A Comparison of Two Optimal Inspection Procedures in the Presence of Errors

It is well known that the Bayes procedure minimizes the expected loss when the a priori probabilities of the states of nature are known, but it is not clear that the procedure continues to have this property in the presence of unknown errors which occur if these probabilities must be estimated. Furthermore, it is possible that the expected loss for another procedure does not increase as fast as that for the Bayes procedure. A procedure which might behave this way is the procedure for a group of N items, designated the N-procedure, because the expected loss for this procedure does not depend explicitly on the a priori probabilities. It is found, however, that the Bayes procedure consistently yields lower expected costs than the N-procedure. The results obtained suggest that the Bayes procedure will give smaller expected losses than other procedures in the presence of unknown errors in the a priori probabilities. Somewhat surprisingly, the superiority of the Bayes procedure increases with the size of the errors of the estimated a priori probabilities, regardless of whether the estimated probabilities lie above or below the correct values.     

Application of a performance measure reduction technique to categorical safety data

This research proposes an interdisciplinary approach that combines correspondence–analytic, information–theoretic, and approximation–theoretic concepts to derive a fast reduction procedure suitable for categorical data. The procedure can also be applied to metric data where it proves to perform as well as linear regression on multivariate-normal data and superior otherwise. All types of monotone relationships, linear or non-linear, are handled well. In addition, the procedure is robust to outliers, which makes it especially desirable for exploratory and control purposes. The procedure also has a very limited data requirement, which distinguishes it from other information–theoretic procedures whose data requirement increases exponentially with the number of variables and which, in turn, are numerically highly unstable. An application of the procedure to an aviation safety data set is presented. The new procedure performs well on this data set and is shown to be analytically robust and consistent with expert judgment.     

Semi-analytical finite element procedure for conduction in anisotropic axisymmetric solids

Through the use of complex series representations and the properties of adjoint differential operators, a semi-analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi-analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.     

Generation of two- and three-dimensional finite elements

Many of the known finite elements are based on a variational procedure in a functional basis of monomials. The present paper attempts to formulate completely a finite element procedure which is non-variational on a functional basis which is left to the choice of the user.     

An integrated management procedure of multi-item mixed-line production system its hierarchical structure and performance evaluation

This paper proposes a design procedure of multi-item mixed-line production system in which various jigs, tools, capable facilities as well as skilled workers are equipped to enhance the capability of product variety. Major traditional technologies for the design of such production systems are classified into two categories, i.e. Line Balancing (LB) procedures which focus on balanced allocation of production resources, and Job Sequencing (JS) procedures which focus on balanced utilization of resources. In this paper, a conventional algorithm minimizing the number of stations is considered for the LB procedure, and an effective sequencing logic based on the ordinary Target Chasing Method (TCM) is proposed as a JS procedure for stable production as well as line stop aversion. Both of these procedures are integrated in terms of a two-stage hierarchical design procedure and its performance is investigated by simulation experiments under various conditions to ascertain its relevance.     

Improved confidence limits for low-dose carcinogenic risk assessment from animal data

An improved procedure is presented for estimating low-dose risks from dichotomous animal data. Based on the multistage model of cancer, the procedure gives a maximum likelihood fit to the experimental data. Because the model is approximately linear in the low-dose range, the procedure may be considered to be a generalized method for linear extrapolation which uses all of the data. The extrapolation procedure is different from an earlier procedure based upon the multistage model in that two improved methods are put forward for calculating statistical confidence limits. (One is a linearized approximation of the other.) A further innovation is a recommendation for the integration of several data sets in the calculation of risk levels.     

Improved method for roadside barrier length of need modeling using real-world trajectories

The 2011 AASHTO Roadside Design Guide (RDG) contains perhaps the most widely used procedure for choosing an appropriate length of need (LON) for roadside barriers. However, this procedure has several limitations. The procedure uses a highly simplified model of vehicle departure, and the procedure does not allow designers to specify an explicit level of protection. A new procedure for choosing LON that addresses these limitations is presented in this paper. This new procedure is based on recent, real-world road departure trajectories and uses this departure data in a more realistic way. The new procedure also allows LON to be specified for a precisely known level of protection – a level which can be based on number of crashes, injury outcomes or even estimated crash cost – while still remaining straightforward and quick to use like the 2011 RDG procedure.     

