weibull
Analysis
Analysis
„
„ Failure Criteria
Failure Criteria
„
„ Generating Weibull Plot
Generating Weibull Plot
„
„ Weibayes Analysis
Weibayes Analysis
„
„ Examples
Examples

Background
Background
„
„ Invented by
Invented by Waloddi
Waloddi Weibull
Weibull
in 1937
in 1937 –
– he used it for
he used it for
fatigue life estimation
fatigue life estimation
„
„ Dr. Robert Abernethy the
Dr. Robert Abernethy the
modern Weibull Analysis
modern Weibull Analysis
expert
expert
„
„ Weibull Analysis first used
Weibull Analysis first used
extensively in aerospace
extensively in aerospace
applications
applications
Waloddi Weibull 1887-1979

Advantages of Weibull Analysis
„
„ Main advantage:
Main advantage: Small sample size
Small sample size
•
• Samples may be expensive
Samples may be expensive
•
• Reduces time/cost of testing
Reduces time/cost of testing
•
• May not have many recorded failures
May not have many recorded failures
„
„ Weibull Analysis is displayed by an
Weibull Analysis is displayed by an
easy to read graphical plot
easy to read graphical plot

Pop Test Failure Criteria
Pop Test Failure Criteria
Example – 250 psig valve
Opens at pressures < 242.5 psig – failure
Opens at pressures > 262.5 psig -- failure

Alternate Failure Criteria
Alternate Failure Criteria
„
„ Reduce the set pressure of relief
Reduce the set pressure of relief
valves when possible
valves when possible –
– then expand
then expand
failure definition
failure definition
„
„ Do not consider low pressure
Do not consider low pressure
opening a failure for those valves
opening a failure for those valves
where that does not create a hazard
where that does not create a hazard

Weibull Analysis Plot
Weibull Analysis Plot
„
„ Most Weibull Analysis done from plot
Most Weibull Analysis done from plot
„
„ To Plot, you need:
To Plot, you need:
•
• Failure criteria
Failure criteria
•
• Number of failures and times
Number of failures and times
•
• Number of suspensions and times
Number of suspensions and times
„
„ From Plot, you get:
From Plot, you get:
•
• Predicted failure rate
Predicted failure rate
•
• Failure mechanism
Failure mechanism

Plotting Data
Plotting Data
„
„ Plot scales
Plot scales
•
• X axis: Age parameter (Units of Hours in Figure)
X axis: Age parameter (Units of Hours in Figure)
•
• Y axis: Cumulative Distribution Function (CDF)
Y axis: Cumulative Distribution Function (CDF)
„
„ Defines percentage of units that will fail up to an age
Defines percentage of units that will fail up to an age.
.

Weibayes Analysis
Weibayes Analysis
„
„ Weibayes is used when there
Weibayes is used when there
are no or very few failures:
are no or very few failures:
•
• Finding the MTTF of a unit after
Finding the MTTF of a unit after
initial testing lead to no failures
initial testing lead to no failures
•
• Redesigned component, several
Redesigned component, several
units tested without failure, is
units tested without failure, is
testing sufficient?
testing sufficient?
•
• Smaller sample sizes needed
Smaller sample sizes needed
with Weibayes since previous
with Weibayes since previous
failure history is known
failure history is known

Weibayes Analysis
Weibayes Analysis
„
„ Weibayes Analysis equation,
Weibayes Analysis equation,
uses an
uses an assumed
assumed β
β
„
„ Can be used when
Can be used when no failures
no failures
have occurred
have occurred
„
„ Need to have back ground
Need to have back ground
failure info
failure info
•
• Company Weibull library
Company Weibull library
•
• Other
Other Weibull
Weibull libraries
libraries
Where:
Where:
N =
N = total number of
total number of
suspensions and failures
suspensions and failures
r =
r = number of failed units
number of failed units
β
β =
= assumed slope
assumed slope
t =
t = time or cycles
time or cycles
/
1
N
i
i=1
t
r
β
β
η
⎡ ⎤
= ⎢ ⎥
⎣ ⎦
∑

Weibayes Analysis
Weibayes Analysis
„
„ Relief valve failure data
Relief valve failure data
shows typical
shows typical β
β value of
value of 1
1
•
• http://www.barringer1.com/
http://www.barringer1.com/
wdbase.htm
wdbase.htm
„
„ Weibayes can be used to
Weibayes can be used to
determine replacement
determine replacement
interval time
interval time
„
„ Can input data into
Can input data into
Weibull program or
Weibull program or
calculate by hand using
calculate by hand using
equation
equation

