SPC Notes

References

• https://www.qimacros.com/pdf/histogram-cheat-sheet.pdf

• https://sixsigmastudyguide.com/process-capability-pp-ppk-cp-cpk/

• https://www.qimacros.com/lean-six-sigma-articles/stability-analysis-vs-capability-analysis/

• https://pressbooks.palni.org/spcleanmanufacturing/chapter/chapter-10a/

• Process stability is when the process is is consistent, and any noise in the output is due to standard variation. If it is unstable, that means there is some special cause variation

  • This is assessed using control charts. Which one you use depends on data. These are for numerical values:
    • X-chart is plotting the mean of each subgroup, over subgroup count. UCL and LCL are 3 sigma of all subgroup averages. This is the alternative to I-MR charts.
    • I-MR chart is plotting individual data points over time. The UCL and LCL are the moving range at each point. This is the alternative to x-charts.
    • R chart is plotting the subgroup range over subgroup count. This is usually presented with X-bar, not on its own. It shows sample dispersion, and is best when sample size is low (n < 10).
    • S chart is plotting the subgroup deviation over subgroup count. This is usually presented with X-bar, not on its own. It shows sample dispersion, and is best when sample size is high (n > 10).
  • These control charts are for attribute data:
    • P-chart
    • U-chart
    • C-chart

• Process capability: can the process can meet the product requirements outputs?

  • Process capability indexes are when you are looking at a subset of the data, like a subgroup or comparing improvements. Uses a sigma estimation.
    • Assumes & requires that process is stable
    • $C_p$ (Capability Index) - how spread is data between the LSL and USL?
    • $C_{p}k$ (Capability Centering Index) - how centered is data between the LSL and USL?
  • Process performance indexes are when you are looking at a the entire set of data, like handing off a batch of wafers to the customer. Uses normal SD.
    • Process does not need to be stable
    • $P_p$ (Performance Index) - how spread is data between the LSL and USL?
    • $P_{p}k$ (Performance Centering Index) - how centered is data between the LSL and USL?
  • Interpreting $P_p,P_{p}k,C_p,C_{p}k$
    • $0\le incapable<1.0$
    • $1.0\le barelycapable<1.33$
    • $1.33\le moderatelycapable<2.0$
    • $2.0\le highlycapable$