Heuristic procedures for the parallel machine problem with tool switches

We address the problem of scheduling a set of parts with given processing times and tool requirements on m identical parallel machines. The problem is to find an allocation of the machines to the parts, a proper sequence for the parts assigned to each machine, and a corresponding tool-switching plan for each machine so as to minimize the makespan. It is demonstrated that this problem is np-hard , and three heuristic procedures are proposed for solving it. The first procedure is a multi-start local improvement procedure, and various neighborhood structures and search strategies are discussed in this context. The second procedure is a variation of the list-processing routine that is commonly used for the parallel machine problem. Finally, the last procedure is an adaptation of a well-known constructive procedure for the k -travelling salesman problem. Results of a limited computational experiment are also presented in which the makespan obtained via each heuristic procedure is compared with a proposed lower bound and with other reference values.     

Sequential inspection for SPC-quarantined production

The problem of inspecting process output in response to a control chart out-of-control signal is addressed. A Bayesian sequential inspection procedure is developed for the case where units can be inspected in reverse of the order in which they were produced. The inspection procedure is used to determine whether the 'out-of-control' production is of sufficiently poor quality to merit further inspection, while simultaneously attempting to curtail inspection by identifying the point at which the process went out-of-control. Examples are presented, and Monte Carlo analysis is used to demonstrate the performance characteristics of the inspection procedure.     

Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems

This paper presents a simple procedure for modifying the dynamic coupled soil-pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used. The solution method is simpler than an alternative suggested by Park¹⁵ and has a direct physical interpretation. This stabilized procedure is efficient in numerical time domain analysis of soil-pore fluid occurring in earthquake and consolidation problems. Numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure.     

Automated retrieval and ranking of similar parts in agile manufacturing

The environment considered is an agile enterprise where manufacturing partners share product related data to come up with new, customized, and high quality products at minimal leadtimes. Given this context, this paper addresses the problem of identifying existing parts that are similar, in one or many characteristics, to a new part at the design stage. The proposed method is based on the principles of group technology (GT), and on the definition of the neighborhood of similarity of critical design attributes. A two-step procedure is proposed: (1) a search procedure, which acquires and processes the designer's search intent to retrieve similar parts; and (2) a sorting procedure, which ranks these parts in order of their similarity to the candidate part. Both procedures are based on GT codes, while the second can employ more detailed critical design information. This information is assumed available in the product databases of distributed partners, and can be generated via an existing GT design processor. The approach employs a systematic procedure to combine independent similarity indexes to a unique measure for sorting. A software system using object-oriented technology has been developed to implement the procedure.     

On the Resource Constrained Project Scheduling Problem

A procedure is presented for establishing lower bounds on the minimum schedule duration for resource constrained projects. This procedure consists of finding the smallest time which satisfies each of four lemmas which are established. The results of testing this procedure on a sample of SO simulated projects are summarized.     

Optimal design and integration of solar systems and fossil fuels for sustainable and stable power outlet

Widespread industrial utilization of solar energy is an important goal that requires overcoming several technical challenges. One of the key hurdles is the need to address the temporal fluctuations in incident solar power (e.g., on an hourly basis or seasonally) which lead to variations in the outlet power. This work is aimed at the development of a systematic design procedure providing a stable power outlet while using solar systems. First, the dynamic performance of solar collectors is parametrically modeled. Next, an optimization formulation is developed as the basis for the design procedure which accounts for the integration of solar and fossil energy sources in a power system. The procedure determines the optimal mix of energy forms (solar vs. fossil) to be supplied to the process, the system specifications, and the dynamic operation of the system. The developed procedure includes gathering and generation of relevant solar and climatic data, modeling of the various components of the solar, fossil, and power generation systems, and optimization of several aspects of the hybrid system. A case study is solved to demonstrate the effectiveness and applicability of the devised procedure.     

Numerical solution of the point contact problem using the finite element method

The elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.     

Rolling horizon production planning for probabilistic time-varying demands

This paper introduces and tests a production planning procedure to be applied in a rolling horizon with probabilistic demands, based on the work of Bookbinder and Tan (1983). First, the case of no lead time for replenishment is considered and trend-seasonal demands are studied. We vary the set-up cost, order cycle and number of periods in the future for which demand forecasts are available. The procedure is compared to that of Silver (1978) in terms of cost performance, percentage of demand short/period and percentage of periods with stock-outs. Each approach appears to have merit. The proposed procedure generally yields a lower solution cost, while Silver's procedure usually has a lower percentage of demand short/period and a smaller percentage of periods with stockouts. Differences between the two procedures were relatively insensitive to which of three lot-sizing rules was employed within them. Finally, we further extended our procedure to consider non-zero lead times for replenishment and different demand patterns, particularly the normal distribution.     