Weibayes Analysis
Weibayes Analysis
Determine New Replacement Interval
Determine New Replacement Interval
for Test with Zero Failures
for Test with Zero Failures
1.
1. Gather suspension data
Gather suspension data
2.
2. Find
Find η
η (as described in next slides)
(as described in next slides)
3.
3. Find k
Find k1
1-
-value from One
value from One-
-Failure Plan
Failure Plan
table for your assumed
table for your assumed β
β and
and
number of samples being tested
number of samples being tested
4.
4. Replacement Interval =
Replacement Interval =η
η(k
(k1
1)
)

Weibayes: Finding
Weibayes: Finding η
η With No Failures
With No Failures
Hand Calculation
Hand Calculation
„
„ Confidence Limit Equation for Zero Failures:
Confidence Limit Equation for Zero Failures:
•
• Use:
Use:
where
where r=# of failures
r=# of failures
T
Ti
i=Time of each replacement
=Time of each replacement
: look up this value from Chi
: look up this value from Chi-
-squared
squared
table for C confidence and 2r+2 degrees of freedom
table for C confidence and 2r+2 degrees of freedom
( )
{ }
2
;2 2
C f
χ ⋅ +
( )
1
2
2 ;2 2 0
i
T C r for r
β
β
η χ
⎧ ⎫
= + ≥
⎨ ⎬
⎩ ⎭
∑

Weibayes: Finding
η With No Failures
With No Failures
WinSMITH Calculation
„
„ Can Select Specific
Can Select Specific
Confidence
Confidence
•
• Enter number of units, all
Enter number of units, all
as suspensions
as suspensions
•
• Select Weibayes method
Select Weibayes method
•
• Choose specific
Choose specific
confidence,
confidence, 63.2%
63.2%
confidence equivalent to
confidence equivalent to
assuming 1 failure is
assuming 1 failure is
imminent
imminent
•
• Find
Find η
η from Weibayes plot
from Weibayes plot

Weibayes Example:
Weibayes Example: No Failures
No Failures
During Testing
During Testing
„
„ Parameters: 30 relief valves used for
Parameters: 30 relief valves used for
5 years, 0 failures, want to increase
5 years, 0 failures, want to increase
Replacement Interval
Replacement Interval
„
„ Question:
Question: How many years can the
How many years can the
valves be used and have at most one
valves be used and have at most one
failure with a 90% confidence?
failure with a 90% confidence?

Weibayes Example:
No Failures
During Testing
During Testing
„
„ Data entered in WinSMITH
Data entered in WinSMITH
•
• 30 suspensions, 5 year time
30 suspensions, 5 year time
•
• Weibayes method,
Weibayes method, β
β=1, 90% Confidence
=1, 90% Confidence
η=65.14

Weibayes Example:
No Failures
During Testing
During Testing
„
„ Table of K
Table of K1
1-
-values For One
values For One-
-Failure Test Plans,
Failure Test Plans, β
β=1
=1
„
„ Read N=30, K
Read N=30, K1
1=0.132
=0.132
„
„ Complete table and equation to derive K
Complete table and equation to derive K1
1-
-values
values
included in Appendix B

Weibayes Example:
No Failures
During Testing
During Testing
„
„ Replacement Interval: 65.14(0.132)= 8.6
Replacement Interval: 65.14(0.132)= 8.6
years
years
„
„ So with a 90% confidence, you can replace
So with a 90% confidence, you can replace
the relief valves every 8.6 years and have
the relief valves every 8.6 years and have
at most one failure during that period
at most one failure during that period
„
„ Reasonable approach: 8.6 years minus 5
Reasonable approach: 8.6 years minus 5
years = 3.6 years/2=1.8 years, so add 1.8
years = 3.6 years/2=1.8 years, so add 1.8
years to 5 year zero failure plan to have
years to 5 year zero failure plan to have
reasonable probability of no failures
reasonable probability of no failures

Weibayes Analysis
Weibayes Analysis
Determine New Replacement Interval for
One or More Failures
One or More Failures During Testing
During Testing
„
„ Most Common
Most Common
„
„ Typically, there will be failures
Typically, there will be failures

Weibayes Analysis
Weibayes Analysis
One or More Failures
One or More Failures During Testing
During Testing
1.
1. Gather failure and suspension
Gather failure and suspension
data
data
2.
2. Find
Find η
η (as described in next slides)
(as described in next slides)
3.
3. Find k
Find k0
0-
-value from Zero
value from Zero-
-
Failure Plan table for your
Failure Plan table for your
assumed
assumed β
β and number of
and number of
samples being tested
samples being tested
4.
4. Replacement Interval =
Replacement Interval =η
η(k
(k0
0)
)

