Gokhale, S. S., Philip, T., and Marinos, P. N. (1996). A non-homogeneous Markov software reliability model with imperfect repair. In 2nd Annual IEEE International Computer Performance&DependabilitySymposium, pages 262--270, Urbana-Champaign, IL. IEEE, IEEE Computer Press.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....I ) Delta I Delta Max(K i ; d N( T I ; ffl I ) M e) Delta Min(M;N( T I ; ffl I ) 22) where K i = d N( T I ; ffl I ) M e: Table 2 in Section 4 shows for an example model the trend of the number of MVMs required for different values of M and I . 3 The approach taken in [Gokhale et al. 1996] to solve reliability growth models, boils down to interval splitting with K i = 1: This will give accurate results if I is chosen large enough, but may not necessarily be computationally best. 1 processor 2(t)c 2 (t)c1 safe failure 2 processors (t) 1 Gamma c 1 ) 2(t) 1 Gamma c 2 ) unsafe ....

.... We will take P k i = P (s) for some s 2 [ k i Gamma 1) Delta; k i Delta] In our experiments we consider five different values for the point s: s = k i Gamma 1) Delta Ptime Delta; for Ptime = 0:0; 0:25; 0:5; 0:75; 1:0: 4 The particular examples of reliability growth models mentioned in [Gokhale et al. 1996] can be solved by using the conversion approach as well. Time Prob(Safe Failure) Prob(Unsafe Failure) 1 3:26013009 10 Gamma3 0:0746811188 2 3:91279939 10 Gamma2 0:246353744 3 1:26777444 10 Gamma1 0:418398740 4 0:229308899 0:536567717 5 0:303324461 0:599521128 Table 1: Results ....

Gokhale, S. S., Philip, T., and Marinos, P. N. (1996). A non-homogeneous Markov software reliability model with imperfect repair. In 2nd Annual IEEE International Computer Performance & Dependability Symposium, pages 262--270, Urbana-Champaign, IL. IEEE, IEEE Computer Press.

....4 shows for an example model the trend of the number of MVMs required for different values of M and I. 4 RESULTS We now apply the algorithms from Section 3 to a simple non homogeneous Markov model and study their accuracy, speed and memory demand. As an example we 3 The approach taken in [Gokhale et al. 1996] to solve reliability growth models, boils down to interval splitting with K i = 1: This will give accurate results if I is chosen large enough, but may not necessarily be computationally best. use a safety model of a duplex system, that has been analyzed in [Rindos et al. 1995] All computations ....

.... 4 0:229308899 0:536567717 5 0:303324461 0:599521128 Table 1: Results for safety model, obtained from transformation to a CTMC more general conditions) 4 To obtain the results in Table 1 we used SHARPE [Sahner et al. 1996] 4 The particular examples of reliability growth models mentioned in [Gokhale et al. 1996] can be solved by using the conversion approach as well. 4.1 Accuracy In the discretization in (11) P k i is a probability matrix that must be representative for the whole k i th interval. We will take P k i = P (s) for some s 2 [ k i Gamma 1) Delta; k i Delta] In our experiments we ....

Gokhale, S. S., Philip, T., and Marinos, P. N. (1996). A non-homogeneous Markov software reliability model with imperfect repair. In 2nd Annual IEEE International Computer Performance & Dependability Symposium, pages 262--270, Urbana-Champaign, IL. IEEE, IEEE Computer Press.

....model[1] Keiller Littleweood model[1] The classification of the software reliability models is shown graphically in Figure 1. The state space view of time domain models that we have adopted has the advantage of being easily extendible to include imperfect detection repair and finite repair times[11]. 4 Time Domain Models In this section, we briefly discuss the various classes of models that fall into the category of time domain models with representative examples. 4.1 Homogeneous Markov Models The models belonging to this class assume that the initial number of faults residing in the ....

S. Gokhale, T. Philip, P.N. Marinos and K.S. Trivedi, "A Non-Homogeneous Markov Software Reliability Model with Imperfect Repair," Submitted to the IEEE Intl. Computer Performance and Dependability Symposium. UrbanaChampaign, IL, Sept. 1996.

....to relax this assumption in a restrictive manner. Both the Markov and the semi Markov models are also subject to an intractably large state space. Methods have been proposed to model the reliability growth of the components which cannot be accounted for by the conventional analytical methods [9, 10, 16], but they are also subject to the state space explosion problem, and=or are computationally very intensive. Some methods have also been proposed to study the effect of correlated versions on various fault tolerant configurations [13, 18, 25] However, a single analytical model which takes into ....

S. Gokhale, T. Philip, and P. N. Marinos. "A Non-Homogeneous Markov Software Reliability Model with Imperfect Repair". In Proc. Intl. Performance and Dependability Symposium, UrbanaChampaign, IL, September 1996.

....to relax this assumption in a restrictive manner. Both the Markov and the semi Markov models are also subject to an intractably large state space. Methods have been proposed to model the reliability growth of the components which cannot be accounted for by the conventional analytical methods [7, 8, 13], but they are also subject to the state space explosion problem, and=or are computationally very intensive. Some methods have also been proposed to study the effect of correlated versions on various faulttolerant configurations [10, 15] However, a single analyt ical model which takes into ....

S. Gokhale, T. Philip, and P. N. Marinos. "A NonHomogeneous Markov Software Reliability Model with Imperfect Repair". In Proc. Intl. Performance and Dependability Symposium (IPDS '96), pages 262--270, Urbana-Champaign, IL, September 1996.

....model[1] Keiller Littleweood model[1] The classification of the software reliability models is shown graphically in Figure 1. The state space view of time domain models that we have adopted has the advantage of being easily extendible to include imperfect detection repair and finite repair times[11]. 4 Time Domain Models In this section, we briefly discuss the various classes of models that fall into the category of time domain models with representative examples. 4.1 Homogeneous Markov Models The models belonging to this class assume that the initial number of faults residing in the ....

....that the faults are not uniformly distributed nor of same severity, and that fault repair does not always result in a better product since there is an opportunity for introducing new faults during the repair process. There are currently known research efforts that are dealing with these issues[11] ....

S. Gokhale, T. Philip, P.N. Marinos and K.S. Trivedi, "A Non-Homogeneous Markov Software Reliability Model with Imperfect Repair," Submitted to the IEEE Intl. Computer Performance and Dependability Symposium. Urbana-Champaign, IL, Sept. 1996.

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Gokhale, S. S., Philip, T., and Marinos, P. N. (1996). A non-homogeneous Markov software reliability model with imperfect repair. In 2nd Annual IEEE International Computer Performance&DependabilitySymposium, pages 262--270, Urbana-Champaign, IL. IEEE, IEEE Computer Press.

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