RGT is a planned test-analyze-and-fix (TAAF) process in which End Unit is tested under actual, simulated, or accelerated environments to disclose design deficiencies and defects. It is intended to provide a basis for early incorporation of corrective actions and for verification of their effectiveness, thus promoting reliability growth. RGT is intended to correct failures that reduce operational effectiveness and failures that increase maintenance and logistics support costs.
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L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT) Plan
For
End Unit
Prepared by:
Hilaire Perera, P.Eng.
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L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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TABLE OF CONTENTS
Page No.
Purpose ---------------------------------------------------------------------------------- 3
Scope ---------------------------------------------------------------------------------- 3
Definitions ---------------------------------------------------------------------------------- 3
Responsibilities ----------------------------------------------------------------------------------- 3
Procedure
Selection of Growth Model ------------------------------------------------- 4
Duane Plot Example using Regression Analysis ------------------------- 4
Approximate Confidence Bounds for the MTBF ------------------------- 6
at the end of Duane Test
Reliability Growth Management -------------------------------------------- 7
Determination of Test Conditions ----------------------------------------- 7
Failure Reporting, Analysis and Corrective Action System ------------ 8
Steps in Creating the Duane Model Plot for Analysis ------------------- 9
Prediction of End Unit RGT Growth Time Using Growth Rate of 0.4-- 9
Reliability Growth Assessment --------------------------------------------- 10
Reliability Growth Success Criteria --------------------------------------- 10
ASSOCIATED
DOCUMENTS MIL-STD-721: Definitions Of Terms For Reliability And Maintainability
MIL-HDBK-189: Reliability Growth Management
MIL-STD-1635: Reliability Growth Testing
MIL-HDBK-338B Electronic Reliability Design Handbook
NIST/SEMATECH Engineering Statistics Handbook
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L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT) Plan
Purpose RGT is a planned test-analyze-and-fix (TAAF) process in which End Unit is tested
under actual, simulated, or accelerated environments to disclose design deficiencies
and defects. It is intended to provide a basis for early incorporation of corrective
actions and for verification of their effectiveness, thus promoting reliability growth.
RGT is intended to correct failures that reduce operational effectiveness and failures
that increase maintenance and logistics support costs.
The formal test program dedicated to reliability growth should be deferred until after
environmental qualification, when the design of the prototype or preproduction
equipment which is to be used in RGT reflects the anticipated configuration and
manufacturing processes to be used in production, but prior to commitment to
production.
Scope Reliability Engineering Tasks in Growth Testing focus on the prevention, detection,
and correction of reliability design deficiencies, weak parts, and workmanship
defects. An effective reliability program stresses early investment in reliability
engineering tasks to avoid subsequent additional costs and schedule delays. MTBF
growth is not expected to increase indefinitely in time, in use no growth or negative
growth may occur.
Definitions Mean Time Between Failure (MTBF) is a measure of reliability for repairable items:
The mean number of hours during which all parts of the item perform within their
specified limits, during a particular measurement interval under stated conditions
Corrective Maintenance (Repair). The actions performed as a result of failure to
restore an item to a specified condition
Observed Mean Time Between Failure is equal to the total operating time of the
equipment divided by the number of relevant failures
Predicted Mean Time Between Failure is that value determined by reliability
prediction methods and is based on the equipment design and the use environment
Reliability Growth. The positive improvement of the reliability of equipment through
the systematic and permanent removal of failure mechanisms
Responsibilities
It is the responsibility of the reliability engineer assigned to the particular project to
prepare the RGT Plan, and together with a test engineer to prepare the RGT Test
Procedure. These documents should be reviewed and approved by the Manager,
Quality and Technical and the Project Manager
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L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Procedure
Reliability Growth Testing (RGT) Plan Continued
Selection of the Growth Model
The approach to reliability growth is based on the Duane model. This model
provides a deterministic approach to reliability growth. In this way the unit MTBF
vs. Operating Hours falls along a straight line when plotted on ‘log-log’ paper That
is, the change in MTBF during development is proportional to T
where T is the
cumulative operating time and is the rate of growth corresponding to the rapidity
with which faults are found, and changes are made to permanently eliminate the
basic causes of the faults observed.
This type of plot is called a Duane Plot and the slope of the best line through the
points is called the reliability growth slope or Duane plot slope
Equation (1) is linearized by taking the “natural log” of both sides
LN (mc) = LN (b) + α LN (T) ------------ (2)
mc = Cumulative MTBF
T = Cumulative Test Time
b = The cumulative mean time between failures at T = 1, the beginning of the
“growth” work
α = The slope of the straight line on the LN-LN plot
Instantaneous MTBF (mi) = (1 / (1-α))mc
The parameters “b” and “α” can also be calculated by applying least squares (Linear
Regression) analysis on equation (2) using EXCEL software
Duane Plot Example using Regression Analysis
The observed failure times used were: 5, 40, 43, 175, 389, 712, 747, 795, 1299 and
1478 hours, with the test ending at 1500 hours. After using this information in a
regression analysis, the following parameters were calculated. (a) Growth Slope α;
(b) MTBF at the end of test; (c) MTBF at 80% Confidence Interval; (d) MTBF at
90% Lower Confidence Limit
Duane Equation: mc = bTα
---------------- (1)
5.