Weibayes: Finding
η With Failures
With Failures
Hand Calculation
Hand Calculation
„
„ Use Weibayes equation to find
Use Weibayes equation to find η
η
„
„ Use:
Use:
to get a
to get a specific confidence
specific confidence, where f=# of
, where f=# of
failures
failures
„
„ : look up this value from
: look up this value from
Chi
Chi-
-squared table for C confidence and
squared table for C confidence and
2f+2 degrees of freedom
2f+2 degrees of freedom
( )
{ }
1/
2
2
;2 2
c
f
C f
β
η η
χ
⎡ ⎤
⋅
⎢ ⎥
=
⋅ +
⎢ ⎥
⎣ ⎦
( )
{ }
2
;2 2
C f
χ ⋅ +

Weibayes: Finding
η With Failures
With Failures
Hand Calculation
Hand Calculation
„
„ Chi
Chi-
-Squared Table, C: 90% Confidence
Squared Table, C: 90% Confidence

Weibayes: Finding
η With Failures
With Failures
„
„ Enter number of failures, all
Enter number of failures, all
with the assumed time of
with the assumed time of
half the usage time
half the usage time
„
„ Enter number of suspensions
Enter number of suspensions
„
„ Choose the specific
Choose the specific
confidence
confidence
„
„ Find
Find η
η from the Weibayes
from the Weibayes
plot
plot

Weibayes Example:
Weibayes Example: One or More
One or More
Failures
Failures During Testing
During Testing
„
„ Parameters: 30 relief valves used for
Parameters: 30 relief valves used for
5 years, 2 failures, don’t know when
5 years, 2 failures, don’t know when
failures occurred
failures occurred
„
„ Question:
Question: How many years can the
How many years can the
valves be used and have zero
valves be used and have zero
failures with a 90% confidence?
failures with a 90% confidence?

Weibayes Example:
One or More
Failures
During Testing
„
„ Data entered in WinSMITH
Data entered in WinSMITH
•
• 28 suspensions, 5 year time
28 suspensions, 5 year time
•
• 2 failures, assumed half of 5 years, or 2.5 years
2 failures, assumed half of 5 years, or 2.5 years
•
• Weibayes method,
Weibayes method, β
β=1, 90% Confidence
=1, 90% Confidence
27.26
η =

Weibayes Example:
One or More
Failures
During Testing
„
„ Table of K
Table of K0
0-
-values For Zero
values For Zero-
-Failure Test Plans,
Failure Test Plans, β
β=1
=1
„
„ Read N=30, K
Read N=30, K0
0=0.077
=0.077
„
„ Complete table and equation to derive K
Complete table and equation to derive K0
0-
-values
values

Weibayes Example:
One or More
Failures
During Testing
„
„ Replacement Interval:
Replacement Interval:
27.26(0.077)= 2.1 years
27.26(0.077)= 2.1 years
„
„ So with a 90% confidence, you can
So with a 90% confidence, you can
replace the relief valves every 2.1 years
replace the relief valves every 2.1 years
and have no failures during the interval
and have no failures during the interval

Remember
Remember
„
„ MI of pipes and vessels is also of high priority
MI of pipes and vessels is also of high priority
„
„ Relief Valves not to be placed back in service
Relief Valves not to be placed back in service
after testing
after testing
„
„ Need judgment to extend the replacement/test
Need judgment to extend the replacement/test
interval
interval
„
„ Failed relief valve may never be needed
Failed relief valve may never be needed

Where to Buy Weibull Material
Where to Buy Weibull Material
„
„ The New Weibull Handbook and the
The New Weibull Handbook and the
WinSMITH software packages can be
WinSMITH software packages can be
purchased at:
purchased at:
•
• http://
http://www.weibullnews.com/contents.h
www.weibullnews.com/contents.h
tm#Prices
tm#Prices

