1 / 35

Chapter 9

Chapter 9. Statistical Thinking and Applications. Statistical Thinking. All work occurs in a system of interconnected processes Variation exists in all processes Understanding and reducing variation are the keys to success. Sources of Variation in Production Processes. Measurement

jeremy-boone
Download Presentation

Chapter 9

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 9 Statistical Thinking and Applications

  2. Statistical Thinking • All work occurs in a system of interconnected processes • Variation exists in all processes • Understanding and reducing variation are the keys to success

  3. Sources of Variation in Production Processes Measurement Instruments Operators Methods Materials INPUTS PROCESS OUTPUTS Tools Human Inspection Performance Machines Environment

  4. Variation • Many sources of uncontrollable variation exist (common causes) • Special (assignable) causes of variation can be recognized and controlled • Failure to understand these differences can increase variation in a system

  5. Importance of Understanding Variation time PREDICTABLE ? UNPREDECTIBLE

  6. Management Mistakes in Attempting Process Improvement • Treating as a special cause any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to common causes • Attributing to common causes any fault, complaint, mistake, breakdown, accident or shortage when it actually is due to a special cause

  7. We’re Going into Business!!! • We have a new global customer and have to start up several factories. So I need teams of 5 to do the work: • 1 production worker • 2 inspectors • 1 Chief Inspector • 1 Recorder

  8. Production Setup • Take the bag in your left hand. • Tear a 3/4” opening in the right corner. • (only large enough for one piece at a • time)

  9. Production Process 1. Production worker produces 10 pieces and places them on the napkin. 2. Each inspector, independently, counts the blue ones, and passes to the Chief Inspector to verify. 3. If Chief Inspector agrees, s/he tells the recorder, who reports it to me.

  10. Do it right the first time! Take Pride in Your Work! Be a Quality Worker!

  11. Lessons Learned • Quality is made at the top, i.e., management is responsible for the system • Rigid procedures are not enough • People are not always the main source of variability • Numerical goals are often meaningless. • Inspection is expensive and does not improve quality. • Variations exists in systems and, if stable, can be predicted

  12. Statistical Methods • Descriptive statistics • Statistical inference • Predictive statistics

  13. Review of Key Concepts • Random variables • Probability distributions • Populations and samples • Point estimates • Sampling distributions • Standard error of the mean

  14. Important Probability Distributions • Discrete • Binomial • Poisson • Continuous • Normal • Exponential

  15. Central Limit Theorem • If simple random samples of size n are taken from any population, the probability distribution of sample means will be approximately normal as n becomes large. • The mean of the distribution of sample means approaches the mean of the population distribution • The standard deviation of the distribution approaches the standard deviation of the population distribution divided by the square root of the sample size

  16. Factors to Consider When Designing a Study • What is the objective of the study? • What type of sample should be used? • What possible error might result from sampling? • What will the study cost?

  17. Sampling Methods • Simple random sampling • Stratified sampling • Systematic sampling • Cluster sampling • Judgment sampling

  18. Sampling Error • Sampling error (statistical error) • Nonsampling error (systematic error) • Factors to consider: • Sample size • Appropriate sample design

  19. Design of Experiments • A test or series of tests to compare two or more methods to determine which is better, or to determine levels of controllable factors to optimize the yield of a process or minimize the variability of a response variable. • Factorial experiment • Analysis of all combinations of factor levels to understand main effects and interactions

  20. Excel Descriptive Statistics Tool • Tools…Data Analysis… Descriptive Statistics

  21. Excel Histogram Tool • Tools…Data Analysis…Histogram

  22. Process Capability • The range over which the natural variation of a process occurs as determined by the system of common causes • Measured by the proportion of output that can be produced within design specifications

  23. The Process (1 of 2) • Over time, the output of any process will have a certain amount of natural or inherent variability • This is also referred to as random or common variability • This variability is due to countless minor factors and is assumed to be out of management’s control in the short run, i.e., it is something you have to live with

  24. Mean The Process (2 of 2) • The distribution of the output of a process has a mean, , and a standard deviation, ; it can have a wide variety of shapes Processdistribution

  25. Process Capability (1 of 3) • When selecting a process to perform an operation on a particular item, the inherent variability of process should be compared to the tolerance (range of output) allowed by the designer’s specifications for that operation

  26. UpperSpecification LowerSpecification Much of the process output fits within specification width A significant portion of the process output falls outside of the specification width Process Capability (2 of 3) process distribution Almost all of the process output fits within the specification width

  27. UpperSpecification LowerSpecification Much of the process output fits within specification width A significant portion of the process output falls outside of the specification width Process Capability (3 of 3) process distribution Almost all of the process output fits within the specification width

  28. Process Capability Study • Where is the process centered? • How much variability exists in the process? • Is the performance acceptable? • Is the process stable? • What factors contribute to variability?

  29. Types of Capability Studies • Peak performance study- how a process performs under ideal conditions • Process characterization study- how a process performs under actual operating conditions • Component variability study- relative contribution of different sources of variation (e.g., process factors, measurement system)

  30. Process Capability Study • Choose a representative machine or process • Define the process conditions • Select a representative operator • Provide the right materials • Specify the gauging or measurement method • Record the measurements • Construct a histogram and compute descriptive statistics: mean and standard deviation • Compare results with specified tolerances

  31. Process Capability (3 of 3) • The process capability index (cp) compares the width of the design specifications with a measure of process variability

  32. UTL - LTL 6s Cp = UTL - m 3s Cpu = m - LTL 3s Cpl = Cpk = min{ Cpl, Cpu } Process Capability Indices A process capability index compares the width of the design specifications with a measure of process variability

  33. PROCESS_CAPABILITY.XLS

More Related