Centralized Scheduling and Priority Implementation Heuristics for a Dynamic Job Shop Model

The problem considered is the scheduling of a job shop with job due dates, intermittent job arrivals, and statistical processing times. Centralized scheduling uses a sequence of static problems for generating priorities at review times. A multi-pass heuristic program, which has proven effective in earlier research, is applied to the up-dated static scheduling problem at each review time. A procedure is proposed for implementing priorities on the shop floor between review times. The procedure is expressly designed to integrate the scheduling of newly arriving jobs to modify the schedule. In simulation experiments using tardiness statistics for evaluation, centralized scheduling and the proposed implementation procedure proved to be an extremely effective combination. Comparison with another procedure that gives the centralized schedule precedence over new arrivals indicates the importance of the implementation procedure when periodic centralized scheduling is used in a dynamic situation.     

On the sensitivity of running-fluid NMR magnetometers

A new procedure for determining the sensitivity of running-fluid NMR magnetometers is considered. The procedure is based on mathematical processing of experimental data that are related to measuring the gradient of a nutation-line slope at the point at which an inverted NMR signal crosses zero. The procedure allows one to determine the sensitivity of running-fluid NMR magnetometers for resonance frequencies of magnetic-field measurements within a range of 0.5 Hz to 840 MHz.     

Stochastic response of nonlinear system in probability domain

A stochastic averaging procedure for obtaining the probability density function (PDF) of the response for a strongly nonlinear single-degree-of-freedom system, subjected to both multiplicative and additive random excitations is presented. The procedure uses random Van Der Pol transformation, Ito’s equation of limiting diffusion process and stochastic averaging technique as outlined by Zhu and others. However, the equations are rederived in generalized form and arranged in such a way that the procedure lends itself to a numerical computational scheme using FFT. The main objective of the modification is to consider highly irregular nonlinear functions which cannot be integrated in closed form and also to solve problems where analytical expressions for probability density function cannot be obtained. The procedure is applied to obtain the PDF of the response of Duffing oscillator subjected to additive and multiplicative random excitations represented by rational power spectral density functions (PSDFs). The results are verified by digital simulation. It is shown that the procedure provides results which compare very well with those obtained from simulation analysis not only for wide-band excitations but also for very narrow-band excitations, which are weak (when normalized with respect to mass of the system.) This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

A parallel domain decomposition boundary element method approach for the solution of large-scale transient heat conduction problems

This paper develops a parallel domain decomposition Laplace transform BEM algorithm for the solution of large-scale transient heat conduction problems. In order to tackle large problems the original domain is decomposed into a number of sub-domains, and a Laplace transform method is utilized to avoid time marching. A procedure is described which provides a good initial guess for the domain interface temperatures, and an iteration procedure is carried out to satisfy continuity of temperature and heat flux at the domain interfaces. The decomposition procedure significantly reduces the size of any single problem for the BEM, which significantly reduces the overall storage and computational burden and renders the application of the BEM to large transient conduction problems on modest computational platforms. The procedure is readily implemented in parallel and applicable to 3D problems. Moreover, as the approach described herein readily allows adaptation and integration of traditional BEM codes, it is expected that the domain decomposition approach coupled to parallel implementation should prove very competitive to alternatives proposed in the literature such as fast multipole acceleration methods that require a complete re-write of traditional BEM codes.     

Solution of Riemann problems for hyperbolic systems of conservation laws modeling two-phase flow in general stream tube geometries

This paper describes a procedure for the analytical solution of Riemann problems for multi-component, two-phase flow in general stream tube geometries in porous media. The procedure is first described for a scalar hyperbolic conservation law modeling waterflooding of an oil reservoir. Thereafter, it is easy to generalize the procedure to Riemann problems for multi-component, two-phase systems of hyperbolic conservation laws, for which the associated 1D Riemann problem has a known solution. The procedure is described for both constant flow rate and constant boundary pressures as imposed Riemann data. In the latter case, the flow rate is time-dependent and its novel analytical solution is constructed in this paper, clearly demonstrating a non-trivial impact of the flow geometry on the solution.