Sources
Sources
„
„ Engineering Safety Relief Systems
Engineering Safety Relief Systems, March 2006.
, March 2006.
by Reindl, D.T, Jekel, T.B., Available from the
by Reindl, D.T, Jekel, T.B., Available from the
Industrial Refrigeration Consortium
Industrial Refrigeration Consortium
„
„ The New Weibull Handbook
The New Weibull Handbook, Fourth Edition, 2000,
, Fourth Edition, 2000,
by Robert Abernethy
by Robert Abernethy
„
„ The New Weibull Handbook
The New Weibull Handbook, Fifth Edition, 2006,
, Fifth Edition, 2006,
by Robert Abernethy
by Robert Abernethy
„
„ Fitness for Service of Pressure Relieving Systems
Fitness for Service of Pressure Relieving Systems,
,
by W. E. Short II, presented at The 2003 ASME
by W. E. Short II, presented at The 2003 ASME
Pressure Vessels and Piping Conference
Pressure Vessels and Piping Conference
„
„ Reliability Testing of Relief Valves
Reliability Testing of Relief Valves, by Robert E.
, by Robert E.
Gross, presented at The 2004 ASME Pressure
Gross, presented at The 2004 ASME Pressure
Vessels and Piping Conference
Vessels and Piping Conference

Sources
Sources
„
„ Plant Guidelines for Technical Management of
Plant Guidelines for Technical Management of
Chemical Process Safety
Chemical Process Safety, pp 169
, pp 169-
-172, by Center
172, by Center
for Chemical Process Safety, 1992
for Chemical Process Safety, 1992
„
„ Armor Swift
Armor Swift Eckrich
Eckrich –
– OSHA settlement
OSHA settlement
agreement of October 9, 1997
agreement of October 9, 1997
„
„ IBP
IBP –
– OSHA settlement agreement of 2001
OSHA settlement agreement of 2001
„
„ Code Requirements for Safety Relief Systems
Code Requirements for Safety Relief Systems,
,
Todd Jekel, 2005 Research and Technology
Todd Jekel, 2005 Research and Technology
Forum, January 20, 2005
Forum, January 20, 2005

Sources
Sources
„
„ Center for Chemical Process Safety (1998).
Center for Chemical Process Safety (1998).
Guidelines for Pressure Relief and Effluent
Guidelines for Pressure Relief and Effluent
Handling Systems
Handling Systems. (pp. 104
. (pp. 104-
-107). Center for
107). Center for
Chemical Process Safety/
Chemical Process Safety/AIChE
AIChE. Online version
. Online version
available at: http://www.knovel.com/knovel2/
available at: http://www.knovel.com/knovel2/
Toc.jsp?BookID
Toc.jsp?BookID=831&VerticalID=0
=831&VerticalID=0
„
„ Center for Chemical Process Safety (1989).
Center for Chemical Process Safety (1989).
Process Equipment Reliability Data with Data
Process Equipment Reliability Data with Data
Tables
Tables. P 212
. P 212

Appendix A:
Appendix A:
Weibull Analysis Background
Weibull Analysis Background

„
„ Weibull Analysis
Weibull Analysis
can be used for:
can be used for:
•
• Failure Distribution
Failure Distribution
•
• Failure Forecasts
Failure Forecasts
and Predictions
and Predictions
•
• Maintenance
Maintenance
Planning
Planning
•
• Effectiveness of a
Effectiveness of a
Redesign
Redesign

Weibull Analysis Software
„
„ WinSMITH Weibull from Fulton
WinSMITH Weibull from Fulton
Findings
Findings
•
• http://www.barringer1.com/wins.htm
http://www.barringer1.com/wins.htm
„
„ Created by Wes Fulton and Dr. Bob
Created by Wes Fulton and Dr. Bob
Abernethey
Abernethey

„
„ Enter age data, suspensions and failures
Enter age data, suspensions and failures
„
„ Software will:
Software will:
•
• Plot Data
Plot Data
•
• Calculate
Calculate Eta
Eta, Beta, and PVE numbers
, Beta, and PVE numbers
•
• Run a distribution analysis
Run a distribution analysis
•
• Generate a results report
Generate a results report

Plotting Data
Plotting Data
„
„ Age must be known for data
Age must be known for data
•
• Standard Life Data: exact age of parts
Standard Life Data: exact age of parts
known
known
•
• Interval Data: Age of parts not exactly
Interval Data: Age of parts not exactly
know, so parts are grouped
know, so parts are grouped
„
„ Could be from weekly, monthly, etc
Could be from weekly, monthly, etc
inspections
inspections
„
„ Age may be operating time,
Age may be operating time,
starts/stops, etc.
starts/stops, etc.

