This paper critically analyses the current industry practices for making reliability prediction prevalent among the aircraft manufacturers and further explores the more accurate and cost effective methods for predicting the failure rate of a component or subsystem during the early design phase of the product development cycle namely NSWC method , PoF approach and SSI theory. It elucidates the effectiveness of these alternative approaches with the help of a case study on Hydraulic Accumulator (HYDAC).

1. Mechanical Reliability Prediction:
A Different Appro ach

2. Abstract
Market trend
Exploring alternative approaches
Introduction to Case Study: Hydraulic Accumulator (HYDAC) Solution
1. Approach to select an appropriate method:
2. PoF, SSI and NSWC methods explained
a. A sample prediction for explaining the PoF approach to predict
Barrel (Cylinder) failure rate:
b. Failure rate calculation using SSI Theory:
c. Sample prediction using NSWC for Dynamic Seal
3. Summary of analysis
Best Practices in the Industry
Common issues with alternative methods
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Reference
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Table of Contents
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3. Mechanical Reliability Prediction: A Different Approach | 3
Abstract
Reliability Prediction is a practice of predicting the failure rate of a component or subsystem during the early design phase
of the product development cycle. This is carried out in an attempt to ensure product reliability. Primarily, reliability
prediction is a design-supportive study intended for the following functionalities
Design feasibility evaluation
Comparing design alternatives
Identifying potential failure areas
Tracking reliability improvements
In the aerospace industry, the failure rates predicted by this study are used for safety assessment in compliance to FAR
25.1309 and ARP 4761. The predicted failure rates are used in FMEA which in turn, provides input to FTA.
The current industry practice uses a standard database approach called NPRD to find failure rates of mechanical
components/systems. In recent times, aircraft manufacturers are increasingly rejecting NPRD predictions, as the failure
rates predicted using this database is arguable in terms of design closeness. Also, in most cases, they were found to vary
with actual failure rates observed in the field.
A possible solution for this problem could be devised using a combination of approaches, ssuucchh aass
Stress Strength Interference (SSI) theory
Physics of Failure (PoF) approach
Naval Surface Warfare Centre (NSWC) methods
Although prediction with the above methods are accurate, these methods are not yet implemented due to a lack of
understanding, increased complexity, requirements of large amounts of design data, and the need for extensive time and
effort. In this whitepaper, we have built a case study around Accumulator. This helps explain an effective solution for
mechanical predictions using a blend of the SSI theory, PoF approach, and NSWC methods.
Market trends
In the current scenario, the NPRD method is extensively used for mechanical product reliability prediction as this method is
relatively easy to predict the part failure rate. NPRD has remained the preferred method for years. However, the current
market trend is moving towards exploring other appropriate methods for mechanical predictions. Aircraft makers feel the
need to explore alternative methods due to the following reasons:
Need for more accurate, precise and reliable failure data which considers actual usage conditions in its prediction
models
Predictions should be specific for each manufacturer. Also, the quality of components and manufacturing
processes should be accounted for
NPRD assumes a constant failure rate, which is not true in all cases
In NPRD, failure rates are not application sensitive and have limited accuracy
It is doubtful that sizeable design improvements will result from the NPRD prediction process
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4. Mechanical Reliability Prediction: A Different Approach | 4
Exploring alternative approaches
A combination of PoF, NSWC and SSI methods can be used appropriately to arrive at more accurate component and
system-level reliability predictions. As field data is rarely available, the use of field data for Reliability Prediction is likely to be
ruled out as an alternative.
Hydraulic Accumulator (HYDAC)
A hydraulic accumulator is a pressure storage reservoir. In this a non-compressible hydraulic fluid is held under pressure by
an external source like a spring, a raised weight, or compressed gas. An accumulator enables a hydraulic system to cope
with extremes of pressure using a less powerful pump. This enables the hydraulic system to respond more quickly to a
temporary demand, and to smooth out pulsations.
Even though all 3 alternative methods can help to arrive at the part failure rate, selecting an appropriate method of
Reliability Prediction is the key. Figure 1 explains the logic behind finalizing a prediction technique.
As seen in Figure 1, a good starting point would be the life-limited items. Aircraft life-limited parts are those ppaarrttss tthhaatt aarree
identified by the aircraft manufacturer or production certificate holder as being limited to a total life counted in hours,
cycles, landings, or by calendar. Typical life-limited parts are seals, bearings and springs.
Figure1. Determination of the prediction technique
In case prediction models are not available in NSWC then either the PoF or SSI approach can be selected by following the
logic explained in above diagram.
The prediction method chosen for each of the accumulator components is shown in Table 3 -“Summary of analysis”.
