Download presentation

Presentation is loading. Please wait.

Published byLilian Bottum Modified over 2 years ago

1
Up to Now – we covered Basic Model: –failure intensity --- by number of failures (only linear relation model) Logarithmic Poisson Model: – failure intensity ---- by number of failures Basic Model: – # of Failures ---- by execution time Logarithmic Poisson Model: –# of Failures ---- by execution time

2
Two Failure Intensity Models in terms of Execution Time (t) Basic Model : – f(t) = f0 e -[(f0*t)/v] where f0 = initial failure intensity t = time v = estimated total number of failures Logarithmic Poisson Model: – f(t) = f0 / [(f0*k*t) + 1] where f0 = initial failure intensity t = time k = decay parameter

3
Failure Intensity as a function of Execution Time (Graphical Curves) Logarithmic Poisson model Basic model execution time, (t) failure-intensity, (f) We need to lengthen the x-axis now that we have changed it from # of failures to execution time. This is because the “time” between failures lengthens as more failures are encountered and fixed the ‘real’ curves would be much smoother!

4
Examples Basic model: – for f0 = 10 failures/cpu-time; v= 100 total failures; and t = 10 cpu- time – F (10) = f0 e -[(f0*t)/v] = 10 e -[(10*10)/100] = 10 e -1 = 10 *.368 = 3.68 failures/cpu-time Logarithmic Poisson model: –for f0= 10 failures/cpu-time ; k =.02 decay factor ; and t = 10 cpu- time – F (10) = f0 / [(f0*k*t) + 1] = 10 / [(10*.02*10)+1] = 10 / [2 + 1] = 3.33 failures/cpu-time

5
Quick Comparison of Models (reminder) BasicLogarithmic Poisson Initial intensity Estimated decay Estimated total failures f0 V --- k

6
Scenarios of Basic Model where F0 ≡ initial failure intensity F0a > F0b and same vF0a F0b v Same F0, but va > vb vavb F0 X-axis = # of failures experiencedX-axis = execution time F0a F0b F0a > F0b and same v F0 t for vb t for va t for v Same F0, but va > vb

7
Scenarios of Logarithmic Poisson Model F0a > F0b and same kF0a F0b Same F0, but ka > kb F0 X-axis = # of failures experiencedX-axis = execution time F0a F0b F0a > F0b and same k F0 v Same F0, but ka > kb ka kb ka

8
Using “derived” value for projection Can we use these model equations for some projections? Assume we started with f0 failure intensity and reached a failure intensity of f1. We want to get to a lower failure intensity of f2 as the objective of our “quality plan”. Then can we project the # of more failures (or ∆v) that must be found to get to f2? f0 v f1 f2 v2v1 Basic model Since : f1 = f0 - [(f0 *v1)/v] (from Basic intensity model formula) f2 = f0 - [(f0* v2)/v] f1 – f2 = (f0*v2)/v - (f0*v1)/v ; subtracting out f0 v ( f1- f2 ) = f0 (v2 –v1) [ v*(f1- f2) ] / f0 = v2 - v1 = ∆ v ∆v = v/f0 * (f1 – f2) for Basic Model ∆v Similarly, if we go through the formula manipulation We will get ∆v = (1/k) * ln(f1/f2) for Logarithmic Poisson Model

9
Example Suppose, for Basic Model we have: –f0 = 10 and estimated v = 100 –Assume we are at f1 failure intensity = 3.68 –Assume that we want to get to f2 =.000454 –Then using the formula: ∆v = 100/10 (3.68 -.000454) ≡ 10 * 3.67 ≡ 36.7 more failures need to be found.

10
“Derived” ∆ for execution time Basic model: – ∆t = (v/f0) * ln( f1/f2 ) where f0 = initial failure intensity f1 = present failure intensity f2 = desired failure intensity Logarithmic Poisson model: – ∆t = 1/k (1/f2 – 1/f1 )

11
Example Suppose, for Basic Model we have same assumption as before: –f0 = 10 and estimated v = 100 –Assume we at f1 failure intensity = 3.68 –Assume that out objective is to get to f2 =.000454 Question: how much more execution time units are required to get to that objective? –Then using the formula: ∆t = 100/10 [ln (3.68 /.000454)] ≡ 10 * ln (8106) ≡ 10 * 9 ≡ 90 more execution time units

Similar presentations

Presentation is loading. Please wait....

OK

6.3 Antidifferentiation by Parts Quick Review.

6.3 Antidifferentiation by Parts Quick Review.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on forward rate agreement quote Run ppt on mac Ppt on tamper resistant paper Ppt on condition monitoring equipment Ppt on principles of object-oriented programming languages Ppt online shopping system Ppt on communication Ppt on second law of thermodynamics for kids Ppt on media research council Ppt on sweat equity shares