Plotting Data
Plotting Data
„
„ Failures
Failures
•
• Establish failure mode
Establish failure mode
•
• Every part displaying
Every part displaying
this mode constitutes a
this mode constitutes a
failure
failure
„
„ Suspensions
Suspensions
•
• Parts that failed via a
Parts that failed via a
different mode
different mode
•
• Parts that have not yet
Parts that have not yet
failed
failed
„
„ Early Suspension: Age
Early Suspension: Age
below age of first
below age of first
failure
failure
„
„ Late Suspension: Age
Late Suspension: Age
above age of last
above age of last
failure
failure

Plotting Data
Plotting Data
„
„ Plot scales
Plot scales
•
• X axis: Age parameter (Units of Hours in Figure)
X axis: Age parameter (Units of Hours in Figure)
•
• Y axis: Cumulative Distribution Function (CDF)
Y axis: Cumulative Distribution Function (CDF)
„
„ Defines proportion of units that will fail up to an age as a
Defines proportion of units that will fail up to an age as a
percentage
percentage

Plotting Data
Plotting Data
WinSMITH Data Plot
WinSMITH Data Plot

Plotting Data
Plotting Data
„
„ Two
Two-
-parameter most widely used Weibull
parameter most widely used Weibull
distribution
distribution
„
„ CDF
CDF (Cumulative Distribution Function):
(Cumulative Distribution Function):
F(t
F(t) = 1
) = 1-
- e
e-
-(t
(t/
/η
η)
)β
β
•
• F(t
F(t) = fraction failing up
) = fraction failing up-
-to
to-
-time t
time t
•
• t= failure time
t= failure time
•
• η
η = characteristic life
= characteristic life
•
• e = 2.718281, the base for natural logarithms
e = 2.718281, the base for natural logarithms
•
• β
β = slope parameter
= slope parameter

Plotting Data on Weibull Paper
„
„ Arrange failures and suspensions in time ascending
Arrange failures and suspensions in time ascending
order
order
„
„ Set up the following table:
Set up the following table:
„
„ Fill in Rank and Reverse Rank, and in Time column,
Fill in Rank and Reverse Rank, and in Time column,
include whether it was a Suspension or Failure
include whether it was a Suspension or Failure
„
„ If two data points have the same time to failure, they
If two data points have the same time to failure, they
are both presented in the column, and they will both
are both presented in the column, and they will both
get median rank values
get median rank values

„
„ Use equation to get Adjusted Rank (A.R.):
Use equation to get Adjusted Rank (A.R.):
A.R.=[Reverse Rank X Previous Rank + (N+1)] / [Reverse Rank + 1]
A.R.=[Reverse Rank X Previous Rank + (N+1)] / [Reverse Rank + 1]
„
„ Use
Use Benard’s
Benard’s Median Rank formula to get
Median Rank formula to get
new Median Rank (since adjusted rank is
new Median Rank (since adjusted rank is
not an integer):
not an integer):
Benard’s
Benard’s M.R.=(i
M.R.=(i-
-0.3) X 100 / (N+0.4)
0.3) X 100 / (N+0.4)
„
„ Fill out previous table, and plot:
Fill out previous table, and plot:
•
• Benard’s
Benard’s M. R. on the y
M. R. on the y-
-axis
axis
•
• Time on x
Time on x-
-axis
axis
„
„ Draw a best fit line through the points,
Draw a best fit line through the points,
make sure it is 1:1 Weibull paper
make sure it is 1:1 Weibull paper

Weibull Example:
Weibull Example: Preparing
Preparing
Weibull Plot by Hand
„
„ Parameters: You are given the
Parameters: You are given the
following data, 8 total parts, 5
following data, 8 total parts, 5
failures at 49,82,96,30, and 90 hours
failures at 49,82,96,30, and 90 hours
and, 3 suspensions at 45,10, and
and, 3 suspensions at 45,10, and
100 hours
100 hours
„
„ Question:
Question: At how many hours can
At how many hours can
you expect approximately 50% of
you expect approximately 50% of
the parts to fail?
the parts to fail?

Weibull Example:
Preparing
„
„ Set up and fill in table:
Set up and fill in table:
„
„ Plot the points on 1:1 Weibull Paper
Plot the points on 1:1 Weibull Paper
„
„ Draw a best fit line through the points and
Draw a best fit line through the points and
draw a line across from the 50% mark and
draw a line across from the 50% mark and
down to the time axis
down to the time axis

Weibull Example:
Preparing
50% fail by 77 hours
50% fail by 77 hours

Interpreting the Plot
„
„ PVE %: Goodness of fit indicator for
PVE %: Goodness of fit indicator for
Weibull line
Weibull line
•
• 10% is acceptable, 50% is average
10% is acceptable, 50% is average
„
„ N/S: Total number of data points/ Number
N/S: Total number of data points/ Number
of Suspensions
of Suspensions
Eta, Beta, PVE,
and N/S

