Simplified analysis of a hyperbolic system

The method of generating equation is used in order to reduce a weakly nonlinear hyperbolic system to the standard form, i.e. the form which admits an asymptotic treatment based on the averaging principle.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25879/1/0000442.pd

Theory of residence-time control by output feedback

The problem of residence-time control by the observer-based output feedback is formulated and solved for the case of linear systems with small additive input noise. Both noiseless and noisy measurements are considered. In the noiseless measurements case, it is shown that the fundamental bounds on the achievable residence time depend on the nonminimum phase zeros of the system. In the noisy measurements case, the achievable residence time is shown to be always bounded, and an estimate of this bound is given. Controller design techniques are presented. The development is based on the asymptotic large deviations theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42624/1/10638_2005_Article_BF02169425.pd

Production variability in manufacturing systems: Bernoulli reliability case

The problem of production variability in serial manufacturing lines with unreliable machines is addressed. Bernoulli statistics of machine reliability are assumed. Three problems are considered: the problem of production variance, the problem of constant demand satisfaction, and the problem of random demand satisfaction generated by another (unreliable) production line. For all three problems, bounds on the respective variability measures are derived. These bounds show that long lines smooth out the production and reduce the variability. More precisely, these bounds state that the production variability of a line with many machines is smaller than that of a single machine system with production volume and reliability characteristics similar to those of the longer line. Since all the variability measures for a single machine line can be calculated relatively easily, these bounds provide analytical tools for analysis and design of serial production lines from the point of view of the customer demand satisfaction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44290/1/10479_2004_Article_326034.pd

Mathematical theory of improvability for production systems

A mathematical model for continuous improvement processes in production systems is formulated. Both constrained and unconstrained cases are addressed. A solution for the case of a serial production line with finite buffers and a Bernoulli model of machines reliability is given. In particular, it is shown that a production line is unimprovable under constraints if each buffer is on the average half full and each machine has equal probability of blockages and starvations. Based on this result, guidelines for continuous improvement processes are formulated.</p

Distributed communications in collision channels with errors

Analysis of distributed communication networks in noisy collision channels is given. Both feedback and feedforward channel errors are considered. A finite number of buffered users is addressed. It is shown that channel errors lead to stabilization of unstable access protocols, i.e. to elimination of the saturation phenomena and to stabilization of a network in a unique, globally asymptotically stable steady state with relatively high-performance characteristics. Thus channel noise, possibly introduced intentionally, could be viewed as a decentralized stabilizing controller.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26161/1/0000238.pd

Multi-job production systems: definition, problems, and product-mix performance portrait of serial lines

This paper pursues two goals: (a) Define a class of widely used in practice flexible manufacturing systems, referred to as Multi-Job Production (MJP) and formulate industrially motivated problems related to their performance. (b) Provide initial results concerning some of these problems pertaining to analysis of the throughput and bottlenecks of MJP serial lines as functions of the product-mix. In MJP systems, all job-types are processed by the same sequence of manufacturing operations, but with different processing time at some or all machines. To analyse MJP with unreliable machines, we introduce the work-based model of production systems, which is insensitive to whether single- or multi-job manufacturing takes place. Based on this model, we investigate the performance of MJP lines as a function of the product-mix. We show, in particular, that for the so-called conflicting jobs there exists a range of product-mixes, wherein the throughput of MJP is larger than that of any constituent job-type manufactured in a single-job regime. To characterise the global behaviour of MJP lines, we introduce the Product-Mix Performance Portrait, which represents the system properties for all product-mixes and which can be used for operations management. Finally, we report the results of an application at an automotive assembly plant

Asymptotically reliable serial production lines with a quality control system

A model of asymptotically reliable serial production lines with a quality control system is introduced. Its performance is analyzed in the case of a two machine, one buffer system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29541/1/0000629.pd

Aiming control: Residence probability and (D, T)-stability,

In this paper, the problem of aiming control is formulated and analyzed in terms of the residence probability measure. Specifically, the notion of residence probability in a domain is introduced and its asymptotic expression is derived for linear systems with small, additive white noise. The associated notion of (D, T)-stability, which characterizes the performance of stochastic systems with no equilibrium points, is introduced and investigated. Finally, the controllability of residence probability is studied and the necessary and sufficient conditions for (D, T)-stabilizability are derived. The development is based on the asymptotic large deviations theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30088/1/0000459.pd

Random Demand Satisfaction in Unreliable Production–Inventory–Customer Systems

A method for calculating the probability of customer demand satisfaction in production–inventory–customer systems with Markovian machines, finite finished goods buffers, and random demand is developed. Using this method, the degradation of this probability as a function of demand variability is quantified. In addition, it is shown by examples that the probability of customer demand satisfaction depends primarily on the coefficient of variation, rather than on the complete distribution, of the demand.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44112/1/10479_2004_Article_5254653.pd

Aiming control: Design of residence probability controllers,

Methods for design of residence probability (RP) controllers for linear stochastic systems are developed. The design of RP controllers requires the selection of a controller gain and an initial `lock in' set. The controller gain is obtained by solving a Riccati equation and the initial set is obtained by solving a Liapunov equation. Examples illustrating the suggested design procedures are given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30089/1/0000460.pd