Applied Stochastic Models and Data Analysis

1993 Applied Stochastic Models and Data Analysis

doi: 10.1002/asm.3150090101

de Bejar, Luis A.; Robinson, Paul F.; Avent, R. Richard

1993 Applied Stochastic Models and Data Analysis

doi: 10.1002/asm.3150090102

Two separate theoretical models are developed to predict the number of heat applications necessary to repair specified bends in damaged steel plates. One model is an application of the theory of reliability; this idealization is subsequently further simplified for practical engineering applications. The second is an application of the theory of stochastic processes: envisioning the record of plastic rotations obtained from the actual heat‐straightening of a subject plate as a finite portion of a member of the infinite ensemble of possible records for the repair, and assuming this process to be stationary and ergodic in the heat‐number domain, the theory of discrete spectral analysis is used to construct the power spectral density function of the process, and simulate artificial records. Then, simple statistical analysis allows the prediction with any desired degree of confidence. These independent probability‐based estimates successfully verify each other. As expected, the required number of repair heats for each test in the ensuing experimental program, under carefully controlled laboratory conditions, was consistently smaller than the corresponding theoretical prediction.

Neogi, D.; Nassar, R.; Fan, L. T.

1993 Applied Stochastic Models and Data Analysis

doi: 10.1002/asm.3150090103

Multiphase flow systems lend themselves to a stochastic description due to their random behaviour. Fluidized beds and bubble columns are notable examples of such systems wherein random generation and coalescence of bubbles lead to pressure and density fluctuations. Analyses of these systems utilizing short‐memory models based on Markovian assumptions have been widely reported. Nevertheless, a review of the available data and the results of preliminary experiments have indicated that the time series of pressure fluctuation signals from various multiphase flow systems exhibit a a long‐term correlation. These signals appear to be better described by a long‐memory model, specifically “fractional Brownian motion” (FBM) comprising fractional Gaussian noise (FGN). In the present work, pressure fluctuations in a gas‐solid fluidized bed and a bubble column have been analysed and modelled by resorting to the relatively new concept of FBM. The stochastic model developed visualizes the bubble motion in a multiphase flow system to be composed of a random movement, generating irregular signals, and a linear movement, generating wave‐like signals. Autocorrelation and spectral density functions have been derived from the model. Comparison between the model‐based and experimentally determined autocorrelation functions has indicated that FBM is indeed a viable model for pressure fluctuations in multiphase flow systems.

Gerontidis, Ioannis I.

1993 Applied Stochastic Models and Data Analysis

doi: 10.1002/asm.3150090104

A continuous time Markov‐renewal model is presented that generalizes the classical Young and Almond model for manpower systems with given size. The construction is based on the associated Markov‐renewal replacement process and exploits the properties of the embedded replacement chain. The joint cumulant generating function of the grade sizes is derived and an asymptotic analysis provides conditions for these to converge in distribution to a multinominal random vector exponentially fast independently of the initial distribution, both for aperiodic and periodic embedded replacement chains. A regenerative approach to the wastage process is outlined and two numerical examples from the literature on manpower planning illustrate the theory.

Nadif, M.; Govaert, G.

1993 Applied Stochastic Models and Data Analysis

doi: 10.1002/asm.3150090105

A clustering method is presented for analysing multivariate binary data with missing values. When not all values are observed, Govaert3 has studied the relations between clustering methods and statistical models. The author has shown how the identification of a mixture of Bernoulli distributions with the same parameter for all clusters and for all variables corresponds to a clustering criterion which uses L1 distance characterizing the MNDBIN method (Marchetti8). He first generalized this model by selecting parameters which can depend on variables and finally by selecting parameters which can depend both on variables and on clusters. We use the previous models to derive a clustering method adapted to missing data. This method optimizes a criterion by a standard iterative partitioning algorithm which removes the necessity either to ignore objects or to substitute the missing data. We study several versions of this algorithm and, finally, a brief account is given of the application of this method to some simulated data.

Hesse, C. H.

1993 Applied Stochastic Models and Data Analysis

doi: 10.1002/asm.3150090106

The engineering sciences have long been interested in models describing the settling (or sedimentation) of particle ensembles in viscous fluids. From a theoretical point of view, sedimentation constitutes a two phase many‐body phenomenon with complex interaction and as such has proved to be quite inaccessible to modelling attempts with relevance in applications. A stochastic model was introduced by Pickard and Tory in 1977 and was subsequently revised. In this paper we expand and refine the stochastic model and present a satisfactory model‐fitting procedure and parameter estimators based on transit times of sedimenting particles.