Economic design of the specification region for multiple quality characteristics

Economic specification limits have typically been developed on the basis of a single quality characteristic. From the viewpoint of the customer, products are often evaluated based on multiple quality characteristics. The specification region for multiple quality characteristics must be determined on an economic basis where we minimize the total loss to both the producer and the customer and thus to the whole society. In this paper a multivariate normal distribution is considered for the quality characteristics. The specification region is given by truncating the multivariate normal distribution. We present the optimization model to develop the specification region for multiple quality characteristics based on the framework of multivariate quality loss function.     

Optimization of engineering tolerance design using revised loss functions

Engineering tolerance design plays an important role in modern manufacturing. Both symmetric and asymmetric tolerances are common in many manufacturing processes. Recently, various revised loss functions have been proposed for overcoming the drawbacks of Taguchi's loss function. In this article, Kapur's economic tolerance design model is modified and the economic specification limits for both symmetric and asymmetric losses are established. Three different loss functions are compared in the optimal symmetric and asymmetric tolerance design: a revised Taguchi quadratic loss function, an inverted normal loss function and a revised inverted normal loss function. The relationships among the three loss functions and process capability indices are established. A numerical example is given to compare the economic specification limits established by using the three loss functions. The results suggest that the revised inverted normal loss function be used in determining economic specification limits.     

Quality assurance and staff training

“G.M.P. Trends” is an american magazine publishing extracts of inspection reports: It is an official statement of errors, faults, omissions observed in the US pharmaceutical industry as regard good manufacturing pratices. A comparison between the “G.M.P. Trends” and the (“BPF”) “Bonnes Pratiques de Fabrication” (Good manufacturing pratices) points out the errors, defects or omissions observed and thus enable t o remodel staff training (1) (2).

Staff training is dealt with different chapters of the “BPF” staff, documents, samples, computerisation and risk generating product. Staff training is regarded as a mean for action: objectives, priority aims, choices and exchanges are to be defined.

We intend t o develop an example of answer to staff training needed in the pharmaceutical industry. The aim of this answer is the implementation of the good manufacturing pratices in a system which guarantees quality. This training is carried out within the framework of the directives and recommandations of the W.H.O. and U.N.I.D.O. with as a target the manufacturing of tablets of essential drugs.     

Combining cost-based and rule-based knowledge in complex resource allocation problems

A major challenge in the formulation of optimization models for large-scale, complex operational problems is that some data are impossible or uneconomical to collect, producing a cost model that suffers from incomplete information. As a result, even an optimal solution may be “wrong” in the sense that it is solving the wrong problem. In many operational settings, knowledgeable experts will already know, at least approximately, how a model should behave, and can express this knowledge in the form of low dimensional patterns: “high powered locomotives should pull intermodal trains” (because they need to move quickly) or “loaded C-141s should not be flown into Saudi Arabia” (for maintenance reasons). Unlike the literature on inverse optimization which uses observed actions to train the parameters of a cost model, we used exogenous patterns to guide the behavior of a model using a proximal point term that penalizes deviations from these patterns. Under the assumption that the patterns are derived from rational behaviors, we establish the conditions under which incorporating patterns will reduce actual costs rather than just the engineered costs. The effectiveness of the approach is demonstrated in a controlled, laboratory setting using data from a major railroad.     

Qualitative Ordinal Scales: The Concept of Ordinal Range

Many practical problems of quality control involve the use of ordinal scales. Questionnaires planned to collect judgments on qualitative or linguistic scales, whose levels are terms such as “good,” “bad,” “medium,” etc., are extensively used both in evaluating service quality and in visual controls for manufacturing industry. In an ordinal environment, the concept of distance between two generic levels of the same scale is not defined. Therefore, a population (universe) of judgments cannot be described using “traditional” statistical distributions since they are based on the notion of distance. The concept of “distribution shape” cannot be defined as well. In this article, we introduce a new statistical entity, the so-called ordinal distribution, to describe a population of judgments expressed on an ordinal scale. We also discuss which of the traditional location and dispersion measures can be used in this context and we briefly analyze some of their properties. A new dispersion measure, the ordinal range, as an extension of the cardinal range to ordinal scales, is then proposed. A practical application in the field of quality is developed throughout the article.     

