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SENG 421 Reliability Demonstration Chart Department of Electrical & Computer Engineering, University of Calgary B.H. Far （ far@ucalgary.ca ） http://www.enel.ucalgary.ca/People/far/Lectures/SENG421/

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SENG421 (Winter 2005)far@ucalgary.ca2 Reliability 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 (T n ), i.e., failure time F Figure from Musa’s Book

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SENG421 (Winter 2005)far@ucalgary.ca3 Parameters 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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SENG421 (Winter 2005)far@ucalgary.ca4 Parameters 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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SENG421 (Winter 2005)far@ucalgary.ca5 Reliability 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 T n =0

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SENG421 (Winter 2005)far@ucalgary.ca6 Reliability Demo Chart /3 Boundary between accept and continue regions ( is the discrimination ratio) Boundary between reject and continue regions

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SENG421 (Winter 2005)far@ucalgary.ca7 Reliability Demo Chart /4 Values of intercepts of boundaries with various horizontal and vertical axes

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SENG421 (Winter 2005)far@ucalgary.ca8 Reliability Demo Chart /5 Values of A and B for various consumer and supplier risk levels Table from Musa’s Book

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SENG421 (Winter 2005)far@ucalgary.ca9 Reliability 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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SENG421 (Winter 2005)far@ucalgary.ca10 RDC: Example /1 Consumer risk = 5% Supplier risk = 5% Discrimination ratio = 2 Figure from Musa’s Book

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SENG421 (Winter 2005)far@ucalgary.ca11 RDC: Example /2 Consumer risk = 1% Supplier risk = 1% Discrimination ratio = 2 Figure from Musa’s Book

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SENG421 (Winter 2005)far@ucalgary.ca12 RDC: Example /3 Consumer risk = 0.1% Supplier risk = 0.1% Discrimination ratio = 2 Figure from Musa’s Book

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SENG421 (Winter 2005)far@ucalgary.ca13 RDC: Example /4 Consumer risk = 10% Supplier risk = 10% Discrimination ratio = 1.2 Figure from Musa’s Book

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SENG421 (Winter 2005)far@ucalgary.ca14 Example 1 Failure number Measure (million transactions) Normalized Measure (MTTF) 10.18750.75 20.31251.25 3 5

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SENG421 (Winter 2005)far@ucalgary.ca15 Example 2 Failure number Measure (CPU hour) Normalized Measure (MTTF) 180.8 2191.9 3606

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SENG421 (Winter 2005)far@ucalgary.ca16 Example 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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SENG421 (Winter 2005)far@ucalgary.ca17 Example 3 (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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SENG421 (Winter 2005)far@ucalgary.ca18 Example 3 (contd.) Because of failing the certification test we will reject the printer.

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