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SPC - General Information

Each of the topics below is intended to eventually have its own page in this wiki.

What NOT to do during an SPC study:

After generating the Phase 1 SPC chart, do not ignore evidence of special cause variation.  If found, its root cause must be identified and eliminated.  The preferred couse of action is not to simply report that it exists and then move on.

The relationship between SPC and DOE

DOE is most useful when the process is stable, giving consistent results over time under specific conditions.

See Relationship Between SPC and DOE

Choices for process control limits

Relationship between control limits, specification limits, natural tolerance limits:

There is no mathematical or statistical relationship between the SPC chart control limits and product specification limits.
  • Control limits are driven by the natural variability of the process (measured by the process stddev), aka the natural tolerance limits of the process.
  • The specification limits are determined 'externally' from the process, and - in the best case - reflect the Voice of the Customer (VOC).

Discussion of constants used to estimate aspects of the process:

Constant d2 and relative range W = R/sigma.  sigma-hat = R/d2
Simulation for d2 and discussion of impact on choice of subgroup sample size (bias in estimate of variance) (link)

PHASE 1 SPC METHODS (Variables control chart)
  • Montgomery p.99
  • X-bar and R charts
  • Independence of measures of central tendency and of variance (for X-bar chart, but not for R chart)
  • Trial control limits
  • What if assignable causes cannot be found? 
  • SPC as Hypothesis Testing
  • ARL1 and ARL2
  • ATS1 and ATS2
  • Choice of subgroup size and frequency based on ARL/ATS
    • If the SPC study includes multiple lots of product and raw materials (and it often should), then the process limits should be calculated for each lot.
    • We would prefer that each lot shows that the process is "in control" (stable) based on control limits calculated for each lot - AND ...
    • ... we should also look for minimal (preferable none) shift if the process mean and process variance across lots.

PHASE 2 SPC METHODS (Variables control chart)
  • Montgomery p. 204
  • Done after Phase 1 methods find initial and eliminate assignable causes of special cause variation.
  • Use methods with more statistical power (EWMA, CUSUM, other) than X-bar and R for faster shift detection without inflating Type 1 error.
  • Discourage use of sensitizing rules (runs rules) in X-bar and R charts for shift detection of a stable process (Type 1 error).
  • Tolerance chart (or tier diagram)
Examples from Montgomery worked using Statistica, with "How To" documents. 
Using R for SPC (link) or see attached .pdf file.

What circumstances might make Cpk less feasible than Ppk?
The time-based production order/sequence is lost between production and time of testing.  For instance, needing to send the product to a sterilizer (or another intermediate processing step) between producing and testing the parts.

What circumstances might make an X-bar and R chart less feasible than an ImR (aka XmR) chart?
See Montgomery.

Other misc considerations:

During an SPC study, the measurement system that is used should have documented evidence that it is properly calibrated (with an unexpired calibration record) and that it has good Repeatability and Reproducibility (MSA/GR&R) properties.
  • How can I tell if the measurement system GR&R is not sufficient during the SPC study?
    • If the Range chart is limited to only a few values, then the measurement system may not have the proper resolution.
    • The GR&R "ndc" value is a good indicator.
If an observation is contributing to special cause variation, and if the measurement system has good GR&R, consider taking new measurements on that part (several) to see if the original measurement falls within the expected range of the new measurements.  (also, what if the parts are prone to changing over time?  for instance, molded plastic parts with shrink charts)
See attachment "SPC scenario - rationale for remeasuring a part.pdf"

If the action standard for a study or protocol is based on Process Capability (e.g. Cpk), then for the action standard to be met requires that the process is statistically in-control and capable.
  • If the process has special cause variation (points outside of the process control limits)
  • If the process has non-random sequences (runs-rules violations)

  • Often, more concern will be shown for special cause variation where a point or points lay outside of the process control limits.
  • For runs-rules violations, these need to be explored, but may not be as likely to lead to a "fail" decision w.r.t. the action standard based on Cpk.

Sampling considerations:
  • See also Sampling and Randomization
  • Do not combine specimens taken across the width of a (film) web or across multiple cavities in the same subgroup.  This is because the behavior of the different groups may represent different populations.  Combining specimens from different populations can inflate the estimate of the within-(sub)group variance and mask issues with process control (stability) and capability.
  • Stratification - and the formation of subgroups - should consider: 
    • mold cavities,
    • packaging process cavities,
    • film or web locations,
    • locations on each specimen (i.e. clock positions 12, 3, 6, 9 on a gasket)
  • The only instances when mixing specimens across cavities in the same subgroup might be legitimate is if there is a study, with data and analysis (maybe ANOVA-based), that shows that the population characteristics between cavities (etc.) are homogenous.  Even then, this is not necessarily a good idea and should be avoided.

StatSoft Electronic Statistics Textbook - Quality Control Charts

NIST Control Charts

Subpages (2): MOSUM Tier Chart