Solving Quadratic Assignment Problems by 'Simulated Annealing'

Recently, an interesting analogy between problems in combinatorial optimization and statistical mechanics has been developed and has proven useful in solving certain traditional optimization problems such as computer design, partitioning, component placement, wiring, and traveling salesman problems. The analogy has resulted in a methodology, termed “simulated annealing,” which, in the process of iterating to an optimum, uses Monte Carlo sampling to occasionally accept solutions to discrete optimization problems which increase rather than decrease the objective function value. This process is counter to the normal 'steepest-descent' algorithmic approach. However, it is argued in the analogy that by taking such controlled uphill steps, the optimizing algorithm need not get “stuck” on inferior solutions.

This paper presents an application of the simulated annealing method to solve the quadratic assignment problem (QAP). Performance is tested on a set of “standard” problems, as well as some newly generated larger problems (n = 50 and n = 100). The results are compared to those from other traditional heuristics, e.g., CRAFT, biased sampling, and a revised Hillier procedure. It is shown that under certain conditions simulated annealing can yield higher quality (lower cost) solutions at comparable CPU times. However, the simulated annealing algorithm is sensitive to a number of parameters, some of whose effects are investigated and reported herein through the analysis of an experimental design.     

An Objective-Oriented Rating System of Vendor Quality Performance

This article establishes a rating system for vendor's performance from the orientation of customer satisfaction by objective-orientation driving. Its purpose is to provide a methodology of “how to integrate the capability between vendor and manufacturer and to apply different strategies under the needs of quality improvement.”

The study is undertaken to specify the interaction and the mutual movement among the three groups in the supply chain “Vendor-Manufacturer-Customer” and to integrate the results of four factors: incoming inspection, performance of line reject, service quality of vendor, and product reliability. It tries to transform these factors into measurable, quantitative, just-in-time (JIT) parameters that are utilized in the planning and establishment of this rating system of vendor's performance. The concept of objective orientation is adopted in the “performance” calculations.

We obtain a very satisfactory completeness, flexibility, effectiveness, and sensitivity of parameters-to-model from the results of simulation and demonstration. The multi-parameters rating system of this study can be very beneficial to manufacturers in selecting the best vendor and in driving quality improvements.     

Validation and calibration of a lateral confinement model for long-rod penetration at ordnance and high velocities

In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, “How wide should the target be to exert enough confinement?” For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement.

We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius “b” at which σ_r (b) = 0 (σ_r = radial stress component). We did this for three cases: ceramic targets, metal targets, and ceramic targets confined in a metal casing. Generally, σ_r (a) is a decreasing function of “a” (“a” = expanding cavity radius, and σ_r (a) = the stress needed to continue opening the cavity). In the usual cavity expansion problem b → ∞, σ_r (a) = const., R =−σ_r (a) (R = resistance to penetration). For finite “b” we estimate R by averaging σ_r (a) over a range o ≤ a ≤ a_r, (where a_r, the upper bound of the range, is calibrated from computer simulations).

We ran 14 computer simulations with the CTH wavecode and used the results to calibrate a_r for the different cases and to establish the overall validity of our approach.

We show that generally for D_t/D_p > 30, the degree of confinement is higher than 95% (D_t = target diameter; D_p = projectile diameter; and degree of CONFINEMENT = R/R_∞; R∞ = resistance of a laterally infinite target). We also show the tensile strength of ceramic targets (represented by the spall strength P_min) has a significant effect on the degree of confinement, while other material parameters have only a minor effect.     

Strategic Allocation of Inspection Effort In A Serial, Multi-Product Production System

For a multi-stage production system, optimal location of inspection activities is an important consideration in minimizing the inspection-related and salvage costs. Set-up and inventory carrying costs also become important factors when several products are produced on the same line due to the product changeovers involved.

In this paper we discuss the effect of these additional costs (set-up and inventory carrying) on the inspection strategy, i.e., “all or none” versus partial inspection. We suggest a shortest path heuristic to determine the strategic location of inspection activities and the production lot sizes.     

