SMU
SYS 7340
NTU
SY-521-N
Logistics Systems Engineering
Maintainability/Serviceability/Human Factors
Dr. Jerrell T. Stracener,
SAE Fellow
1
Maintainability
• Maintainability is
- an engineering and management function
spanning the product or service life cycle
- a characteristic of equipment design and
installation which is expressed in terms of ease and
economy of maintenance, availability of the
equipment, safety and accuracy in the performance
of maintenance actions.
2
Maintainability
• Objective of maintainability
- to design and develop systems and
equipment which can be maintained in the least
time, at the least cost, and with a minimum
expenditure of support resources, without
adversely affecting the item performance or safety
characteristics
3
Product/Service Support Resources
• logistics personnel utilization
• spare parts
• tools and test equipment
• support services
• support facilities
4
What is Maintainability?
Converters for driving factory belts
1. Motor Burn-out
2. Wire replacements
3. Torque Adjustments
4. Lubrication
– What are its associated cost?
Down time: Staffing
Production: Product to market
Human factors: Stress, Leaning Curve
Reliability: Service performance and
guarantees
5
What is Maintainability?
• Maintainability greatly influences reliability and
availability of a system or subsystem.
• Maintainability must be addressed early in the
design stage to prevent or reduce failure or
down times of the system.
6
Why is Maintainability Required?1
• Infinite Reliability is not achievable
• When a system is discarded, it must be
discarded or it must be repaired
• Cost usually dictates that a faulty system must
be repaired
• In addition to repair, most systems must be
serviced (Consumables replaced - fuel, oil,
coolant, etc.)
• Incipient failures must be detected
7
Why is Maintainability Required?1
• To verify that equipment has not deteriorated,
its overall capability to perform must be
reviewed
• Maintenance is the repair, servicing, and
inspection of equipment
8
Maintenance Concept
• Maintenance defines all those activities
performed on an item to retain it in or to
restore it to s specified state.4
• Can be divided into two categories:
1. Preventive Maintenance
Prescribe procedures to reduce the
probability of failure or degradation
2. Corrective Maintenance
Initiated after fault recognition
Regain state of system for
performing required function
9
Maintenance Concept
10
Maintenance Concept
Failure Occurs
Detection
Corrective Maintenance Cycle6
Failure Confirmed
Preparation for
Maintenance
Active Maintenance Commences
Location and
Isolation
Faulty Item Identified
Disassembly
(Access)
Disassembly Complete
or
Removal of
Fault Item
Repair of
Equipment
Installation of
Spare/Repair Part
Re-assembly
Alignment
and Adjustment
Re-assembly Complete
Condition
Verification
Repair Completed
11
Maintenance is Conducted:7
• On equipment repair
– Remove and replace faulty item
– Adjust of align an item that has drifted out of
specification
• Off equipment repair
– In a local shop
– In and industrial facility
12
Achieving Maintainability
• Achieving maintainability is done through
planning and realizing maintenance concepts:
– Fault Detection and isolation
– Partitioning equipment or systems into LRUs
– User documentation
– Training
– Logistical Support
13
Achieving Maintainability
• Fault Detection and isolation
– Goal is to localize faults down to LRU’s (last
repairable unit / line replacement unit) by
performing the following:
BIT (Built-in test):
1. Degree of fault
2. Degree of isolation
3. Correctness of the fault isolation
4. Test duration
14
Achieving Maintainability
BITE (Built-in test equipment):
1. Simplicity
2. Standardization
3. Reliability
4. Maintenance
• Equipment and System Partitioning
– Partition complex equipment and systems
into LRUs: PCB
– Accessibility: Ease of LRU
– Adjustment: Digital reduces need
– Exchange: Careful of obsolescence
15
Achieving Maintainability
• User Documentation
– General Description
– Operating Manual
– Preventive Maintenance
– Corrective Maintenance
– Illustrated Spare Parts Catalog
– Logistical Support
• Training of Operating & Maintenance Personnel
– Well trained and motivated
– Human Errors
16
Achieving Maintainability
• User Logistical Support
– Four Levels
1. Operating personnel
2. First line maintenance personnel
3. Maintenance personnel
4. Specialist from arsenal or industry
17
Achieving Maintainability
• Specify
– Specifications, Contracts, Warranties
– Program Plan
• Design
– Equipment Arrangement
– Equipment Location
– Servicing Locations
– Weapon Location
– Turnaround Arena
– Accessibility
– Fault and Servicing Cues
18
Achieving Maintainability
• Plan
– Predesign Homework
– By Analysis
– Mock Ups
• Demonstrate Supportability
– Verify Operation Environment
19
Achieving Maintainability
20
Bottoms Up Models
• Provide output to monitor design progress vs.
requirements
• Provide input data for life cycle cost
• Provide trade-off capability
– Design features vs. maintainability
requirements
– Performance vs. maintainability requirements
• Provide Justification for maintenance
improvements perceived as the design
progresses
21
Bottoms Up Models
• Provide the basis for maintainability
guarantees/demonstration
• Provide inputs to warranty requirements
• Provide maintenance data for the logistic
support analysis record
• Support post delivery design changes
• Inputs
– Task Time (MH)
– Task Frequency (MTBM)
Number of Personnel-Elapsed Time (hours)
For each repairable item
22
Bottoms Up Models
• Input Data Sources
– Task Frequency
Reliability predictions de-rated to account
for non-relevant failures
Because many failures are repaired on
equipment, the off equipment task
frequency will be less than the task
frequency for on equipment
23
Bottoms Up Models
• Input Data Sources (Continued)
– Task Time
Touch time vs. total time
 That time expended by the technician to
effect the repair
 Touch time is design controllable
Total Time
 Includes the time that the technician
expends in “Overhead” functions such as
part procurement and paper work
 Are developed from industrial engineering
data and analyst’s estimates
24
Task Analysis Model
• Task analysis modeling estimates repair time
– MIL-HDK-472 method V
– Spreadsheet template
Allow parallel and multi-person tasks
estimation
Calculates elapsed time and staff hours
Reports each task element and total repair
time
Sums staff hours by repairmen type
Estimates impact of hard to reach/see
tasks
25
Why Do Maintainability Modeling?
• To identify the important issues
• To quantify and prioritize these issues
• To build better design and support systems
26
Design Guidelines for Maintainability9
• General Guidelines
– Plan and Implement a concept for automatic
fault detection down to the last LRU
– Partition the equipment
– Aim for standardization of parts, tools, and
testing equipment
– Conceive operation and maintenance
procedures to be as simple as possible
– Consider environmental conditions
27
Design Guidelines for Maintainability9
• Testability
– Degrees of failure detection and isolation
– The correctness of test results
– Test duration
• Accessibility and Exchangeability
– Provide self-latching access flaps
– Plan for accessibility
– Use preferably indirect plug connectors
– Provide for speedy replaceability
– Prevent faulty installation or connection
28
Design Guidelines for Maintainability9
• Operation and Adjustment
– Use high standardization in selecting
operational tools
– Consider human aspects
– Order all steps of a procedure in a logical
sequence
– Describe system status
– Avoid any form of hardware adjustments
29
Elements & Terminology of Maintainability
• MTTR: Mean Time to Repair
• T0.5: Median Time to Repair
• TMAX: Maximum Time to Repair)
usually the 95th percentile
• MTTPM: Mean Time to Preventive Maintenance
• MTBPM: Mean Time Between Preventive
Maintenance
• MDT: Mean Down Time
• MTBM: Mean Time Between Maintenance
30
Maintainability Prediction
• System Mean Time to Repair, MTTRS
System without redundancy
E1
E2
En
n
n
MTTR i
λ i MTTR i


