SENG 421SENG 421Reliability Reliability Demonstration ChartDemonstration Chart
Department of Electrical & Computer Engineering, University of Calgary
B.H. Far （ [email protected] ）http://www.enel.ucalgary.ca/People/far/Lectures/SENG421/
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Reliability Demo Chart /1Reliability Demo Chart /1 An efficient way of
checking whether the FIO (F) is met or not.
It is based on collecting failure data at time points.
Vertical axis: failure number (n)
Horizontal axis: normalized failure data (Tn), i.e., failure time F
Figure from Musa’s Book
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Parameters Involved /1Parameters Involved /1 Discrimination ratio (Discrimination ratio ():): Acceptable error in
estimating failure intensity. Customer risk (Customer risk () :) : Probability that the developer
is willing to accept of falsely saying the failure intensity objective is met (i.e., acceptance) when it is not.
Developer risk (Developer risk () :) : Probability that the developer is willing to accept of falsely saying the failure intensity objective is not met (i.e., rejection) when it is.
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Parameters Involved /2Parameters Involved /2
For =10% and = 10% and =2 There is 10% risk ()) of wrongly accepting the
software when its failure intensity objective is actually equal or greater than twice ( =2) the failure intensity objective.
There is 10% risk () of wrongly rejecting the software when its failure intensity objective is actually equal or less than half ( =2) the failure intensity objective.
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Reliability Demo Chart /2Reliability Demo Chart /2
A changes rapidly with customer risk but very slightly with developer risk and it determines the intercept of accept boundary with the horizontal line n=0
B changes rapidly with developer risk but very slightly with customer risk and it determines the intercept of reject boundary with the vertical line Tn=0
1ln ln
1A B
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Reliability Demo Chart /3Reliability Demo Chart /3 Boundary between accept and continue regions
( is the discrimination ratio)
( is the discrimination ratio)
Boundary between reject and continue regions
ln
1 1n
AT n
ln
1 1n
BT n
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Reliability Demo Chart /4Reliability Demo Chart /4
Values of intercepts of boundaries with various horizontal and vertical axes
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Reliability Demo Chart /5Reliability Demo Chart /5Values of A and B for various consumer and supplier risk levels
Table from Musa’s Book
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Reliability Demo Chart /6Reliability Demo Chart /6 When risk levels ( and ) decrease, the
system will require more test before reaching the accept or reject regions, i.e., the continue region becomes wider.
When discrimination ratio () decreases, the system will require more test before reaching the accept or reject regions, i.e., the continue region becomes wider.
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RDC: Example /1RDC: Example /1 Consumer risk
= 5% Supplier risk
= 5% Discrimination
ratio = 2
Figure from Musa’s Book
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RDC: Example /2RDC: Example /2 Consumer risk
= 1% Supplier risk
= 1% Discrimination
ratio = 2
Figure from Musa’s Book
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RDC: Example /3RDC: Example /3 Consumer risk
= 0.1% Supplier risk
= 0.1% Discrimination
ratio = 2
Figure from Musa’s Book
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RDC: Example /4RDC: Example /4 Consumer risk
= 10% Supplier risk
= 10% Discrimination
ratio = 1.2
Figure from Musa’s Book
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Example 1Example 1
Failure number
Measure
(million transactions)
Normalized
Measure
(MTTF)
1 0.1875 0.75
2 0.3125 1.25
3 1.25 5
4 failures/million transactions
%10
%10
2
F
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Example 2Example 2
Failure number
Measure
(CPU hour)
Normalized
Measure
(MTTF)
1 8 0.8
2 19 1.9
3 60 6
0.1 failures/CPU hour
0.05
0.05
2
F
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Example 3Example 3 We are going to buy a new colour laser printer for
our department. We have borrowed the printer for the test run and we are going to conduct certification test on it. Maker’s data shows that we need to change the toner every 10,000 pages. We would like to have the system running without any failure between the two consecutive toner changes and in the worst case having only one failure during the period.
a) What shall be our failure intensity objective for the system?
F = 1/10000 pages
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Example 3 Example 3 (contd.)(contd.)
b)We observe that failures occur at 4,000 pages, 6,000 pages, 10,000 pages, 11,000 pages, 12,000 pages and 15,000 pages of output. Using the reliability demonstration chart, what can we conclude about this printer?
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Example 3 Example 3 (contd.)(contd.)
Because of failing the certification test we will reject the printer.