Rents, Rights N'Rhythm: Cooperation, Conflict and Capabilities in the Music Industry

The need for better informed copyright policy and management is a huge problem because of the enormous and growing size and scope of the creative industries. In this paper we challenge the prevailing thinking dominating the theoretical literature on the economics of copyrights. By integrating the very real effect of cooperation (strategic interaction and creative interdependence) and conflict (asymmetric relationships in terms of interests, financial dominance, power and capabilities) throughout the economic system in generating value and appropriating rent from music copyrights, we argue how prevailing theory on copyright can be improved by integrating it into a framework of New Institutional Economics. Focus is on the interplay between (i) the “institutional environment” (or “rules of the game”) with respect to the regulation of copyrights underpinned by the economic rationales; and (ii) the “institutions of governance” (or the “play of the game”) with respect to the specific institutional mechanisms in organizing the creation and distribution of value and revenue from music copyrights, and with respect to royalty management.     

A note on capacitated lot sizing with setup carry over

The “capacitated lot sizing problem with setup carry over” is based on the well known “capacitated lot sizing problem” and incorporates the possibility of preserving a setup state between successive periods. The approach at hand is to decompose the problem using Lagrangean relaxation. Subproblems are to be solved optimally employing dynamic programming techniques. Subgradient optimization guides the approach to heuristic solutions of the original problem. The present paper shows that this algorithm does not necessarily provide the optimal solution to the subproblems. The algorithm's flaw is corrected such that it allows to solve the subproblems optimally.     

Viewing Strategy and Window Effects on Dynamic Visual-Inspection Accuracy

Equally-spaced product units, moving on a belt at a uniform velocity, were exposed for visual inspection over a fixed viewing window. Viewing windows were equal to the product unit interspacing and twice this distance to give respectively 1 and 2 product units within the window. Three different belt speeds were used. Subjects performed short runs of visual inspection using their self-directed strategies of viewing the sequence of product units and then these subjects repeated all conditions of this task using a “directed viewing strategy.” Improved viewing discipline was expected from this “directed” strategy and eye motion monitoring was employed to verify that the subjects used the “directed” strategy. Inspection errors of each type were observed under twelve experimental conditions. Both types of errors were found to be greater with: 1) the smaller viewing window, 2) self-directed viewing strategies in contrast to the “directed” strategy, and 3) higher belt velocities. Contrasts were also made between error types and between high- and low-performing subject groups. Inferences on the apparent cost of each error type were made from these data and compared with rational objectives. Economic implications are shown for these viewing-strategy and viewing window effects.     

Imaging X-ray fluorescence spectroscopy: laboratory measurements

Following on from the proof-of principle measurements of Martin et al. (X-ray Spectrom. 28 (1999) 64) we further describe the development of an imaging X-ray fluorescence (IXRF) spectrometer with no moving parts. Our laboratory system is based on a microchannel plate (MCP) “lens”, a CCD X-ray detector with good sub-keV quantum efficiency and a conventional electron bombardment X-ray source. We have used this equipment to form images of a standard XRF target, demonstrating that “elemental maps” (images of the target in the characteristic X-rays of one particular element) may be formed with sub-millimetre resolution. In addition to fluorescent X-rays, we detected X-rays which had been Bragg reflected from the polycrystalline aluminium substrate of the target. It is possible that the resulting “Bragg images” may be exploited to measure spatially varying strain, manifested as lattice distortion, introduced, for example, by thin films deposited on the surface of a sample.     

Allocating resources to research and development projects in a competitive environment

Firms who are involved in R&D activities are often “racing” against competitors to become the lirst to attain the desired breakthrough. The goal might indeed be to "beat" the competitors in as many such R&D races as possible. However, when resources are limited, and competitors' budget allocation to these R&D activities unknown, the challenge becomes to devise a method of allocating R&D budgets to activites in a strategically “optimal” way. We model the decision problem of a firm wishing to allocate a fixed budget among several activities, so as to maximize the expected profit from the activities it captures. The probability of capturing an activity is an increasing function of one's allocation to it, and a decreasing function of the competitor's allocation. For a specific plausible capture-probability function, we find the optimal allocation between two activities conditional on the competitor's allocation (the “reaction curve”). Nash and Stackelberg equilibria for that model are then characterized. Wc also briefly explore the implications of more general, or different, capture-probability functions.     

