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    Overview of Statistics: Sampling & Job Satisfaction

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    Provide an overview of the contents of this article and apply the concepts to the Job Satisfaction survey (Job Satisfaction Survey is listed below article). It is important to cover the concept of the techniques used to estimate sample size.

    Sampling Size: What the Books Don't Tell You
    Trying to develop the perfect sampling strategy in an imperfect world is not easy; especially when the cost of monitoring is increasing looked at skeptically as non-value-adding activity. However, this is precisely the reason why arriving at a practical, workable sampling strategy that changes as the product lifecycle changes is so critical in today's fabs. Kathy Hall of Hewlett-Packard's Technology Development Operation examined the issue of sample size determination and presented her findings at the first annual ISMI Semiconductor on Manufacturing Effectiveness in Austin, hosted by Sematech,

    One of the main problems with taking a "textbook" approach to data sampling is the fact that these strategies are typically based on a normal, Gaussian distribution of defects. Unfortunately, defects are often randomly distributed in time, space and cause. They can be clustered and independent of one another. Based on this behavior, the goal, according to Hall, is to then estimate a population parameter with minimal variation. However, business realities are such that there are time or event-dependent events. There are spatial, nested effects. And therefore the more important goal is to quickly make good decisions, not to estimate parameters. So the metrology expert or statistician must accept some management responsibility for asking a number of important questions with respect to the action that will be made based on the data, why the data is being collected, and when the sampling plan will be reviewed or changed. In other words, distillation and analysis of the importance of the data is the most critical step in the process.

    The volume of data being analyzed changes throughout the product lifecycle - from idea stage to development, prototype, release and manufacturing, to the mature stage. In the idea stage, a large amount of data is collected to observe behavior and understand what data is required and to determine how it should be collected. In the development phase, the metrology methods are often developed concurrently with the product or process. Sometimes a "measure everything" mentality takes over, because it is often not clear which factors arc important? Moving into the prototype phase, the engineer focuses in on data for metrology optimization, data to detect and eliminate spatial issues, and data to characterize and optimize the processes.

    Once a product moves into manufacturing, the data volume often shifts drastically down. The priority shifts from process optimization and characterization to sampling only on an as-needed basis. Sampling is performed for process control reasons and to maintain process stability. It is done to attain adaptive control and meet regulatory requirements. Gone are the testing phases and exploring new parameters.

    In production operation, of course, optimal performance from the metrology tools is demanded. Therefore, the tool must be quantified for measurement uncertainty and this uncertainty' must he understood by all users. Tool-to-tool uncertainty must also be understood for all metrology systems. It is also key to identify and eliminate spatial metrology effects from the stage, wafer position, lens, etc.

    During process development and characterization, basic tool characterization, recipe development and optimization is performed. Wafer and tool zone specific behavior must be neutralized. Variance components should be identified. The control scheme (adaptive control, process control) should he identified as well. Because through put is always an issue, it is also important to identify time and usage aspects of process outputs. The dynamic aspect of sampling should not be underestimated. As processes mature, fewer measurements are required and should be performed to check stability, not to gain understanding. Processes are less variable, so there is less to control, and many variables will not impact product performance during the mature stages. For these reasons, Hall suggests using an infrequent, extensive audit for baseline monitoring. She warns against assuming failures occur randomly on individual units. Failures, she noted, are often tied to equipment age and often follow maintenance procedures.

    Finally, sampling strategy must consider failure modes, the reason for the sample, possible resulting actions and time and spatial patterns. It's important to verify specifications on individual die and not on a summary statistic. Hall emphasized that metrologists should know the impact of metrology error. She also recognized the significance of company management culture. She emphasized asking the right questions, "Do you want to know how many to sample to meet fixed criteria? Or do you want to maximize the amount of useful information, given the capacity of the metrology tool and competing business needs?"


    1. What decision will you make when you have this data?
    2. Are the criteria set for raw data or a summary statistic?
    3. What actions will you take based on the decision?
    4. Why do we need to collect this data?
    5. When will we review the sample plan to see if our needs for the data have changed?

    (see data in attached file)

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    Solution Summary

    By addressing the questions, this solution overviews of the contents of the article: "Sampling size: What the books don't tell you." It then applies the statistical concepts to the Job Satisfaction survey. It overviews the the techniques used to estimate sample size e.g. sample size, data collection, summary statistics, etc.