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Abstract: Most companies maintain warranty
data bases for purposes of financial reporting and cost forecasting. In
some cases, there are attempts to extract engineering information (e.g.,
on the reliability of components) from such data bases. Warranty data bases
are frequently thought of as being "dirty" and containing little useful
information. Previously published work has shown how careful application
of statistical methods can be used to extract useful information from warranty
data. Building on this previous work, this talk will describe methods that
are being developed for three applications of the use of warranty data.
1. Methods for early detection of potential reliability problems in
the field. Usually this would be an unanticipated failure mode or a known
failure mode occurring much earlier and with higher frequency than was
expected based on product design reliability budgeting.
2. Use of reliability-based methods to improve traditional time series
based forecasts of total warranty costs.
3. Development and verification of "transfer function" models to predict
field performance from life test data.
Examples from several different industries will be used to illustrate
the methods.
Abstract: We introduce the notion of a hazard potential as the amount of resource that an item is endowed with at inception. The item fails when the hazard potential is exhausted. The hazard potential has an exponential (1) distribution. Dependent lifetimes are a consequence of dependent hazard potentials. The hazard potential is an abstract parameter akin to parameters in physics. It provides a vehicle for conceptualizing dependence.
Abstract: Illustrations of how to do reliability
analysis, such as availability modeling, random block diagrams, and stochastic
Petri nets, using the software package SHARPE.
Abstract: Well-defined chartered projects are critical to the success of deploying Six Sigma in organizations. If this is not done well and the projects lack the appropriate metrics needed to measure progress and goal attainment, we find the time for project completion is lengthened and the magnitude of the benefits is severely impacted. Well-planned projects based on business goals and good metrics are keys to successful Six Sigma deployment. These are absolutely necessary ingredients along with strong senior management support and the right infrastructure of change agents including Champions, Masters, Black Belts and Experts. In this talk we will discuss some of the metrics we use in a wide range of processes including manufacturing, finance, and product development. Also, there will be discussion on how Honeywell monitors Six Sigma performance gains with reports to senior management at specified intervals.
Spencer B. Graves, PDF Solutions, San José, CA, USAAbstract: Leading proponents of Six Sigma recommend the use of "rolled throughput yield" (RTY) as an aggregate measure of overall process performance. This article will describe RTY in more detail and provide a procedure for computing statistical control limits. The use of RTY to construct a "forecasted Pareto" will also be discussed.
RTY is computed as the product of the yield at each step of a process. In this regard, RTY is similar to total process yield (TPY), although leading works on Six Sigma define RTY based on Poisson counts of defects, while TPY was based on binomial counts of defectives. The Six Sigma literature states that RTY estimates the proportion of units in which no defects were found. Unfortunately, for processes with scrap in a parallel step, the number of units may be different in different paths. In such cases, neither RTY nor TPY can, strictly speaking, be described as a proportion of units except in some approximate sense, although they still provide useful indices of process quality.
Forrest W. Breyfogle III, Smarter Solutions, Austin, TX, USAAbstract: The metrics of Six Sigma can be useful or they can be deceiving. For example, the equations for process capability indices are basically very simple; however, these equations are very sensitive to an input value for standard deviation. Unfortunately, users often do not realize that within Six Sigma there are typically several approaches to determine standard deviation for a given situation, which can result in the misperception of a customer relative to quantification of the capability of a process. This paper address the confusion and deception that often accompanies Six Sigma metrics along with a strategy that can improve the communication of process capability issues.
Abstract: Non-normal responses are common in many industrial experiments. When there are factors whose levels are difficult and/or costly to control, the experiment is typically run within a split-plot context. Liang and Zeger (1986) proposed the use of generalized estimating equations (GEEās) for longitudinal bio-medical studies involving both normal and non-normal responses. The application of GEEās to split plot response surface experiments is natural as one could consider the whole plot units as Īsubjectsā and the subplots as Ītimesā or Īspaceā. GEE coefficient estimates and their associated standard errors can be easily obtained using PROC GENMOD of the SAS System. In this talk we discuss the use of GEEās as well as the use of generalized linear mixed models in split plot experiments involving non-normal responses. Specifically, we consider a mixture experiment with process variables in which the responses have a gamma distribution.
Doug Montgomery, Arizona State Univ, Tempe, AZ 85297-5906, doug.montgomery@asu.eduAbstract: The effective use of response surface methodology (RSM) has been well-established as a crucial part of industrial research and development for both process development and product design. This presentation focuses on the integration of generalized linear models (GLMs) into the RSM framework. A GLM can be viewed as a unification of linear and nonlinear regression models with a flexible response variable distribution, the exponential family. This extends RSM to a much wider scope of potential applications. Several applications of GLMs in a RSM setting are presented and the usefulness of the GLM approach demonstrated. Other applications including process robustness studies are also discussed.