Virtual Inspection: Optimum Sample Size for POD Experiment

Engineers responsible for life prediction and inspection of aerospace components are often tasked with demonstrating the capability of an inspection. It is extremely important to establish that the quality of the particular nondestructive inspection procedure is good enough to satisfy the safety requirements specified by the Federal Aviation Administration and/or the Military Organizations. The established and accepted metric for characterizing the capability of a nondestructive evaluation procedure is the probability of detection (POD) as a function of the crack size. Typically, such a demonstration requires the fabrication of a number of specimens with controlled, quantified defects or cracks. Engineers planning a demonstration need to know how many specimens they should include in the test plan. Determining the number of test specimens to be produced has been more guesswork than science. Producing arbitrarily a large number of defect specimens is not a good option because producing such defect specimens is a very costly activity in most cases. On the other hand, if too few defect specimens are produced in an unplanned way the assessment of the POD function will not be good. Therefore, it is important to use a sample of appropriate minimum size that still achieves the quantitative requirement for demonstrating the capability of a nondestructive inspection scheme. In this article, we will develop a simulation-based algorithm that will help users of the nondestructive evaluation procedures to choose an optimal sample size and a test plan such that the “standard” requirement is satisfied.     

The Single Period Stochastic Plant Layout Problem

In this paper we present an optimal solution procedure for the single period stochastic plant layout problem. The procedure only requires solving a “deterministic” from-to flow matrix. This “deterministic” matrix is a weighted-average of all from-to flow matrices. Since it may be difficult to estimate the probabilities of occurrence of the various states of nature, we developed a simulation model to test the robustness of our approach. For over 26,000 problems examined, the average error of using our approach was very small, only about one-sixth of one percent.     

Dual-Response Surface Optimization: A Weighted MSE Approach

Dual-response surface methodology is a powerful tool for simultaneously optimizing the mean and the variance of responses in quality engineering. In this article, we suggest a weighted mean squared error (MSE) approach to improve the optimization procedure. In addition, we propose a data-driven approach to determine the weights when the prior information is vague. This is based on the idea of an “efficient curve.” Examples are given to illustrate the superiority of the proposed method, as compared with other existing procedures.     

Randomized Complete Block Designs in Industrial Studies

Product quality is a function of several performance characteristics. If it is desired to optimize a single performance characteristic of the product, traditional mathematical models may be used. But, when all the optimum performance characteristics need to be integrated into the product then the problem has to be formulated as a multi-objective optimization problem. In most of the real life situations, the customers' requirements are fuzzy in nature, e.g., minimum surface roughness or maximum strength. This inexact information creates a problem, i.e., where to draw a line between what is required and what is not. This inexactness in the nature of the goals can be studied well through the use of fuzzy set logics.

In the present work, a multi-objective optimization model using the concept of fuzzy set logic is developed. A case study “Obtaining an optimal set of V-process parameters that yields the optimum composite quality features to Al-11% Si alloy castings” is also included in this paper.     

An upside-down normal loss function-based method for quality improvement

Traditional measures of process quality do not offer much information on how much better or worse a process is when finding optimal settings of a given problem. The upside-down normal loss function (UDNLF) is a weighted loss function that provides a more reasonable risk assessment to the losses of being off-target in product engineering research. The UDNLF can be used in process design and optimization to accurately reflect and quantify the losses associated with the process in a way which minimizes the expected loss of the upside-down normal (UDN). The function has a scale parameter which can be adjusted by the practitioners to account for the actual percentage of materials failing to work at specification limits. In this article, the ‘target is best’ case is addressed to estimate the expected loss of UDN due to variation from target in the robust process design and response surface modelling context. An approach is proposed to find the control factor settings of a system by directly minimizing the expected loss. The procedure and its merits are illustrated through an example.     

ECONOMIC PRODUCTION QUOTAS FOR PULL MANUFACTURING SYSTEMS

We consider the problem of using “safety capacity” to ensure due date integrity in a pull manufacturing system and quantify the basic tradeoff between lost revenue opportunity and overtime costs. In this context, we address the question of when it is economically attractive to use “under capacity scheduling” and the problem of setting economic production quotas.

We develop four models for addressing the quota setting problem. The first three assume that quota shortfalls cannot be carried over to the next regular time production period. Models 1 and 3 assume that these shortages are made up on overtime and incur fixed or fixed plus variable costs. Model 2 does not use a capacity buffer and treats shortages as lost sales. Finally, Model 4 assumes that shortages can be backlogged to the next regular time production period at a cost. For this model, we compute both an optimal quota and an overtime “trigger,” which represents the minimum shortage for which overtime is used. We give computational results that illustrate and contrast the various models.