Robert H. Storer

Disturbance detection and isolation by dynamic principal component analysis

Abstract In this paper we extend previous work by ourselves and other researchers in the use of principal component analysis (PCA) for statistical process control in chemical processes. PCA has been used by several authors to develop techniques to monitor chemical processes and detect the presence of disturbances [1–5]. In past work, we have developed methods which not only detect disturbances, but isolate the sources of the disturbances [4]. The approach was based on static PCA models, T2 and Q charts [6], and a model bank of possible disturbances. In this paper we use a well-known ‘time lag shift’ method to include dynamic behavior in the PCA model. The proposed dynamic PCA model development procedure is desirable due to its simplicity of construction, and is not meant to replace the many well-known and more elegant procedures used in model identification. While dynamic linear model identification, and time lag shift are well known methods in model building, this is the first application we are aware of in the area of statistical process monitoring. Extensive testing on the Tennessee Eastman process simulation [7] demonstrates the effectiveness of the proposed methodology.

ROBUSTNESS MEASURES AND ROBUST SCHEDULING FOR JOB SHOPS

Abstract A robust schedule is defined as a schedule that is insensitive to unforeseen shop floor disturbances given an assumed control policy. In this paper, a definition of schedule robustness is developed which comprises two components: post-disturbance make-span and post-disturbance makespan variability. We have developed robustness measures and robust scheduling methods for the case where a “right-shift” control policy is used. On occurrence of a disruption, the right-shift policy maintains the scheduling sequence while delaying the unfinished jobs as much as necessary to accommodate the disruption. An exact measure of schedule robustness is derived for the case in which only a single disruption occurs within the planning horizon. A surrogate measure is developed for the more complex case in which multiple disruptions may occur. This surrogate measure is then embedded in a genetic algorithm to generate robust schedules for job-shops. Experimental results show that robust schedules significantly outper...

One-machine rescheduling heuristics with efficiency and stability as criteria

Abstract Heuristics for the problem of rescheduling a machine on occurrence of an unforeseen disruption are developed. The criteria include minimization of the makespan (schedule efficiency) and the impact of the schedule change (schedule stability). The impact of schedule change is a non-regular performance measure defined in two ways: (1) the starting time deviations between the new schedule and the original schedule, and (2) a measure of the sequence difference between the two schedules. Three local search procedures are developed for the bicriterion problem and a set of experiments are conducted to test the efficacy of the heuristics. The heuristic solutions are shown to be effective in that the schedule stability can be increased significantly with little or no sacrifice in makespan.

An approximate dynamic programming approach for the vehicle routing problem with stochastic demands

This paper examines approximate dynamic programming algorithms for the single-vehicle routing problem with stochastic demands from a dynamic or reoptimization perspective. The methods extend the rollout algorithm by implementing different base sequences (i.e. a priori solutions), look-ahead policies, and pruning schemes. The paper also considers computing the cost-to-go with Monte Carlo simulation in addition to direct approaches. The best new method found is a two-step lookahead rollout started with a stochastic base sequence. The routing cost is about 4.8% less than the one-step rollout algorithm started with a deterministic sequence. Results also show that Monte Carlo cost-to-go estimation reduces computation time 65% in large instances with little or no loss in solution quality. Moreover, the paper compares results to the perfect information case from solving exact a posteriori solutions for sampled vehicle routing problems. The confidence interval for the overall mean difference is (3.56%, 4.11%).

Heuristic and exact algorithms for scheduling aircraft landings

The problem of scheduling aircraft landings on one or more runways is an interesting problem that is similar to a machine job scheduling problem with sequence-dependent processing times and with earliness and tardiness penalties. The aim is to optimally land a set of planes on one or several runways in such a way that separation criteria between all pairs of planes (not just successive ones) are satisfied. Each plane has an allowable time window as well as a target time. There are costs associated with landing either earlier or later than this target landing time. In this paper, we present a specialized simplex algorithm which evaluates the landing times very rapidly, based on some partial ordering information. This method is then used in a problem space search heuristic as well as a branch-and-bound method for both single-and multiple-runway problems. The effectiveness of our algorithms is tested using some standard test problems from the literature.