Methods of failure analysis
a. Physics of Failure (PoF) is a science-based mathematical approach for reliability predictions that uses modeling and
simulation to design-in reliability. This approach models the root causes of failure such as fatigue, fracture, wear, and
corrosion. Fatigue and fracture are the two root-causes considered in this case study. Various models were applied for
these two causes and the failure rates were predicted.
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5. Mechanical Reliability Prediction: A Different Approach | 5
The accumulator Barrel will be subjected to 1,951,000 pressure cycles at different pressure levels shown in Table 1. It is also
subjected to a static pressure of 3500 psi. As per the logic explained in an earlier section “Approach to select an appropriate
method:”, the SSI method would be used for static failure rate estimation caused by 5000psi pressure and fatigue
calculations would be used for failures caused by 1,951,000 pressure cycles. A combination of SSI and PoF approach should
be used for ‘Barrel’ failure predictions.
LUBRICATION PASSAGE
Failure rate calculation using the PoF theory
5,000 to 3,950 to 5,000
5,000 to 3,700 to 5,000
5,000 to 3,600 to 5,000
5,000 to 1,900 to 5,000
5,000 to 3,450 to 5,000
5,000 to 2,000 to 5,000
220000 ttoo 55,,000000 ttoo 220000
Step 1: List all types of stress on the Barrel (Cylinder):
Types of stresses: Hoop stress, longitudinal stress and stress at the weakest location.
In Figure 2, and
This Barrel is a thin walled cylinder. (Criteria for thin wall cylinder:
Cycles per Aircraft
life (ni)
160,000
800,000
500,000
15,000
24,000
350,000
11,,995511,,000000
Step 2: Convert all pressure cycles into stress values:
Convert all minimum and maximum pressure levels into both ‘longitudinal’ and ‘hoop stress values’. The ‘stress at the
weakest location’ test would be calculated by Finite Element Analysis.
Hope Stress,
Longitudinal Stress,
Whereas,
)
AIRPORT
PISTON
HYDRAULIC FLUID PORT
END CAP
END CAP
PACKING &
BACKUP RING
BARREL ASSEMBLY
Pressure Cycle
(psig)
Total Cycles 1,951,000
Table 1: Pressure cycles at different Pressure Levels
Figure 2. Barrel showing all the stresses
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6. Mechanical Reliability Prediction: A Different Approach | 6
Step 3: Convert the spectrum of stress into an equivalent stress:
Equivalent stress equation for Barrel material 13‐8Mo CRES, as taken from MMPDS database is Seq = Smax(1-R)0.11
Where, Seq = Equivalent Stress,
Smax = Maximum Stress (Stress induced by maximum pressure in a pressure cycle)
R = Stress Ratio =
Minimum Stress (Stress Induced by minimum pressure in a pressure cycle)
Maximum Stress
Repeat the above step for all three stresses (hoop, longitudinal and stress at the wweeaakkeesstt llooccaattiioonn))..
Step 4: Calculate number of cycles before failure:
The empirical relationship for S-N curve as given in MMPRD for 13‐8Mo CRES.
Log Nf = 18.12 - 6.54 lod (Seq)
Where Nf = Number cycles to failure at an Equivalent stress of Seq
Step 5: Use Minor’s rule to calculate cumulative damage caused by each set of pressure cycles
Cumulative damage caused by each Pressure cycles
Number of cycles over the design life, ni Life to failure corresponding
Table 2: Cumulative Damage Calculation
to stress, Nf
Damage due to each set of
pressure cycle
Cumulative Damage
ni
Nf
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7. Mechanical Reliability Prediction: A Different Approach | 7
a. In Table 2 Cumulative damage of 8.25E-02 % damage is caused by 1,951,000 cycles
b. 1,951,000 cycles would take 102,000 hours to complete
c. This means 8.25E-02 % damage is caused in 102,000 hours
d. Time for first failure (MTBF) = Time for 100% damage = 102000 / 8.25E-02 = 1.2E6 hours
e. Failure rate = 8.09E - 09 failure per flight hour
The above values 8.09E-09 are the failure rate due to longitudinal stress . But in Hoop stress , the equivalent stress is
less than the Endurance Limit of the 13‐8Mo CRES (AMS 5629). This means that failure rates should be almost zero
under such stress levels. Then the failure rate caused by stress at the weakest location is calculated as,
= 9.27E-03 and as zero. The weakest locations and levels of stress at those
locations are calculated from Finite Element Analysis.
b. SSI theory: Fracture and deformation analysis was performed using Stress/Strength Interference theory. Stress/Strength
Interference analysis is a practical engineering tool used for designing and quantitatively predicting the reliability of
mechanical components subjected to mechanical loading. This method treats both stress and strength as random variables
subject to natural scatter. If failure is defined by Stress > Strength, then the failure probability would be equivalent to the
interference of stress and strength distribution.
