Normal Distribution in Statistics
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Questions and Answers

What is the main application of normal distribution in manufacturing?

  • Product design
  • Material testing
  • Statistical analysis
  • Quality control (correct)

    • What is the mean lifetime of car tires in the given example?

  • 80,000 km (correct)
  • 60,000 km
  • 70,000 km
  • 90,000 km

    • What is the standard deviation of the car tires' lifetime in the example?

  • 4,000 km (correct)
  • 2,000 km
  • 6,000 km
  • 8,000 km

    • What is the logarithm of x in a lognormal distribution?

    <p>Normally distributed</p> Signup and view all the answers

    What is the typical application of lognormal distribution?

    <p>Metal powder for 3D printing</p> Signup and view all the answers

    What causes 'stackup' in manufacturing?

    <p>All of the above</p> Signup and view all the answers

    What is the main reason for process variations in manufacturing?

    <p>Multiple factors</p> Signup and view all the answers

    What type of variation can be isolated and possibly predicted or removed?

    <p>Systematic variation</p> Signup and view all the answers

    What is the purpose of understanding variation in manufacturing?

    <p>To improve product quality</p> Signup and view all the answers

    What is the main advantage of using normal distribution in quality control?

    <p>Accurate prediction of defects</p> Signup and view all the answers

    What is the definition of quality?

    <p>The ability of a product to consistently meet customer needs</p> Signup and view all the answers

    What is the term for the allowable or permissible limit of variation of a process?

    <p>Tolerance</p> Signup and view all the answers

    What is the goal of measuring variation in a process?

    <p>To quantify the variation statistically</p> Signup and view all the answers

    What is the normal distribution used for in understanding variation?

    <p>To understand the variation of a process</p> Signup and view all the answers

    What is the term for the natural outcome of a process?

    <p>Process variation</p> Signup and view all the answers

    What is the purpose of monitoring variation?

    <p>To maintain process control</p> Signup and view all the answers

    What is the term for the probability distribution of the occurrence of a data?

    <p>Normal distribution</p> Signup and view all the answers

    What is the result of 6 standard deviations from the mean?

    <p>3.4 defects per million</p> Signup and view all the answers

    What is the customer's role in understanding variation?

    <p>Their perceived 'good quality' should be related to the specifications of the product</p> Signup and view all the answers

    What is the importance of understanding variation in manufacturing?

    <p>It is essential</p> Signup and view all the answers

    What is the primary cause of random variation in a process?

    <p>Uncontrollable factors</p> Signup and view all the answers

    What is the relationship between molecular weight of polymer and accuracy in injection molding?

    <p>Direct relationship</p> Signup and view all the answers

    What is the definition of accuracy in measurement?

    <p>The difference between the measured and true value</p> Signup and view all the answers

    What is the relationship between depth of cut and surface roughness in machining?

    <p>Direct relationship</p> Signup and view all the answers

    What is the definition of repeatability in measurement?

    <p>The ability to tell the same story many times</p> Signup and view all the answers

    What is the definition of resolution in measurement?

    <p>The minimum increment that can be measured</p> Signup and view all the answers

    What is the relationship between injection pressure and accuracy in injection molding?

    <p>Direct relationship</p> Signup and view all the answers

    What is the relationship between tool life and accuracy in machining?

    <p>Direct relationship</p> Signup and view all the answers

    What is the primary characteristic of random variation?

    <p>Steady but random</p> Signup and view all the answers

    What is the general model of process variation?

    <p>Both random and systematic variation</p> Signup and view all the answers

    Study Notes

    Variation and Quality

    • Variation refers to the change in outcome of a process, while quality is the ability of a product or service to consistently meet customer needs.
    • Tolerance is the allowable or permissible limit of variation of a process.

    Measure of Quality

    • Quality is measured by how well a product or service meets customer needs, which should be related to the specifications of the product.
    • Quantifying variation statistically is important to understand the measurement of variation from a process.

    Normal Distribution

    • A normal distribution helps quantify the outcome of a process and understand the measurement of variation from a process.
    • It is a probability distribution of the occurrence of data, and naturally occurring phenomena tend to approximate the normal distribution.
    • In manufacturing, normal distribution is a means of quality control.

    Normal Distribution Examples

    • Car tires can be modeled using a normal distribution, with a mean lifetime and standard deviation.
    • The normal distribution can be used to calculate the fraction of tires that can be expected to wear out within a certain range.

    Other Types of Distributions

    • Lognormal distribution: the logarithm of x is distributed normally, used in applications such as metal powder for 3D printing.
    • Lognormal distribution is used when the data is not symmetric around the mean.

    Process Sensitivity

    • Process sensitivity refers to the factors that affect process variations, including process, material, equipment, operator, environment, and measurement.

    Factors Affecting Process Variations

    • Process: inherent capability, change of settings
    • Material: raw material variation, defects
    • Equipment: tool wear, equipment maintenance or calibration
    • Operator: procedure, distraction, fatigue
    • Environment: temperature, humidity, vibration
    • Measurement: capability of the tool (resolution), need for calibration

    Types of Variation

    • Systematic ("special cause") variation: influences of process parameters or external disturbances that can be isolated and possibly predicted or removed.
    • Random ("common cause") variation: caused by uncontrollable factors that result in a steady but random distribution of output around the average of the data.

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    Related Documents

    Variation and Quality - ME 134 2SAY2324 L23

    Description

    This quiz covers the concept of normal distribution, its application in quality control, and related probability density functions and cumulative distribution functions.

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