„
„ Eta
Eta -
- Characteristic life: Age at which
Characteristic life: Age at which
63.2% of parts will fail
63.2% of parts will fail
•
• Parameter most effected by suspensions
Parameter most effected by suspensions

„
„ Beta
Beta –
– Slope of Weibull line: Failure Mode
Slope of Weibull line: Failure Mode
•
• Beta < 1.0 indicates infant mortality
Beta < 1.0 indicates infant mortality
•
• Beta = 1.0 indicates random failures that are
Beta = 1.0 indicates random failures that are
independent of age
independent of age
•
• Beta > 1.0 indicates wear out failures
Beta > 1.0 indicates wear out failures

„
„ Use PVE number to evaluate fit of
Use PVE number to evaluate fit of
line
line
„
„ Use Beta to evaluate failure method
Use Beta to evaluate failure method
„
„ Look for “Bad” Weibull characteristics
Look for “Bad” Weibull characteristics

Bad Weibull
Bad Weibull
„
„ Curved Weibull data
Curved Weibull data
•
• Origin not at t=0, must
Origin not at t=0, must
use three
use three-
-parameter
parameter
Weibull
Weibull
„
„ Outlying data points
Outlying data points
•
• Look at engineering
Look at engineering
aspects of data
aspects of data
recording, test records,
recording, test records,
calibrations, etc.
calibrations, etc.
„
„ Two different slopes of
Two different slopes of
Weibull data
Weibull data
•
• More than one failure
More than one failure
mode represented by
mode represented by
data, try to separate
data, try to separate
data
data

Bad Weibull
Bad Weibull
„
„ Close Serial Numbers
Close Serial Numbers
•
• Batch problem
Batch problem
„
„ If PVE number is unacceptable
If PVE number is unacceptable
•
• Look to different distributions, Log
Look to different distributions, Log
normal, Three
normal, Three-
-parameter Weibull
parameter Weibull
„
„ Careful, few data points leads to high
Careful, few data points leads to high
PVE number
PVE number

Failure Forecasting
Failure Forecasting
„
„ Expected number of
Expected number of
failures that may
failures that may
occur in a specific
occur in a specific
period of time
period of time
„
„ Predicts:
Predicts:
•
• Future failures when
Future failures when
failed units are replaced
failed units are replaced
•
• Future failures when
Future failures when
failed units are not
failed units are not
replaced
replaced

Failure Forecasting
Failure Forecasting
„
„ Additional input needed:
Additional input needed:
•
• Age of components in service
Age of components in service
•
• Usage rate
Usage rate
•
• Introduction rate of new units
Introduction rate of new units
•
• Failed parts replacement info
Failed parts replacement info

Appendix B: Weibayes
Appendix B: Weibayes
Extras
Extras

Weibayes: Finding
η With No Failures
With No Failures
Hand Calculation
Hand Calculation
„
„ Assume at Least One Failure is Imminent:
Assume at Least One Failure is Imminent:
•
• Use Weibayes equation to find
Use Weibayes equation to find η
η
•
• Assume 1 failure (r=1) since a failure is
Assume 1 failure (r=1) since a failure is
imminent (yields 63% confidence)
imminent (yields 63% confidence)
•
• Use the following table to achieve different
Use the following table to achieve different
confidences:
confidences:

Zero Failure Plan Table,
Zero Failure Plan Table, β
β = 1
= 1
„
„ K=[(
K=[(-
-1/N)*ln(0.1)]
1/N)*ln(0.1)](1/
(1/β
β)
)

Chi Squared Table for Use With
Chi Squared Table for Use With
Weibayes Hand Calculations
Weibayes Hand Calculations
„
„ Use 0.10 column for 90% Lower Bound,
Use 0.10 column for 90% Lower Bound,
0.05 for 95% Lower Bound, etc.
0.05 for 95% Lower Bound, etc.

One
One-
-Failure Test Plan Table,
Failure Test Plan Table, β
β = 1
= 1
„
„ (1
(1-
-Confidence)=(
Confidence)=(e
e-
-(k
(k)
)β
β
)
)N
N+N(e
+N(e-
-(k
(k)
)β
β
)
)N
N-
-1
1(1
(1-
- e
e-
-(k
(k)
)β
β
)
)

R&T 2007 - Replacement Interval Calculations - Elder.pdf

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