Failure rate calculation using SSI Theory
In case of ‘Barrel’, the SSI theory was used for calculating failure rate resulting from a static pressure of 5000psi. In this
method, the corresponding Hoop stress, Longitudinal stress, Stress at the weakest location on the air and fluid side of the
‘Barrel’ are calculated at a pressure level of 5000 psi. The interference when stress exceeds strength is calculated using
a. Using the standard Normal distribution table, the Interference probability was calculated for each stress based
on ‘Z’ value
b. Reliability = 1- Interference Probability
c. Failure rate was calculated using the relationship: , where R = Reliability, = Failure rate and t = flight
operating hours
d. Failure rate was calculated as, 1.46E-05 failures per flight hour
Total Failure rate for Barrel: The ‘Barrel’ failure rate would be the addition of failure rates calculated from both PoF and
SSI methods.
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8. Mechanical Reliability Prediction: A Different Approach | 8
c. NSWC methods are based upon identified failure modes and their causes. The equations were derived for each failure
mode from design and published experimental data. An example model for dynamic seals is given below
Sample Prediction using NSWC for a Dynamic Seal
Failure rate model for a dynamic seal as given in the NSWC hand book:
Where, = Generic failure rate of the PTFE seal in failures/million hours
= Base failure rate of PTFE seal, 22.8 failures/million hours
After identifying and quantifying all design and environmental parameters, the applicable Pi factors (multiplication) factors
are finally calculated. A DFMEA would help to identify relevant Pi factors and remove irrelevant factors. Each
multiplication factor value is calculated using the empirical relationship given in the NSWC handbook.
An example: The Pi factor for allowable leakage CQ .
Allowable Leakage Multiplying Factor (CQ): Determination of allowable leakage multiplication
factor can be done be using below equations.
In our case the allowable leakage is 0.025 cu.in / min. So = 2.225
Similarly all the factors are calculated and multiplied with base failure rate of 22.8 to arrive at the failure rate of 0.6986
failures per million flight hours.
PI Factors Description Calculated Value
Effect of fluid pressure
Effect of allowable leakage
Effect of seal size
Effect of contact stress and seal hardness
Effect of seat smoothness
Effect of fluid viscosity
EEffffeecctt ooff tteemmppeerraattuurree
Effect of contaminants
Effect of pressure velocity co-efficient
CP
CQ
CDL
CH
CF
CV
CT
CN
CPV
0.250
2.225
2.927
0.553
1.000
0.089
00..335544
1.081
1.000
Failure rate of Dynamic Seal
= 22.8 * 0.25 * 2.225 * 0.553 * 1.00 * 0.089 * 0.354 * 1.081 * 1.00
= 0.6986 failures per million flight hours
Findings
As explained above, the failure rate for each of the applicable items in the Hydraulic Accumulator were calculated and then
summarized in table 3. It can be seen that the NPRD failure rate for the ‘Barrel’ is very low and thus the design seems to be
good. But the PoF approach, which considers all applicable design and environmental parameters and applies them on
proven mathematical models, reveals the possibility of high failure rate in the ‘Barrel’ assembly. This is applicable for Piston
seals as well as NPRD in the same way.
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9. Mechanical Reliability Prediction: A Different Approach | 9
This would help the designer to improve upon his design during the early design phase rather than making design changes
after noticing frequent field failures.
S. Remarks
No
Failure
Rate
(Failure rate x
Qty)
PoF Results
15.388
0.1588
0.0256
0.176
0.015
0.6986
00..00000066
15.388
0.1588
0.0256
0.704
0.03
0.6986
00..00000066
Total failure rate per 10 6 Hours 17.0056 0.6031
50,000 hours
58,804
V
MTBF Requirement in Hours
Calculated MTBF in Hours
Table 3: Summary of Analysis
Description Qty
Method of
Reliability
Prediction
NPRD
Results
Barrel SSI, Miner’s
rule (PoF)
NSWC
SSI
NSWC
NSWC
1
1
1
4
2
1
1
1
2
3
4
5
6
7
0.008
0.2
0.032
0.2564
0.064
0.0107
00..003322
Possibility of High
failure rate is revealed
by PoF method.
Not a high difference
infailure rate
Exact equivalent part
for Helical Insert is not
found in NPRD
PoF method reveals the
possibility of high failure
rate
NPRD value is very
generic not application
specific
Piston
End cap
Helical
Insert
Mounting
Strap
Seal, Piston
Packing
Backup ring
1,658,009 NPRD method is too
optimistic
Industry Best Practices
Even though these alternate methods provide more accurate and reliable failure rate predictions, the best practices should
focus on field data analysis and test data analysis.
