Meta Modeling for Business Process Improvement

Conducting business process improvement (BPI) initiatives is a topic of high priority for today’s companies. However, performing BPI projects has become challenging. This is due to rapidly changing customer requirements and an increase of inter-organizational business processes, which need to be considered from an end-to-end perspective. In addition, traditional BPI approaches are more and more perceived as overly complex and too resource-consuming in practice. Against this background, the paper proposes a BPI roadmap, which is an approach for systematically performing BPI projects and serves practitioners’ needs for manageable BPI methods. Based on this BPI roadmap, a domain-specific conceptual modeling method (DSMM) has been developed. The DSMM supports the efficient documentation and communication of the results that emerge during the application of the roadmap. Thus, conceptual modeling acts as a means for purposefully codifying the outcomes of a BPI project. Furthermore, a corresponding software prototype has been implemented using a meta modeling platform to assess the technical feasibility of the approach. Finally, the usability of the prototype has been empirically evaluated

IFRA or DMRL survival under the pure birth shock process

Suppose that a device is subjected to shocks and that P^, k • 0, 1, 2,00denotes the probability of surviving k shocks. Then H(t) = E P(N(t) = k)P,k=0is the probability that the device will survive beyond t, where N = (N(t): t > 0} is the counting process which governs the arrival of shocks. A-Hameed and Proschan (1975) considered the survival function H(t) under what they called the Pure Birth Shock Model. In this paper we shall prove that H(t) is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.digitalisering@um

On some classes of bivariate life distributions

During the last years efforts have been made in order to define suitable bivariate and multivariate extensions of the univariate IFR, IFRA, NBU NBUE and DMRL classes (with duals) of life distributions. In this paper we suggest two new bivariate NBUE (NWUE) and several bivariate HNBUE (HNWUE) definitions. Furthermore, we discuss some of the classes of multivariate life distributions proposed by Buchanan and Singpurwalla (1977). We also study two bivariate shock models. Suppose that two devices are subjected to shocks of some kind. Let P(k^,k2), k^,k2 = 0,1,2,..., denote the probability that the devices survive k^ and k2 shocks, respectively, and let T. denote the time to failure of device number j, j = 1,2, and let H(t^,t2) = P(T^ > t^,T2 > t2)• We study the shock models by Marshall and Olkin and by Buchanan and Singpurwalla and give sufficient conditions, containing P(k^,k2), k^,k2 = 0,1,2,..., under which H.(t^,t2) is bivariate NBU (NWU), bivariate NBUE (NWUE) and bivariate HNBUE (HNWUE) of different forms.There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.digitalisering@um

Testing exponentiality against HNBUE

Let F be a life distribution with survival function F = 1 - F and00 —finite mean y = /q F(x)dx. Then F is said to be harmonic new better00 —than used in expectation (HNBUE) if / F(x)dx < y exp(-t/y) for t > 0. If the reversed inequality is true F is said to be HNWUE (W = worse). We develop some tests for testing exponentiality against the HNBUE (HNWUE) property. Among these is the test based on the cumulative total time on test statistic which is ordinarily used for testing against the IFR (DFR) alternative. The asymptotic distributions of the statistics are discussed. Consistency and asymptotic relative efficiency are studied. A small sample study is also presented.This is a revised version of Sections 5 and 6 in Statistical Research Report 1979-9, Department of Mathematical Statistics, University of Umeå.There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.digitalisering@um

Some properties of the HNBUE and HNWUE classes of life distributions

The HNBUE (HNWUE) class of life distributions (i.e. for which f F (x)dx< (>)00 t< (>) y exp(-t/y) for t > 0, where y = / F(x)dx) is studied. We prove0that the HNBUE (HNWUE) class is larger than the NBUE (NWUE) class. We alsopresent some characterizations of the HNBUE (HNWUE) property by using theTotal Time on Test (TTT-) transform and the Laplace transform. Further weexamine whether the HNBUE (HNWUE) property is preserved under the reliabilityoperations (1) formation of coherent structure, (2) convolution and(3) mixture. Some bounds on the moments and on the survival function of aHNBUE (HNWUE) life distribution are also presented. The class of distributionswith the discrete HNBUE (discrete HNWUE) property (i.e. for which00 00 00I P. < (>) y(l-l/y)k for k = 0,1,2j=k J "where yi=0 JI p. and P. = E p, )J k=j+l kis also studied.There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.digitalisering@um

IFRA or DMRL survival under the pure birth shock process

Suppose that a device is subjected to shocks and that P^, k • 0, 1, 2,00denotes the probability of surviving k shocks. Then H(t) = E P(N(t) = k)P,k=0is the probability that the device will survive beyond t, where N = (N(t): t > 0} is the counting process which governs the arrival of shocks. A-Hameed and Proschan (1975) considered the survival function H(t) under what they called the Pure Birth Shock Model. In this paper we shall prove that H(t) is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.digitalisering@um

Some tests against aging based on the total time on test transform

Let F be a life distribution with survival function F = 1 - F and00 —finite mean y * j n F(x)dx. The scaled total time on test transform-1F( t ) —<P,,(t) = /n /F(x)dx/y was introduced by Barlow and Campo (1975) as ar Utool in the statistical analysis of life data. The properties IFR, IFRA, NBUE, DMRL and heavy-tailedness can be translated to properties of tp„(t).rWe discuss the previously known of these relationships and present some new results. Guided by properties of <P„(t) we suggest some test statisticsrfor testing exponentiality against IFR, IFRA, NBUE, DMRL and heavy-tailed-ness, respectively. The asymptotic distributions of the statistics are derived and the asymptotic efficiencies of the tests are studied. The power for some of the tests is estimated by simulation for some alternatives when the sample size is n = 10 or n = 20.This is a revised version of Statistical Research Report 1979-4, Department of Mathematical Statistics, University of Umeå.There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.digitalisering@um

HNBUE survival under some shock models

Suppose that a device is subjected to shocks governed by a counting processN = {N(t): t > 0}. The probability that the device survives beyond t is00then H(t) = E P(N(t) = k)P, , where P, is the probability of survivingk=0 _k shocks. In this paper we prove that H(t) is HNBUE (HNWUE), i.e.00 00/ H(x)dx < (>) y exp(-t/y) for t > 0, where y = / H(x)dx, under semet " 0 — 00different conditions on N and ^^^=0' ^or ^nstance we stuc^y the casewhen the interarrivai times between the shocks are independent and HNBUE(HNWUE). This situation includes the cases when N is a Poisson processor a stationary birth process. Further a certain cumulative damage modelis studied.There are some occurring misspellings in the formulas in the abstract on this webpage. Read the abstract in the full-text document for correct spelling in formulas, see the downloadable file.digitalisering@um