MTTF H (Ci )) N (0, 1), / n in Visual Studio .NET Creation QR Code in Visual Studio .NET MTTF H (Ci )) N (0, 1), / n MTTF H (Ci )) N (0, 1), / nQR-Code Creator In .NETUsing Barcode encoder for .NET Control to generate, create Denso QR Bar Code image in VS .NET applications.MARKOVIAN MODELS FOR DEPENDABILITY ANALYSIS Recognizing QR Code JIS X 0510 In VS .NETUsing Barcode reader for .NET Control to read, scan read, scan image in Visual Studio .NET applications.where N (0, 1) is the standard normal distribution, when the number n of cycles tends to in nity In other words, just by dividing both the numerator and denom inator by Hn = n 1 n H (Ci ), i=1 n(MTTF MTTF) N (0, 1), /Hn when the number n of cycles tends to in nity A Monte Carlo standard estimation of the MTTF will be inef cient because the denominator is the probability of a rare event (it will be the numerator if we deal with the unavailability) IS is a relevant way to cope with that problem The rst class of IS strategies is called dynamic importance sampling (DIS) We will not rede ne IS here; for a more precise description, see 2 Basically, we replace the transition matrix P by another one P (with corresponding probability measure P and expectation E) If the likelihood ratio over a cycle is L(x0 , , xT ) = P{(X0 , , XT ) = (x0 , , xn )} = P{(X0 , , XT ) = (x0 , , xn )}Making Barcode In .NET FrameworkUsing Barcode creation for VS .NET Control to generate, create barcode image in .NET framework applications.T 1 i=0 P(xi , xi+1 ) , T 1 i=0 P(xi , xi+1 )Recognize Bar Code In .NETUsing Barcode recognizer for .NET framework Control to read, scan read, scan image in .NET framework applications. provided T has nite expectation under P, then for any random variable Z de ned over paths, E[Z] = E[ZL] A new estimator of the MTTF is then MTTF =Create QR Code 2d Barcode In Visual C#.NETUsing Barcode encoder for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in Visual Studio .NET applications.n i=1 G(Ci )Li n i=1 H (Ci )Li QR Code Generation In Visual Studio .NETUsing Barcode printer for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.where Li is the likelihood associated with the ith cycle Another method, measure-speci c dynamic importance sampling (MSDIS), giving better results, was introduced in  This involves simulating independently the numerator and denominator of (63), using different IS measures P1 for the numerator and P2 for the denominator Indeed, the functions being different, reducing the variance for one does not necessary mean the same for the other Of the total of n cycles, n are used to estimate the numerator, and (1 )n for the denominator A new estimator is then MTTF =Draw QR In Visual Basic .NETUsing Barcode maker for VS .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications. n (1) (1) i=1 G(Ci )Li /( n) (1 )n H (Ci(2) )L(2) /((1 )n) i i=1 Barcode Generation In Visual Studio .NETUsing Barcode maker for .NET framework Control to generate, create bar code image in .NET framework applications.where the Ci(1) and L(1) (Ci(2) and L(2) ) are the cycles and likelihood ratios i i corresponding to IS measure P1 (P2 )Encode Code 128 In VS .NETUsing Barcode encoder for Visual Studio .NET Control to generate, create Code 128 Code Set C image in VS .NET applications.MARKOVIAN MODELS FOR DEPENDABILITY ANALYSIS Code 39 Full ASCII Generator In .NETUsing Barcode printer for .NET Control to generate, create Code 3 of 9 image in .NET framework applications.We then have the following result, using independent cycles (thus, the covariance term does not exist anymore): if H(1 )n = 1 (1 )nBar Code Encoder In .NET FrameworkUsing Barcode creator for VS .NET Control to generate, create barcode image in .NET framework applications.(1 )n Painting Leitcode In .NETUsing Barcode generator for .NET Control to generate, create Leitcode image in Visual Studio .NET applications.H (Ci(2) )L(2) i Drawing Data Matrix ECC200 In VB.NETUsing Barcode printer for .NET Control to generate, create ECC200 image in .NET framework applications.is an estimator of EP2 (H L(2) ), and if 2 2 2 = 1 (GL(1) ) + (MTTF)2 2 (H L(2) ) where i2 ( ) is for the variance using Pi as the underlying probability measure, then n(MTTF MTTF) N (0, 1) /H(1 )nCode39 Creation In VB.NETUsing Barcode maker for Visual Studio .NET Control to generate, create USS Code 39 image in Visual Studio .NET applications.632 Importance sampling simulation schemes and robustness properties UPC - 13 Drawer In .NETUsing Barcode generator for ASP.NET Control to generate, create European Article Number 13 image in ASP.NET applications.Many IS simulation schemes have been proposed in the literature The basic principle is to increase the occurrence of failures We review such schemes here, dividing them into three categories: rst the basic schemes rst; then those using some topological information; and nally those directly trying to approach the zero-variance change of measure In each case, we will discuss the robustness properties as 0 The properties the literature has looked at are bounded relative error (BRE) and bounded normal approximation (BNA) Recall that BRE means that the relative variance remains bounded as 0, so that the relative precision of the con dence interval is insensitive to the rarity of the event, and BNA is a suf cient condition to assert that the coverage of the con dence interval will remain valid whatever the rarity For more precise de nitions, see 4 devoted to robustness properties Those properties have been discussed at great length for highly reliable Markovian systems [27, 39, 41, 42] Looking at all sample paths, necessary and suf cient conditions have been obtained Basically, it is not suf cient that the most likely paths to failure are not rare (ie, their probability is (1)) under the IS measure; other paths should not be too rare either (but not necessarily (1)) A string of properties has also been shown in [41, 42]: BNA implies that paths contributing the most to the variance are (1) under IS measure, meaning that the variance is asymptotically properly estimated ( 4 illustrates the problems that could occur otherwise), implying BRE, implying in turn that most likely paths to failure are (1) under IS measure For all those implications, the reverse assertion is not true in general; counterexamples have been highlighted in  In what follows, since in our model transitions are either failures or repairs, we denote by F the set of failures and by R the set of repairs If x = 0, we also denote Fx = {y : (x, y) F} and Rx = {y : (x, y) R}, and let fx =Barcode Printer In JavaUsing Barcode generator for Java Control to generate, create bar code image in Java applications.Make Code 39 Full ASCII In JavaUsing Barcode generation for Java Control to generate, create Code-39 image in Java applications.Code 3/9 Encoder In C#.NETUsing Barcode creator for .NET framework Control to generate, create Code 39 Extended image in .NET framework applications.