Abstract: This presentation will begin with a brief history of Engineering Data Analysis (EDA) in the Semiconductor Industry and move on to describe current state-of-the-art tools. A discussion of tools and techniques for incorporating artificial intelligence and neural network techniques into systems that monitor and diagnose manufacturing issues. Benefits, pitfalls and issues will be raised. The talk will conclude with a discussion of future directions and challenges for EDA.
William D. Heavlin, Advanced Micro Devices, MS 117, One AMD Place, Sunnyvale, CA 94088-3453, e-mail: bill.heavlin@amd.comAbstract: This work introduces the distance-in-space coefficients (DiSCo) model. DiSCo is a class of linear models appropriate for several responses, many factors, and roughly specified second-order interactions. The principal idea associates with each response and each factor a coordinate point in a low-dimensional space. For a given response, the main effect of a factor is stronger when its coordinates lie closer to those of the response. Further, for a given response, the interaction of a given pair of factors is stronger when the distances among the corresponding factors and response are small. Advantages revolve around DiSCo's relative parsimony, ease of visualization, and linkage to a priori cause-effect networks. The running example considers the tolerancing of an advanced semiconductor manufacturing technology.
George M. Kaupas, Advanced Micro Devices, MS 591, 5204 E. Ben White Blvd. Austin, TX 78741, e-mail: george.kaupas@amd.comAbstract: This presentation documents the creation of an open software architecture designed to facilitate the development and sharing of engineering analysis tools. The framework borrows features of web-based e-commerce solutions such as state and session management, business-logic hosting, and load balancing. Analyses written in any language can be added to the system and are driven by shared language-specific engines. The contributor only adds the fragment of code specific to the analysis. Common elements such as selection of datasets and variables are separate reusable components. The architecture handles limitations inherent in web-based applications such as browsers timing out while waiting on long analyses to complete. The user can save the configuration of an analysis and its results for reviewing or resubmitting on demand or at some future time. In this presentation, the components of this architecture and their interactions will be described, and integration of a new analysis will be reviewed, demonstrating the framework's goal of minimization of effort required to quickly respond to end-users' new analysis requests.
Abstract: Many of the methods from univariate
statitical process control carry over to the multivariate setting. The
Shewhart Xbar chart becomes the Hotelling T^2 chart; the exponentially
weighted moving average has a direct multivariate analog. Univariate likelihood-based
change-point formulations such as the maximum t similarly yield multivariate
equivalents such as the maximum T^2 directly.
There are some differences though. The univariate cusum is set up using
a target out-of-control state, but is not critically dependent on the choice
of target. The multivariate cusum by contrast does require that its target
be "in the right direction", a difficult to impossible task in high dimensions.
Another issue is that of in-control parameter estimation. Estimating
the mean vector and covariance matrix well enough for the Hotelling T^2
chart to work reliably requires large samples, but not impossibly so. EWMA
and cusum methods require much higher precision in their estimates and
consequently need much larger samples.
An interesting development is a less-parametric approach to multivariate
SPC. The i{th} anti-rank of an observation vector is the index of the measurement
providing the i{th} largest component. Many process shifts change the distribution
of the anti-ranks, leading to new SPC diagnostics. As these do not require
multivariate normality, they provide an escape from the normal straitjacket
that most multivariate SPC methods have to live within.
Abstract: We discuss methods for on-line detection and diagnosis of variation shifts in multidimensional data. The problem is motivated by applications to fixture failure diagnostics in automotive body assembly. We study various methods for detecting and diagnosing shifts in variation in one or more known directions and compare the performance of the methods with those for the general unknown direction case. Shewhart, CUSUM, and Shiryaev-Roberts type Bayesian monitoring schemes are developed for various hypotheses of interest. Their properties are studied through both asymptotic analysis and simulation.
Abstract: Many control charts used in practice have difficulty combining simplicity with high statistical power (for example, Shewhart charts are not suitable for detecting moderate changes and Cusum charts can be slow in detecting very large changes in monitored parameters. Hybride charts (like Cusum-Shewhart) or Likelihood Ratio charts can provide more reliable statistical power, but at the expense of higher complexity, especially in cases involving multivariate and/or serially correlated data. Regenerative Likelihood Ratio schemes discussed in this paper provide a balance between power and simplicity that should appeal to practitioners. We discuss a number of applications of this approach in semiconductor industry.
Abstract: The Statistical Engineering Division at the National Institute of Standards and Technology and the Statistical Methods Group at SEMATECH, have recently completed an online statistical methods handbook for engineers and scientists. The Handbook is an update of the NBS Handbook 91: Experimental Statistics a popular guide published by the Bureau of Standards in 1963. The goal of the Handbook is to help engineers and scientists incorporate statistical methods into their work as efficiently as possible. The approach is problem oriented and includes step-by-step procedures for planning experiments and analyzing data. Numerous examples using industrial data are also used to illustrate the procedures. Data analysis software developed at NIST is integrated with the Handbook and can be used to re-work examples from the text. This introductory talk gives an demonstration of the Handbook, providing an overview of its structure, scope and interactive nature.