i 1 MTBFi
MTTRs  n
 i 1 n
1
λi


i 1 MTBFi
i 1
31
Maintainability Prediction
• Example 1: Compute the mean time to repair
at the system level for the following system.
MTTF = 500 h
MTTR =
2h
MTTF = 400 h
MTTR = 2.5 h
MTTF = 250 h
MTTR =
1h
MTTF = 100 h
MTTR = 0.5 h
• Solution:
2h
2.5h
1h
0.5h
0.01925
MTTRs  500h  400h  250h  100h 
 1.04h
1
1
1
1
1
0.0185h
500h 400h 250h 100h
32
Maintainability Prediction
• Example 2: How does the MTTRs of the system
in the previous example change if an active
redundancy is introduced to the element with
MTTF = 100 h
MTTF = 100h?
MTTR =
MTTF = 500 h
MTTR =
2h
• Solution:
MTTF = 400 h
MTTR = 2.5 h
MTTF = 250 h
MTTR =
1h
0.5 h
MTTF = 100 h
MTTR = 0.5 h
2h
2.5h
1h
0.5h 0.5h
0.02425
MTTRs  500h  400h  250h  100h  100h 
 0.85h
1
1
1
1
1
1
0.0285h
500h 400h 250h 100h 100h
33
MTTF and MTBF
Mean Time to Failure (or Between Failures) MTTF
(or MTBF) is the expected Time to Failure (or
Between Failures)