L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT) Plan Continued
MTBF Data for Regression Analysis
Age (Hrs) Cum MTBF (Hrs) LN‐Age LN‐Cum MTBF
5 5 1.609437912 1.609437912
40 20 3.688879454 2.995732274
43 14.33333333 3.761200116 2.662587827
175 43.75 5.164785974 3.778491613
389 77.8 5.963579344 4.354141431
712 118.6666667 6.568077911 4.776318442
747 106.7142857 6.616065185 4.670155036
795 99.375 6.678342115 4.598900573
1299 144.3333333 7.169350017 4.972125439
1478 147.8 7.298445102 4.995860009
1500 150 7.313220387 5.010635294
Growth Slope = 0.61
Instantaneous MTBF at the end of 1500 Hour Test = 159/0.39 = 408 Hours ----- Use Eqn. (1)
MTBF (MTBFlow = 288; MTBFhigh = 475) @ 80% Confidence Interval
MTBF = 288 @ 90% Lower Confidence Limit
6.
L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT) Plan Continued
Approximate Confidence Bounds for the MTBF at
End of Duane Test
Confidence Level = 80%, Significance Level (α) = 20%
Standard Normal Distribution result for significance α/2, for Two sided z 0.539827
MTBF 408 Hours
Number of failures in the Growth Time r 10
mL MTBF
r r 1( )[ ]
r
z
2
4
r
z
2
2
z
4
16
0.5
2
mL 288.483 MTBF Lower Bound
mU MTBF
r r 1( )[ ]
r z
r
2
.5
2
mU 474.939 MTBF Upper Bound
Confidence Level = 90%, Significance Level (α) = 10%
Standard Normal Distribution result for significance α, for Single sided z 0.539827
mL MTBF
r r 1( )[ ]
r
z
2
4
r
z
2
2
z
4
16
0.5
2
mL 288.483 MTBF Lower Bound
Note:
MTBF Upper & Lower Bounds are calculated
using the shown equations in “MATHCAD”
software program.
The “z” value is from “EXCEL” software
program, and if needed the required MTBF
values can be calculated using the equations in
“EXCEL”
Slope Calc.xls
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L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT) Plan Continued
Procedure
(Continued) Reliability Growth Management
Reliability growth management is the systematic planning for reliability
achievement as a function of time and other resources and is used for
controlling the ongoing rate of achievement by reallocation of resources based
on comparisons between planned and assessed reliability values. Reliability
growth management is part of the system engineering process. It does not take
the place of the other basic reliability program activities such as predictions,
apportionment, failure mode and effect analysis, and stress analysis. Instead,
reliability growth management provides a means of viewing all the reliability
program activities in an integrated manner. It is imperative to recognize that a
total reliability program is needed for effective reliability growth management.
Determining the Test Conditions
The initial step is the development of a representative Mission/Life Cycle Profile, by
determining the most stressful environmental conditions and durations of stress that
the system will experience during its life cycle.
For systems that have multiple missions and/or environmentally distinct mission
phases, thorough environmental simulation in the RGT often is impractical. In these
cases, the choice of mission(s), phase(s) or combined mission profiles to be simulated
should be driven by the combination of operational relevance and feasibility of
measurement. Almost always, the RGT combined environments should include
temperature cycling and vibration as a minimum, along with operational stresses such
as on/off cycling and variation in inputs (e.g. line voltage) and outputs (e.g. loads).
Rate of Growth is depicted by the slope of the growth curve. This, in turn, is governed
by the amount of control, rigor, and efficiency by which failures are discovered,
analyzed, and corrected through design and quality action. Test programs which foster
the discovery of failures, coupled with management supported analysis and timely
corrective action, will result in a faster growth rate and consequently less total test
time.
8.
L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT) Plan Continued
Procedure Failure Reporting, Analysis and Corrective Action System (FRACAS)
(continued)
A disciplined and aggressive closed-loop FRACAS is an essential element in the RGT
process. The essence of a closed-loop FRACAS is that failures and faults of both
hardware and software are formally reported, analysis is performed to determine
failure cause, and positive corrective actions are identified, implemented, and verified
to prevent further recurrence.
For a successful RGT process, all failures must be analyzed to the extent needed to
determine the root cause of the failure. In many instances, this will not require a
detailed laboratory analysis because the cause of the failure, such as test procedure
errors, wrong parts, overstressed parts, workmanship errors, etc., will be readily
apparent. Likewise, the corrective actions for many of these failure types will be
relatively straightforward and easily implemented.
