This document presents methodology to be used to predict mechanical component reliability using the Stress/Strength Interference Method. This method assumes that the material properties are time independent because of their slow change, and the components are not subjected to wear related failure modes

1. Hilaire Ananda Perera
Long Term Quality Assurance
https://www.linkedin.com/in/hilaireperera 1
Reliability Prediction Procedure
for
Mechanical Components
1.0 Reliability Prediction
This document presents methodology to be used to predict mechanical component reliability
of the JSF PTMS Controller using the Stress/Strength Interference Method. This method
assumes that the material properties are time independent because of their slow change, and
the components are not subjected to wear related failure modes. The following tasks are to be
performed in sequence to obtain the reliability of the mechanical component. The task
responsibility is shown as Reliability  R; Mechanical Design  MD
1.1 Define The Design (Reliability) Requirement In Relation To The Mission
Profile:   R
Design Requirement: To obtain the probability of failure free operation of the PTMS
Controller mechanical components (All none-wear related components) in Storage, and Free
Flight environments.
1.2 Determine the Design Variables and Parameters Involved:   MD
Derive all applicable stress and strength design equations
Determine all design variables and parameters. These should be:
(a) mission significant
(b) unique, not duplicated
(c) measurable before, during and after test (Note: Not an essential criterion)
1.3 Conduct a Failure Modes, Effects and Criticality Analysis:   MD & R
Identify all significant failure modes of each component and their effects on the PTMS
Controller success.
1.4 Determine the Dependence or Independence of the Component’s Failure
Modes:   MD & R
Assume all failure modes to be independent of each other. The stresses and strengths for the
failure modes should be calculated without taking into account the effects of all other failure
on it.

2. Hilaire Ananda Perera
Long Term Quality Assurance
https://www.linkedin.com/in/hilaireperera 2
1.5 Determine the Failure Governing Criterion Involved in each Failure Mode:
  MD
Obtain the correct failure governing stress. The more commonly used failure governing stress
criteria are the following:
(a) maximum principal normal or direct stress
(b) maximum principal shear stress
(c) maximum distortion energy
(d) maximum strain energy
(e) maximum strain
(f) maximum deflection
(g) combination of the mean and alternating stresses into the maximum shear or distortion
energy criterion, in the case of fatigue
(h) maximum total strain range in the case of fatigue
(i) maximum allowable corrosion
(j) maximum allowable vibration amplitude
(k) maximum allowable creep
(l) other criteria, depending on the nature of the significant failure modes
1.6 Formulate the Failure Governing Stress Function:   MD
Obtain the failure governing stress function of each failure mode using the functional
relationships between the loads, dimensions, temperature, physical properties, application and
operation environment factors and other design factors
1.7 Determine the Distribution of each Design Stress Variable and Factor for
each Failure Mode:   R & MD
Assume Normal Distribution if the Coefficient of Variation (the ratio of Standard Deviation
to the Mean of a sample) of a variable or factor is equal to or less than 0.1
1.8 Determine the Failure Governing Stress Distribution for each Failure
Mode:   R
Assume Normal stress Distribution if Normal Distributions are used in paragraph 1.7
1.9 Formulate the Failure Governing Strength Function:   MD & R
The failure governing strength should be the stress-at-failure for the specific failure mode
involved. It should be that strength which if exceeded, may result in a failure in that specific
failure mode. The probability that the failure mode will take place is the unreliability of that
failure mode. It is the correct strength distribution when properly coupled with the failure-
governing stress distribution that will give the component reliability for that failure mode

3. Hilaire Ananda Perera
Long Term Quality Assurance
https://www.linkedin.com/in/hilaireperera 3
1.10 Determine the Distribution of each Design Strength Variable and Factor
for each Failure Mode:   R & MD
Assume Normal Distribution if the Coefficient of Variation of a variable or factor is equal to
or less than 0.1
1.11 Determine the Failure Governing Strength Distribution for each Failure
Mode:   R
Synthesize the Failure Mode Strength Distribution from the distributions of the respective
variables and factors. A Normal Strength Distribution is expected if all the variable and factor
distributions are Normal.
1.12 Determine the Component’s Reliability for each Failure Mode:   R
Calculate reliability of the failure mode using the associated Stress/Strength Distributions
(Example is in Page 4)
Safety Margin (SM) =
 
   
 
 
S s
S s


2 2
If the Standard Deviation of Stress is not available, assume the Stress on the component to have a Coefficient of
Variation (CV = / ) of 10% to calculate s
Reliability (R) = 1 -
1
2
2
2

e dt
tSM 

1.13 Determine the Component’s Reliability for All Failure Modes:  R & MD
Repeat the preceding steps (1.1 to 1.12) for all significant and critical failure modes of each
component
1.14 Determine the Overall Component Reliability Considering All Failure
Modes:   R
Assume each and every failure mode to be initiated and propagated independently. When at
least one of these failure modes occur, the component is said to have failed.
The component reliability RC is given by: RC = Ri
i
n


1
Where R1 ........ Rn are the calculated reliabilities of all mission significant failure modes
s = Mean Stress of the failure governing Stress function
s = Standard Deviation of the Stress
S = Mean Strength of material
S = Standard Deviation of the material Strength

4. Hilaire Ananda Perera
Long Term Quality Assurance
https://www.linkedin.com/in/hilaireperera 4
EXAMPLE
In the Space Station Liquid Carry Over Sensor , the Sensor Ring substrate will be subjected to reversing mechanical
loads, and will exhibit a failure mode of fracture. The reliability was designed in by selecting the probability number
representing the Safety Margin (SM)
The failure governing stress criteria for operation is the Von Mises stress for the fail safe criteria for the limit load
specification. The fail safe criteria considers the condition where 1 bolt has failed on the electronic side of the sensor. The
limit load criteria is 92g quasi static acceleration.
MACOR Flexural Strength = 15000 psi
Maximum Von Mises Stress = 3533 psi
It is assumed that : (1) Standard Deviation of material Strength is 10% of Mean Strength, (2) Standard Deviation of
failure governing Stress is 20% of Mean Stress
Predicted Safety Margin (SM) = 6.92
The Reliability shall be better than 0.999999 (SM=5) for a 90 Day operational use
Safety Margin SM
 S  s
 S
2
 s
2
 s = Mean Stress  s = Standard Deviation of Stress
 S = Mean Strength  S = Standard Deviation of Strength
______________________________________________________________________________
TOL 0.00001 i ..1 10 SM i
.0.5 i
B1 0.31938153 B2 0.356563782 B3 1.781477937
B4 1.821255978 B5 1.330274429
A i
1
1 .0.2316419 SM i
C i
.B1 A i
.B2 A i
2 .B3 A i
3 .B4 A i
4 .B5 A i
5
Reliability R i
1 ..( ).2 
0.5
e
SM
i
2
2
C i
Reference: Approximation for Normal Probability Function
Handbook of Mathematical Functions - Abramowitz/Stegun, Ref 26.2.17
_____________________________________________________________________________
SM i
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
R i
0.69146247
0.84134474
0.93319277
0.97724994
0.99379032
0.99865003
0.99976733
0.99996831
0.9999966
0.99999971
R i
.7.5 10
8
0.69146239
0.84134467
0.9331927
0.97724986
0.99379025
0.99864996
0.99976725
0.99996824
0.99999652
0.99999964
REL - High
Boundary
REL - Low
Boundary