How to measure reliability

Ammar Alkhaldi
Real Reliability
15 March 2016
PART 1: why you shall not use MTBF!!!
How to Measure Reliability

Measurement can help us to answer the followings
question:
Are we doing good or bad ?
Is our performance increasing or decreasing ?
Which unit is performing better ? (Benchmarking)
What/How to improve ?
“You can’t improve what you can’t measure”
Why are we measuring things ?

1. MTBF is a misleading indicator.
 Example: 1000 Units, one unit fail @ 1 Hour, MTBF = 1000 Hours
1 Unit fail @ 1000 hours, MTBF = 1000 Hours
Is it the same ?
 First of all:-
How you shall not measure reliability!!!
𝑴𝑻𝑩𝑭 = 𝜽 =
𝑶𝒑𝒆𝒓𝒂𝒕𝒊𝒏𝒈 𝑯𝒐𝒖𝒓𝒔
# 𝑭𝒂𝒊𝒍𝒖𝒓𝒆𝒔
How to measure reliability ?

2. MTBF Can’t be used for benchmarking.
 Example:
SYSTEM #2 seems to be performing better
 First of all:-
SYSTEM January February
SYSTEM #1 150 𝐻𝑜𝑢𝑟𝑠
6 𝐹𝑎𝑖𝑙𝑢𝑟𝑒𝑠
MTBF = 25 690 𝐻𝑜𝑢𝑟𝑠
MTBF = 46
MTBF = 50

2. MTBF Can’t be used for benchmarking.
 Example:
But not really.
Any sense ?
 First of all:-
SYSTEM January February TOTAL
MTBF = 40
MTBF = 35

3. MTBF is time independent.
 Example: 12 failures over 12 months, MTBF = (365/12) = 30.4
MTBF = 30.4
 First of all:-
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12
F1 F2 F3 F4 F5 F7F6 F8 F9 F10 F11 F12

MTBF= 30.4, But the failure rate is
increasing?
 First of all:-
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12
F
1
F
2
F
3
F
4
F
5
F
7
F
6
F
8
F
9
F
1
0
F
1
1
F
1
2

decreasing?
 First of all:-
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12
F
1
F
2
F
3
F
4
F
5
F
7
F
6
F
8
F
9
F
1
0
F
1
1
F
1
2

decreasing? When to plan PMs ?
 First of all:-
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12
F
1
F
2
F
3
F
4
F
5
F
7
F
6
F
8
F
9
F
1
0
F
1
1
F
1
2

4. MTBF considering normal distribution, is your data so ?
 Example:
But first, how different distribution can
make different result/decision ?
 First of all:-

Here is the beautiful normal
distribution AKA Bell shape.
Where MEAN = MEDIAN = MODE
The normal distribution
MEAN TIME BETWEEN FAILURES
So we are talking about the mean, and our
X-axis is time, and Y-Axis is failures

IS YOUR DATA FOLLWING THE
NORMAL DISTRBUTION ?

IS YOUR DATA FOLLWING THE
NORMAL DISTRBUTION ?
Let’s see

Let’s say we are studding
the failure of lightbulb,
we have a group of 100
bulb, and we are running
in the constant failure
rate part of the bath
curve (Phase 2)

curve (Phase 2), we’ll
assume this rate = 1%,
Remember
MTBF = 1/failure rate
MTBF = 1/1% = 100
MTBF = 100

curve (Phase 2), we’ll
assume this rate = 1%,
Remember
MTBF = 1/failure rate
MTBF = 1/1% = 100
MTBF = 100
So half of the population
should be failed by the @
100 hours
Let’s try it

The data points will
followings:-
100 – 1% = 99
99 – 1% = 98.01
98.01-1%= 97.02
97.02 – 1% = 96.05
And so on…
@ 100 hours we left with
37 units…
But why ? We suppose to
get MEAN=50 unit ???
Simply because the failure
pattern unfirming an
exponential distribution.
For exponential :
MEAN ≠ MEDIAN ≠ MODE
But is everything followings
exponential pattern ?
NO
EVERY FAILURE MODE HAVE
IT’S UNIQUE DISTRBUTION
SHAPE.
0
20
40
60
80
100
120 1
13
25
37
49
61
73
85
97
109
121
133
145
157
169
181
193
205
217
229
241
253
265
Units
Time in Hours
@ 100 hours only 37 units survives

If you think MTBF is not the wright way
to measure reliability then stay toned
for the upcoming post.
Salam
Ammar Alkhaldi, CSSBB
So how to measure reliability then ?

How to measure reliability

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