Abstract: Besides just being an excellent online reference, the ESI Handbook can also be used as a source for constructing corporate statistical training material. I will demonstrate a tool developed by AMD that facilitates extracting pages from the ESI Handbook and including them in topic-specific online training material. This tool significantly reduces development time by allowing the user to browse the handbook (or other online training material), bookmark the desired pages and then assemble them into self-contained course. This software will be made freely available through the ESI Handbook site.
Abstract: This talk will describe experiences in linking other statistical software packages with the NIST/SEMATECH Handbook. It will describe two approaches: (1) constructing sample data files and StatFolios for use with STATGRAPHICS Plus; and (2) embedding Java applets from STATLETS directly into the Handbook's web pages. An on-line demonstration will be included.
Abstract: Data warehousing, also known as OLAP (On Line Analytical Processing), is the application of databases and tools to the analysis of data. Data warehouse system deployment is exploding worldwide, with annual expenditures expected to top $100 billion in the next few years. A typical Fortune 500 company has thousands of employees using data warehouses. In the coming years, data warehouses will be used to make decisions that affect nearly every aspect of our lives. In spite of this data warehouse revolution, awareness in the fields of Statistics and Quality and Productivity Improvement remains low. This talk discusses opportunities for applying data warehouse techniques to quality and productivity improvement.
Abstract: This paper shows how a genetic algorithm can be used to find >near-optimal Bayesian experimental designs for regression models. The design criterion considered is the expected Shannon information gain of the posterior distribution obtained from performing a given experiment compared with the prior distribution. Genetic algorithms are described and then applied to experimental design. The methodology is then illustrated with a wide range of examples: linear and nonlinear regression, single and multiple factors, and normal and Bernoulli distributed experimental data.
Abstract: Much has been written about the capability development needs of Six Sigma Master Black Belts (MBB's) and Black Belts (BB's). Very little has been written, however, about the capability development needs of Champions. This is an important oversight, since many commentators credit most of the success of Six Sigma initiatives to a unique implementation strategy, rather than to the use of a pre-existing set of statistical tools. This session will argue that making Champions "mini-MBB's" or "mini-statisticians" is missing the point, and that their development should match the skills required to perform their role, which is primarily non-technical.
Abstract: Honeywell (which includes the former AlliedSignal) has been deploying Six Sigma since late 1994. Through 1999, it has had documented benefits of $2 Billion in savings. In addition to the Masters, Black Belts, Green Belts, Lean and Total Productive Maintenance Experts, the success of the deployment strategy depends on actively involved senior leadership and Champions. Our Champions or Six Sigma leaders have been instrumental in making sure the right projects are selected that are based away from the business goals and the right people are matched against those projects whether they be Masters, Black Belts or Experts. We will discuss the roles of the Champions, their selection and training. The statistical thinking elements of the training will be discussed.
Abstract: This presentation will talk about the format of leadership training at different levels and discuss the statistical content in each. The levels of leadership training addressed are the executive level, business team level, Champion level and Site / Functional level. The statistical content for each session expands with the Champion session most heavily addressing the statistical tools. Examples of workshop content and exercises will be presented along with a recommendation for statistical training in the leadership ranks.
Jesús Cuéllar, Cuéllar and Associates Los Pinos No. 12, Casa 1, Atempan, Tlax. 90010 México, Phone: 011-52-246-6-2120, Fax: 011-52-246-6-2119 Email: jcuellarf@prodigy.net.mxAbstract: Six Sigma Champions are the key link between senior management and the Six Sigma Black Belts implementing the Black Belt improvement projects. They support the Six Sigma Black Belt candidates, ensure advancement of the improvement projects, and verify that the continuous improvement methodology is appropriately followed. While they will not carry out the statistical analyses that Black Belts are trained to do, they must understand enough of the methods and the reports that will be generated to manage differently. At Motorola University, we have developed a four-day Champions class that provides a detailed overview of the methods and reports covered in the integrated six-course statistical methods portion of our Black Belt curriculum. The Champions training focuses on the questions that management should ask Black Belts during project reviews. In turn, Black Belt candidates are taught how to answer the questions as part of their training. This presentation will provide a brief overview of the Champions training, highlighting the statistical methods training and the related management questions.
Abstract: The existing procedures for designing exponentially weighted moving average (EWMA) control charts assume known process parameters. In practice, these parameters are often unknown and replaced with unbiased estimates from an in-control reference sample. Using parameter estimates with design procedures intended for known parameters can lead to significantly deteriorated chart performance. In this paper, the assumption of known parameters is relaxed and design procedures for the EWMA chart are developed accordingly. It is shown that EWMA charts developed using these procedures outperform traditional EWMA charts when parameter estimates are used.