Field data analysis: A field item similar to the new item under design is considered for predicting failure rate. The
drawback in this method is that the field failure data is often not available. Even when available, the data is not grouped and
time to failure for individual items is not available.
TTeesstt ddaattaa aannaallyyssiiss:: Testing the actual component would yield prediction with the highest accuracy as compared to all other
methods, as actual loading conditions are simulated during testing. However, most of the predictions are performed during
the early design stage. Hence, this method may not be practical as it needs a physical prototype for testing. Moreover,
testing a completely new design needs a dedicated testing program which may turn out to be an expensive proposition.
Due to the limitations mentioned above, designs cannot completely rely on field data and test data analysis results, thus we
prefer to go with alternative methods of predictions.
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10. Mechanical Reliability Prediction: A Different Approach | 10
Common Issues with alternative methods
To get more accurate failure rates, the reliability engineers need to spent more time and effort. They need significant
volumes of design inputs, analysis results, material properties, usage environment data, and valid assumptions.
Some of the common concerns are
Need for detailed design information (like operating pressure, temperature range, types of loads, material used
etc.). Though this is difficult to obtain in the early design stage, it is still not entirely impossible.
Need to make many design assumptions which should be valid enough (e.g. operating temperature range, level of
vibration etc.)
Structural analysis results (FEA results) are necessary to make reliability predictions for structural items (e.g.
Accumulator Barrel, Piston and End Cap)
Accuracy of prediction is not as good as field/ test data analysis but still better than NPRD predictions
No methods available to validate the results of predictions, unless the design is tested or exposed ttoo fifieelldd.. TThhiiss
limitation is also applicable for NPRD methods.
Involves complicated calculations, which take time and effort on the part of the reliability engineer. (The reliability
team has already developed standard input templates for PoF/ SSI methods and Excel Macros for performing
NSWC calculations for standard items like seals, springs and bearings)
Conclusion
The current industry practice of using the NPRD database for making reliability predictions is quick, easy and inexpensive.
However, it ignores the fact that a new design would be used in a different environment which is not the same in which the
NPRD data has been collected. Moreover, the design and material properties of new items under design may not be similar
to the one considered in the NPRD database. Also, at times, the exact matching part cannot be found in NPRD.
AAss lleeaaddiinngg aaiirrccrraafftt mmaannuuffaaccttuurreerrss iinnccrreeaassiinnggllyy aapppprreecciiaattee tthhee aaccccuurraaccyy ooff NNPPRRDD,, tthheeyy aarree ddrriivviinngg tthheeiirr ssuupppplliieerrss ttoo uussee mmoorree
accurate and reliable methods for reliability predictions. It has now become a necessity for reliability engineers to explore
new methods for prediction and then bring them into practice on a large scale.
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11. Mechanical Reliability Prediction: A Different Approach | 11
Highly recommended methods like field / test data analysis are either highly difficult to perform or not practical to perform
during the design phase. Additionally, these methods have proven to be expensive. If we consider any new methods, they
should reflect the actual usage environment unlike NPRD. Also, unlike field / test data analysis, those mmeetthhooddss sshhoouulldd bbee
possible to use in actual practice and should not be expensive. Considering all these requirements, we can strongly
conclude that the methods explained in this paper - namely NSWC, the PoF approach, and SSI theory - would be highly
suitable to meet the new demands in the aerospace industry for making accurate and cost effective reliability
predictions.
Reference
A. NSWC-11 Handbook of Reliability Prediction Procedures for Mechanical Equipment
B. RADC-TR-66-710 Reliability Prediction Mechanical Stress/Strength Interference Models
C. MMPDS Metallic Materials Properties Development and Standardization
D. NPRD 95 Non-electrical Parts database
E. FMD 97 Failure Mode / Mechanism Distribution 1997
F. “Uncertainties in Material Strength Geometric and Load Variables” by Paul E.Hess, Daniel Bruchman, Ibrahim A. Assakkaf, Bilal M. Ayub.
Author Info
Murali Krishnamoorthy
HCL Engineering and RD Services
Abhay Waghmare
HCL Engineering and RD Services
Designed By: Mayuri Infomedia
This whitepaper is published by HCL Engineering and RD Services.
The views and opinions in this article are for informational purposes only and should not be considered as a substitute for professional business advice. The use herein of any
trademarks is not an assertion of ownership of such trademarks by HCL nor intended to imply any association between HCL and lawful owners of such trademarks.
For more information about HCL Engineering and RD Services,
Please visit http://www.hcltech.com/engineering-rd-services
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