0
0
MTBF   tf (t )dt   R(t )dt

Remarks:
MTBF provides a reliability figure of merit for expected failure
free operation MTBF provides the basis for estimating the
number of failures in a given period of time Even though an
item may be discarded after failure and its mean life
characterized by MTTF, it may be meaningful to characterize
the system reliability in terms of MTBF if the system is
restored after item failure.
34
SMU
SYS 7340
NTU
SY-521-N
Logistics Systems Engineering
Modeling & Analysis of Time to Repair
Dr. Jerrell T. Stracener,
SAE Fellow
35
Definition
• Maintainability is an inherent design
characteristic of a system or product and it
pertains to the ease, accuracy, safety, and
economy in the performance of maintenance
actions.2
• Maintainability can be created into a four-part
definition:3
1. Maintainability is the probability that a failed
system
2. will be restored to specified performance
3. within a stated period of time
4. when maintained under specified conditions.
36
Definition
• Maintainability is a characteristic of an item,
expressed by the probability that preventive
maintenance (serviceability) or repair
(repairability) of the item will be performed
within a stated time interval by given
procedures and resources (number and skill
level of the personnel, spare parts, test
facilities, etc.).4
• Maintainability is the ability of an item to be
retained in, or restored to, a specified condition
when maintenance is performed by people
having specified skill levels, using prescribed
procedures and resources.5
37
Maintenance and Design8
• The system’s design determines its
requirements for maintenance
– Reliability (How often maintenance)
– Configuration (How much time for access)
– Built in Test (Fault Isolation Time)
– Subassembly life span (Inspection/forced
replacement)
– Adjustment/alignment requirements
(Inspection)
– Capacity/fill rate (Servicing)
– Corrosion susceptibility (Inspection/repair)
38
Normal Distribution:
A random variable X is said to have a normal (or
Gaussian) distribution with parameters  and ,
where -  <  <  and  > 0, with probability
density function
1
f (x) 
e
 2
where

 = 3.14159…
1
2
2

x



2
-<x<
and
e = 2.7183...
f(x)
x
39
Normal Distribution:
• Mean or expected value of X
Mean = E(X) = 
• Median value of X
X0.5 = 
• Standard deviation
Var(X )  
40
Normal Distribution:
Standard Normal Distribution
If X ~ N(, ) and if
Z
X 

, then Z ~ N(0, 1).
A normal distribution with  = 0 and  = 1, is called
the standard normal distribution.
41
Normal Distribution:
f(z)
f(x)
x

Z
z
x
0

42
Normal Distribution:
Standard Normal Distribution Table of Probabilities
http://www.smu.edu/~christ/stracener/cse7370/normaltable.html
Enter table with
Z
f(z)
x

and find the
value of 

0
z
z
43
Normal Distribution - example
The following example illustrates every possible
case of application of the normal distribution.
Let X ~ N(100, 10)
Find:
a. P(X < 105.3)
b. P(X  91.7)
c. P(87.1 < X  115.7)
d. the value of x for which P(X  x) = 0.05
44
Normal Distribution - example solution
a. P(X < 105.3)
=
 x   105.3  100 
P


10
 

= P(Z < 0.53) = 0.7019
f(x)
f(z)
x
100 105.3
z
0 0.53
45
Normal Distribution - example solution
b. P(X  91.7)
=
 x   91.7  100 
P


10
 

= P(Z > - 0.83)
= 1 - P(Z  -0.83) = 1 - 0.2033
= 0.7967
f(x)
f(z)
x
91.7 100
z
-0.83 0
46
Normal Distribution - example solution
c. P(87.1 < X  115.7) =
 87.1  100 x  

P

 115.7 
10



f(x)
= P(-1.29 < Z < 1.57)
= F(1.57) - F(-1.29)
= 0.9418 - 0.0985 = 0.8433
x
87.1 100 115.7
47
Normal Distribution - example solution
d.
P(X  x) = 0.05
P(Z  z) = 0.05
P(X  x) =
implies that z = 1.64
x  100 
 x   x  100 

P

  P Z 

10 
10 
 

therefore
x  100
 1.64
10
f(x)
x - 100 = 16.4
x = 116.4
x
100 116.4
48
Normal Distribution - Example:
The time it takes a field engineer to restore a
function in a logistics system can be modeled with
a normal distribution having mean value 1.25 hours
and standard deviation 0.46 hours. What is the
probability that the time is between 1.00 and 1.75
hours? If we view 2 hours as a critically time,
what is the probability that actual time to restore
the function will exceed this value?
49
Normal Distribution - Example Solution:
P1.00  X  1.75
1.75  1.25 
 1.00  1.25
 P
X