Abstract: In our experience, control charting
often fails. We feel this happens because the goal of the charting in the
particular application is not clearly articulated.
Classically, SPC is used to reduce process variation by aiding in the
identification of special causes which are then removed. As well, control
charting is sometimes used as a part of a feedback control scheme to signal
the need for adjustment. SPC can also provide a historical and ongoing
record to indicate whether or not the process is stable. Finally the use
of SPC may be dictated by customer requirements - anything goes as long
as your auditor cannot understand it.
It is difficult to plan for success or to tell when you have achieved
it if you do not understand what you hope to accomplish. Furthermore, a
clear statement of purpose will lead to the consideration of alternatives
to SPC and a rational decision of the best approach.
In this presentation, we explore these ideas more fully and make recommendations
as to when and how SPC should be used.
Abstract: We investigate how a non-linear price schedule can be used to influence stocking decisions and supply chain performance in single period interactions between a supplier and buyer(s). Thus, our model represents situations in which lead times are long relative to the selling season and where there is significant demand uncertainty. In contrast to much of the work that has been done on single period supply contracts, we assume that there is no opportunity for ongoing interactions between the supplier and the buyer(s) after demand information is revealed. Furthermore, we assume that there are either heterogeneous buyers that face different distributions of demand or that there is a single buyer that has better information about the distribution of demand than does the supplier.
Abstract: When selecting the best project configuration, managers are often faced with an assessment that involves multiple performance measures (e.g., cost, duration, and resource utilization). In this paper, we present a methodology designed to select the best project configuration from a set of alternative configurations. The procedure combines multiple attribute utility theory with statistic ranking and selection. We demonstrate our analysis on a simulation model of a large project that has six performance measures.
Edward G. Anderson Jr. and Douglas J. MorriceAbstract: In this paper, we investigate the dynamic behavior of service-oriented supply chains in the presence of varying demand and information sharing. Each stage holds no finished goods inventory, rather only backlogs that can be managed solely by adjusting capacity. These conditions reflect the reality of many service (and custom manufacturing) supply chains. While there is a growing literature on finished good inventory management in supply chains, relatively little exists on managing capacity in the absence of finished goods inventory. To address this problem, we develop a capacity management model for a serial chain. At each stage in the supply chain, our model relates capacity, processing, backlog, and service delays to capture the aggregate dynamic interactions between the different stages. Using control theory and signal analysis techniques, we establish the potential for a bullwhip effect an increase in demand variability as one looks up the supply chain using a one-stage model. We then study the impact of different management strategies and levels of information visibility on capacity and service delay variability in a two-state model.
Conventional wisdom strongly supports lead-time reduction in order to mitigate the bullwhip effect. We show that lead-time reduction can exacerbate the bullwhip effect in a service-oriented setting if it is not carefully coordinated with capacity adjustment. In particular, lead-time reduction generally reduces backlog variance locally but often increases backlog variances at higher stages. Further, sharing end-customer demand reduces backlog variances as in inventory supply chains but over-reliance on it relative to local information may actually increase processing variances. Finally, we show that the natural tendency to pursue system-wide process improvement by imposing uniform parameter targets across the supply chain exacerbates capacity and backlog variance at higher stages. Instead, we show that a superior policy is asymmetric, holding the bulk of system backlog at the stage closest to the customer.
Abstract: Deming introduced the concept of analytic studies in the 1960ās but he did not provide specific guidelines for incorporating the principles of experimental design in an analytic study. The aim of an analytic study is prediction that one of several alternatives will perform better than the other alternatives in the future.
Methods used to design analytic studies must be suited to a dynamic environment. Because of the effect of changing conditions, the primary source of uncertainty in an analytic study lies in identifying which variables will have the most influence on future outcomes of the product or process. Statistical theory does not provide quantification of the magnitude of this uncertainty.
This presentation will discuss extending R. A. Fisherās principles of experimental design to the environment of an analytic study. The appropriate use of experimental patterns, blocking (or planned grouping), randomization, and replication will be illustrated with examples of analytic studies. The analysis of data from analytic studies will also be presented.
Ramon Leon, U of TennesseeAbstract: We discuss how the traditional ANOVA analysis of Latin and Greco-Latin squares can lead to misleading or incomplete conclusions if the experiment is analytic rather than enumerative.
Peter John (Univ of Texas) Email: pwmj@mail.ma.utexas.eduAbstract: Engineers are often obliged to make their experimental runs in sequence. Two strategies of selecting a sequence or run order are discussed. They are: choosing a sequence to give the engineer some protection against unplanned early termination of the experiment and choosing a sequence that offers protection against time trends during the experiment.