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Understanding Variability in Process Data: Statistical Analysis Tools and Techniques

This course outlines statistical analysis tools essential for understanding variability in process data. It covers the motivation for using these tools, different types of data, and methods of data collection. Key topics include sources of variability, such as instrumentation and environmental factors, and examples of process improvements and quality monitoring. Students will learn how to classify variability patterns, utilize statistical methods for decision-making under uncertainty, and effectively present results, contributing to better understanding and management of variability in manufacturing processes.

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Understanding Variability in Process Data: Statistical Analysis Tools and Techniques

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  1. CHEE320Analysis of Process Data J. McLellan Fall, 2001

  2. Outline • motivation for statistical analysis tools • types of data • data collection • course objectives • course overview J. McLellan

  3. suppose we take a number of measurements e.g., mileage for Mercedes obtain range of values, with pattern of occurrence frequency of occurrence - histogram How does variability arise? a process perspective... Variation J. McLellan

  4. Sources of Variability • instrumentation and measurements • electronic noise • physical location of the instrument • single thermocouple for tank - impact of mixing • inconsistent sampling times / scan frequencies • models and process representation • unmodeled components become lumped as disturbances • oversimplified model form J. McLellan

  5. Sources of Variability (con’t…) • operator interventions • process disturbances • flow fluctuations - channeling • deterioration • external disturbances • from upstream units • ambient conditions • - e.g., air temperature These sources produce - • random fluctuations - “stochastic” • definite fluctuations - deterministic J. McLellan

  6. Example - Process Improvement • reactive extrusion - operating variables • screw speed • initiator type • monomer concentration • barrel temperature • which factor has the greatest impact on conversion? • repeat series of experiments • coefficient of barrel temperature varies • 1st time: 0.3, 2nd time: -0.03, … 0.05, 0.1, 0.05 • does temperature have a significant effect on conversion? J. McLellan

  7. Example - Quality Monitoring • given samples of polyethylene pellets from 3 batches • have 5 individuals take series of 4 melt index measurements • to what extent do • batch • individual • instrumentation affect the measurement obtained? • what components of variation are present? • ... J. McLellan

  8. Example - Quality Monitoring • components of variation • within group variability • measurement variation associated with individuals/procedures • between group variability - • variation between test samples from a given batch • batch to batch variability • each component may be of interest • impact on decision-making • implications for measurement procedures • broader implications - components of variation in manufacturing ANalysis Of VAriance J. McLellan

  9. Example - Quality Monitoring components of variation - batch technicians measurements J. McLellan

  10. Role of Statistical Methods 1. Decision-making in the presence of uncertainty - e.g., • has the process operation shifted? • has the environmental loading of contaminant changed appreciably? • is the mileage better? • Basis - confidence limits and hypothesis tests J. McLellan

  11. Role of Statistical Methods (con’t...) 2. “Coordinates” for Variability • provide a reference framework for classifying variability patterns • e.g., “normally distributed” - with mean and variance • e.g., “Poisson distributed” - with mean time to occurrence • STRUCTURE + CHARACTERISTIC PARAMETERS 3. Basis for “variability accounting” - transmission of variability • e.g., in measurement schemes - impact? J. McLellan

  12. Role of Statistical Methods (cont…) 4. Data “Microscope” • identify relationships in data • e.g., systematic relationship between screw speed and conversion • e.g., correlations between chemical species in air samples - “thumbprint” of a chemical plant 5. Effective presentation of results • in terms of a few key parameters or graphics J. McLellan

  13. Types of Data Discrete • variable of interest takes on a distinct set of values • examples • count data - integer values • number of defects • numbers of failures • attributes • colours • taste • course evaluations ... J. McLellan

  14. Types of Data Continuous • measurements take on a continuum of values • examples • temperature • pressure • composition • chemical examples are frequently continuous • parts manufacturing examples are frequently discrete • continuum - infinite? • Can temperature take on values in an infinite range? • Implications for certain distributions used - normal J. McLellan

  15. Data Collection The manner in which data is collected has important implications for its interpretation… Passive Collection • record process values without actively intervening in the operation • historical databases tend to be passive Active Collection - Intervention • make a series of planned moves on the process • increases information content, guarantees of “cause and effect relationships” J. McLellan

  16. Course Objectives • Why is it important to account for variability in physical analyses? • How can variability be described? • fundamentally and from data • How can variability be incorporated in decision-making? J. McLellan

  17. Course Overview • types of data • describing data • developing a framework for variability • probability • describing variability patterns from collected data • decision-making in the presence of uncertainty • quality control • empirical (data-based) modeling of (physical) behaviour J. McLellan

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