Download
slide1 n.
Skip this Video
Loading SlideShow in 5 Seconds..
Chapter 8. Process and Measurement System Capability Analysis PowerPoint Presentation
Download Presentation
Chapter 8. Process and Measurement System Capability Analysis

Chapter 8. Process and Measurement System Capability Analysis

393 Vues Download Presentation
Télécharger la présentation

Chapter 8. Process and Measurement System Capability Analysis

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Chapter 8. Process and Measurement System Capability Analysis

  2. Natural tolerance limits are defined as follows: Process Capability

  3. Uses of process capability

  4. Process may have good potential capability Reasons for Poor Process Capability

  5. Data collection steps:

  6. Example 7-1, Glass Container Data

  7. Mean and standard deviation could be estimated from the plot Probability Plotting • The distribution may not be normal; other types of probability plots can be useful in determining the appropriate distribution.

  8. Process Capability Ratios Example 5-1:

  9. Practical interpretation PCR = proportion of tolerance interval used by process For the hard bake process:

  10. One-Sided PCR

  11. Cp does not take process centering into account • It is a measure of potential capability, not actual capability

  12. Measure of Actual Capability Cpk: one-sided PCR for specification limit nearest to process average

  13. Normality and Process Capability Ratios • The assumption of normality is critical to the interpretation of these ratios. • For non-normal data, options are: • Transform non-normal data to normal. • Extend the usual definitions of PCRs to handle non-normal data. • Modify the definitions of PCRs for general families of distributions. • Confidence intervals are an important way to express the information in a PCR

  14. Confidence interval is wide because the sample size is small

  15. Confidence interval is wide because the sample size is small

  16. Process Performance Index: Use only when the process is not in control.

  17. Specifications are not needed to estimate parameters. Process Capability Analysis Using Control Chart

  18. Since LSL = 200

  19. Process Capability Analysis Using Designed Experiments

  20. Gauge and Measurement System Capability Simple model: y: total observed measurement x: true value of measurement ε: measurement error

  21. k = 5.15 → number of standard deviation between 95% tolerance interval Containing 99% of normal population. k = 6 → number of standard deviations between natural tolerance limit of normal population. For Example 7-7, USL = 60 and LSL = 5. With k =6 P/T ≤ 0.1 is taken as appropriate.

  22. Estimating Variances

  23. Signal to Noise Ration (SNR) SNR: number of distinct levels that can be reliably obtained from measurements. SNR should be ≥ 5 The gauge (with estimated SNR < 5) is not capable according to SNR criterion.

  24. Discrimination Ratio DR > 4 for capable gauges. For example, 7-7: The gauge is capable according to DR criterion.

  25. Usually conducted with a factorial experiment (p: number of randomly selected parts, o: number of randomly selected operators, n: number of times each operator measures each part) Gauge R&R Studies

  26. This is a two-factor factorial experiment. • ANOVA methods are used to conduct the R&R analysis.

  27. Negative estimates of a variance component would lead to filling a reduced model, such as, for example:

  28. σ2: repeatability variance component → → For the example: With LSL = 18 and USL = 58: This gauge is not capable since P/T > 0.1.

  29. Linear Combinations

  30. Nonlinear Combinations → R is higher order (2 or higher) remainder of the expansion. R → 0 →

  31. Assume I and R are centered at the nominal values. α = 0.0027: fraction of values falling outside the natural tolerance limits. Specification limits are equal to natural tolerance limits. Assuming V is approximately normal: →

  32. For normal distribution with unknown mean and variance: Estimating Natural Tolerance Limits • Difference between tolerance limits and confidence limits • Nonparametric tolerance limits can also be calculated.