Critical variables of solder paste stencil printing for micro-BGA and fine-pitch QFP

Stencil printing continues to be the dominant method of solder deposition in high-volume surface-mount assembly. Control of the amount of solder paste deposited is critical in the case of fine-pitch and ultrafine-pitch surface-mount assembly. The process is still not well understood as indicated by the fact that industry reports 52-71% surface-mount technology (SMT) defects are related to the solder paste stencil printing process. The purpose of this paper is to identify the critical variables that influence the volume, area, and height of solder paste deposited. An experiment was conducted to investigate the effects of relevant process parameters on the amount of solder paste deposited for ball grid arrays (BGAs) and quad flat packages (QFPs) of five different pitches ranging from 0.76 mm (30 mil) to 0.3 mm (12 mil). The effects of aperture size, aperture shape, board finish, stencil thickness, solder type, and print speed were examined. The deposited solder paste was measured by an inline fully automatic laser-based three-dimensional (3-D) triangulation solder paste inspection system. Analysis of variance (ANOVA) shows that aperture size and stencil thickness are the two most critical variables. A linear relationship between transfer ratio (defined as the ratio of the deposited paste volume to the stencil aperture volume) and area ratio (defined as the ratio of the area of the aperture opening to the area of the aperture wall) is proposed. The analysis indicates that the selection of a proper stencil thickness is the key to controlling the amount of solder paste deposited, and that the selection of maximum stencil thickness should be based on the area ratio. The experimental results are shown to be consistent with a theoretical model, which are also described.

Datapath synthesis using a problem-space genetic algorithm

This paper presents a new approach to datapath synthesis based on a problem-space genetic algorithm (PSGA). The proposed technique performs concurrent scheduling and allocation of functional units, registers, and multiplexers with the objective of finding both a schedule and an allocation which minimizes the cost function of the hardware resources and the total time of execution. The problem-space genetic algorithm based datapath synthesis system (PSGA-Synth) combines a standard genetic algorithm with a known heuristic to search the large design space in an intelligent manner. PSGA-Synth handles multicycle functional units, structural pipelining, conditional code and loops, and provides a mechanism to specify lower and upper bounds on the number of control steps. The PSGA-Synth was tested on a set of problems selected from the literature, as well as larger problems created by us, with promising results. PSGA-Synth not only finds the best known results for all the test problems examined in a relatively small amount of CPU time, but also has the ability to efficiently handle large problems. >

Problem and Heuristic Space Search Strategies for Job Shop Scheduling

In a recent paper we discussed “problem” and “heuristic” spaces which serve as a basis for local search in job shop scheduling problems. By encoding schedules as heuristic, problem pairs (H,P) search spaces can be defined by perturbing problem data and/or heuristic parameters. In this paper we attempt to determined, through computational testing, how these spaces can be successfully searched. Well known local search strategies are applied in problem and heuristic space and compared to Shifting Bottleneck heuristics, and to probabilistic dispatching methods. An interesting result is the good performance of genetic algorithms in problem space. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Critical variables of solder paste stencil printing for micro-BGA and fine pitch QFP

Stencil printing continues to be the dominant method of solder deposition in high volume surface mount assembly. Control of the amount of solder paste deposited is critical for fine pitch and ultra-fine pitch SMT assembly. The process is still not well understood as indicated by the fact that industry reports 52-71% of SMT defects are related to the solder paste stencil printing process. The purpose of this paper is to identify the critical variables that influence the deposited solder paste volume, area, and height. An experiment was conducted to investigate the effects of relevant process parameters on the amount of solder paste deposited for BGAs and QFPs of 5 different pitches, ranging from 0.76 mm (30 mil) to 0.3 mm (12 mil). The effects of aperture size and shape, board finish, stencil thickness, solder type, and print speed were examined. The deposited solder paste was measured by an in-line fully automatic laser-based 3D triangulation solder paste inspection system. Analysis of variance (ANOVA) shows that aperture size and stencil thickness are the two most critical variables. A linear relationship between transfer ratio (defined as the ratio of deposited paste volume to stencil aperture volume) and area ratio (defined as the ratio of the area of the aperture opening to the area of the aperture wall) is proposed. Analysis indicates that proper stencil thickness selection is the key to controlling the amount of solder paste deposited and that the selection of maximum stencil thickness should be based on the area ratio. The experimental results are shown to be consistent with a theoretical model, which is also described.

A sample average approximation approach to stochastic appointment sequencing and scheduling

This article develops algorithms for a single-resource stochastic appointment sequencing and scheduling problem with waiting time, idle time, and overtime costs. This is a basic stochastic scheduling problem that has been studied in various forms by several previous authors. Applications for this problem cited previously include scheduling of surgeries in an operating room, scheduling of appointments in a clinic, scheduling ships in a port, and scheduling exams in an examination facility. In this article, the problem is formulated as a stochastic integer program using a sample average approximation. A heuristic solution approach based on Benders’ decomposition is developed and compared to exact methods and to previously proposed approaches. Extensive computational testing shows that the proposed methods produce good results compared with previous approaches. In addition, it is proved that the finite scenario sample average approximation problem is NP-complete.