Early elimination of failure modes, and thus early implementation of a good
FRACAS, has the following advantages:
• Cost and schedule savings.
• Ample time to assess corrective actions.
• Reduction of previously identified failure modes; reducing redundant data
analysis.
• Adequate time to address all failures prior to full rate production (i.e.
prevention of corrective action backlog).
If RGT results are to be interpreted correctly, all test conditions and occurrences must
be recorded accurately and completely. A solution and key complement to FRACAS
is the test log because a major source of problems is the dynamic status of test item
configurations. By definition, when reliability growth is taking place, the equipment
is changing (normally both hardware and software). In addition, temporary
repairs/replacements usually are permitted so that testing may continue while
permanent fixes are being explored.
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L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT) Plan, Continued
Procedure
(Continued)
Steps in Creating the Duane Model Plot (Page 11) for Analysis
a. Using three cycle ln-ln paper, draw horizontal lines at the required MTBF
value and the predicted MTBF
b. Plot growth line start point at 100 test hours and 15% of predicted MTBF
c. The suitable range of reliability growth is represented by the Growth Rate α
of 0.3 and 0.6. Draw a line representing Growth Rate α = 0.4. The selected
Growth Rate line is considered the baseline against which reliability growth
can be evaluated during the reliability growth test
d. Once 5 Failure/Time data points are obtained, determine Growth Slope α
and draw the growth rate line. Continue test
e. The intersection of the selected growth rate line and the required MTBF line
yields an approximation of total test time required
Prediction of End Unit Growth Time using Growth Rate of 0.4
The End Unit that has undergone environmental Stress Screening (ESS) [ESS
should be conducted on all electronic equipment scheduled for RGT. This helps
prevent overloading the RGT with problems not directly related to design] should
be tested for the predicted Growth Time based on the following conditions..
Specified MTBF = 6000 Hours ______ Predicted MTBF = 12645 Hours _______
Preconditioning (Initial Test ) Time = 100 Hours
The End Unit undergoing RGT should assume to have the following
characteristics:
(a) Assumed Growth Rate = 0.4 (Suitable Growth Rates are between 0.3 & 0.6)
used as an aggressive reliability program is being followed
(b) A Starting point of 15% of the predicted MTBF for the cumulative MTBF Line
(c) A Starting point of 25% (100 * 0.15 / (1-)) of the predicted MTBF for the
instantaneous MTBF Line
Duane Model
LN (Specified MTBF) - LN (0.15 of Predicted MTBF)
=
LN (Test Time = T) - LN (Preconditioning Time)
10.
L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
Page 10
Reliability Growth Testing (RGT) Plan, Continued
LN (6000) – LN (1897)
0.4 =
LN (T) – LN (100)
8.70 – 7.55
0.4 =
LN (T) – 4.61
LN (T) = 2.875 + 4.61
T = e7.485
Reliability Growth Assessment
The reliability growth assessment should be obtained by calculating the Growth
Rate α, using data from the tests. The reliability of the End Unit will be
monitored by a Growth Plot (Cumulative MTBF vs Cumulative Test Time). The
Instantaneous MTBF (Cumulative MTBF/ (1- α) ) plots should be included in
periodic reports, according to Schedule requirements
Reliability Growth Test Success Criteria
The reliability growth test and its associated failure analysis and corrective action
activity should be considered satisfactory if any of the following conditions exist:
The plotted MTBF values remain on or above the planned growth line
The best-fit straight line is congruent with or above the planned line
The best-fit straight line is below the planned line, but its slope is such
that a projection of the line crosses the horizontal (Specified MTBF) line
by the time the planned growth line reaches the same point
If none of the above conditions exist, it should be assumed that the planned
reliability growth cannot be achieved with the current level of activity. Before a
corrective action plan is determined, a careful analysis of the End Unit design
and related failures should be made, to ascertain the problem areas and possible
design modifications.
Predicted
RGT Time (T) = 1781 Hours
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L o n g T e r m Q u a l i t y A s s u r a n c e ( L T Q A ) ,
h i l a i r e p e r e r a @ r o g e r s . c o m
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Reliability Growth Testing (RGT), Continued
Procedure
(Continued)
.
The Instantaneous MTBF is the model mathematical representation of MTBF if
all previous failure occurrences are corrected
Instantaneous MTBF = (1 / (1 – α)) times Cumulative MTBF
15% of 12645
=1897
100
MTBF (predicted) =12645
MTBF (specified) =6000
MTBF ‐ Hrs
Cumulative Test Time (T) ‐ Hrs
T=100
Total Test Time
Required
T = 1781
Planned
Cumulative MTBF
Growth Line has
α = 0.4
25% of 12645 =
3161
Planned Instantaneous
MTBF
Duane Model Plot