0.46 
 0.46
 P 0.54  X  1.09
 1.09  0.54
 0.8621  0.2946  0.5675
50
Normal Distribution - Example Solution:
2  1.25 

P  X  2   P Z 

0.46 

 PZ  1.63  1  1.63
 0.0516
51
The Lognormal Model:
Definition - A random variable X is said to have the
Lognormal Distribution with parameters  and ,
where  > 0 and  > 0, if the probability density
function of X is:
f (x) 
1
x 2
0

e
1
2
2

ln
x



2
,
for x > 0
,
for x  0
52
Properties of the Lognormal Distribution
Probability Distribution Function
 ln x   
F( x )  

  
where (z) is the cumulative probability distribution
function of N(0,1)
Rule:
If T ~ LN(,), then Y = lnT ~ N(,)
53
Properties of the Lognormal Model:
• Mean or Expected Value
E ( X)  e
1 2
 
2
• Median
x0.5  e

• Variance
Var (X)  e
2   2
e
2

1
54
Lognormal Model example
The elapsed time (hours) to repair an item is a
random variable. Based on analysis of data, elapsed
time to repair can be modeled by a lognormal
distribution with parameters  = 0.25 and  = 0.50.
a. What is the probability that an elapsed time to
repair will exceed 0.50 hours?
b. What is the probability that an elapsed time to
repair will be less than 1.2 hours?
c. What is the median elapsed time to repair?
d. What is the probability that an elapsed time to
repair will exceed the mean elapsed time to repair?
e. Sketch the cumulative probability distribution
function.
55
Lognormal Model example - solution
a. What is the probability that an elapsed time to
repair will exceed 0.50 hours?
X ~ LN(, ) where  = 0.25 and  = 0.50
note that:
Y = lnX ~ N(, )
P(X > 0.50) = P(lnX > -0.693)
 lnX  μ  0.693  0.25 
 P


0.50
 σ

 PZ  1.89
 0.9716
56
Lognormal Model example
b. What is the probability that an elapsed time to
repair will be less than 1.2 hours?
P(X < 1.20) = P(lnX < ln1.20)
 lnX  μ 0.182  0.25 
 P


0.50
 σ

 PZ  0.136
 0.4404
57
Lognormal Model example
c. What is the median elapsed time to repair?
P(X < x0.5) = 0.5
ln x0.5   

 P Z 




 PZ  0
therefore
 0.5
ln x0.5  
0

ln x0.5    0.25

x0.5  e  e
0.25
 1.284
58
Lognormal Model example
d. What is the probability that an elapsed time to
repair will exceed the mean elapsed time to repair?
MTTR  e
e
σ2
μ
2

0.502
0.25
2
 e 0.375
 1.455
59
Lognormal Model example
P(X > MTTR) = P(X > 1.455)
= P(lnX > 0.375)
 lnX  μ 0.375  0.25 
 P


0.50
 σ

 PZ  0.25
 0.4013
60
Lognormal Model example
e. Sketch the cumulative probability distribution
function.
Cumulative Probability Distribution Function
1
P(t<x)
0.8
0.6
0.4
0.2
0
0
1
2
tmax
3
4
5
6
time to repair
61
References
1
2
3
4
5
6
7
8
Clint Van Pelt, “Maintainability and Modeling Analysis”, March 31, 1992
Benjamin S. Blanchard and Wolter J. Fabrychy, “Systems Engineering
and Analysis,” Second Edition (Englewood Cliffs, New Jersey: PrenticeHall, Inc., 1990), pp. 389-390.
Daniel L. Babcock, “Managing Engineering and Technology,” Second
Edition (New Jersey: Prentice-Hall, Inc., 1996), p. 209.
Prof. Dr. Alessandro Birolini, “Reliability Engineering: Theory and
Practice,” Third Edition (Germany: Springer-Verlag Berlin Heidelberg,
1999), p.115.
USAF R&M 2000
Benjamin S. Blanchard and Wolter J. Fabrychy, “Systems Engineering
and Analysis,” Second Edition (Englewood Cliffs, New Jersey: PrenticeHall, Inc., 1990), p. 394.
Clint Van Pelt, “Maintainability and Modeling Analysis”, March 31, 1992
Ibid
62
References
9
Prof. Dr. Alessandro Birolini, “Reliability Engineering: Theory and
Practice,” Third Edition (Germany: Springer-Verlag Berlin Heidelberg,
1999), pp. 145-148.
63