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How to Get More from a Metric Like PPM-D (Parts-Per-Million Defective)



Introduction

Today, many SQEs are confronted with geographically disperse suppliers - often overseas and at times, in locations where resources that can manage quality systems are in short supply. Electronic Data Interchange (EDI), ftp exchange of files and even faxes of hardcopy quality data are common forms of a data exchange across the supplier/customer interface (1). Simplicity, cost and ease of implementation at the supplier usually leads to optimal results in defining and maintaining underlying quality systems infrastructure. A minimalist approach that has been used successfully is the publishing of a secure and restricted data source on a web-enabled server at the supplier site.* The data source gets updated routinely and is under the administration of the supplier. The appropriate statistics that have been agreed to are posted at the data source. In this example (see Table 1), that includes lot attributes such as Date, Supplier Site, etc. and a key supplier performance indicator, PPM-D, or Parts-per-Million Defective, which is derived from the Qty_Supplier_Rejected column shown in the appendix.


Table 1. Simple text delimited table securely published on remote system at supplier site visible via network mount to Statit e-QC™. Only a few rows of approximately 8,000 records shown.

Analysis

One can chart and disposition an indicator like Qty_Supplier_Rejected and use historical performance alone to monitor a supplier's performance. However, there is additional analysis that can reveal shifts in the variation of the data that, when viewed over a sufficient time horizon, can indicate changes to the supplier process that might not be known or anticipated (2). We always want our suppliers to improve, but in a controlled manner that does not result in unexpected consequences. Figures 1 and 2 illustrate typical supplier quality process control charts that, when automated using Statit e-QC, provide automated reporting that gets delivered directly to email (3). Note that cpk of the process of the time horizon shows stability although this supplier is clearly challenged to produce lots within defectivity specifications.


Figure 1. cpk of process where defectivity (rejects) is used as a global Quality Metric for conformance to specification


Figure 2. Trending cpk over time for baseline control

Figure 3 presents the identical dataset analyzed using variance of the metric using a Cum probability plot. Now, one can see there is underlying structure within the distribution of the Quality Metric. Is that structure sufficient to declare a shipment in violation of spec? Most likely, not. However, the inquisitive SQE would like to know the source of the variation, if possible, and potentially query a supplier on possible changes to process, their supply-chain dependencies, etc., as a preventative measure to ensure unexpected or heretofore uncontrolled product attributes are within acceptable limits.


Figure 3. Cum plot of distribution where continuous tails (no disjoints) indicate natural variation and discontinuous jumps reveal mechanisms or systematic factors affecting the Quality Metric

Figures 4 and 5 show the drilldown, or segmentation, of the supplier's quality data based on an attribute the supplier has provided in the usual course of data exchange. Note the even stronger signal associated with Vendor Site indicating that Vendor Site #3 is broadening the overall variation in the data to a greater extent than the other sites.


Figure 4

Figures 4, 5. Drilldown into segmented dataset by splitting on "VendorSite" illustrates Site #3 as showing more variability than Sites' 1, 2 and 4.

Also of note, the variation at Vendor Site #3 has a marked slope change. This indicates a change in mechanism, a process change and/or possibly a measurement change. The chronological signature is evidenced as shown in Figure 6. These changes in variation get masked in routine quality data acquisition/analysis and do not always appear as deflections with sufficient signal strength in cpk charts to warrant an alarm. For example, both a shift in baseline and shift in the width of the distribution would have the net effect of leaving the cpk metric unchanged.

Figures 6, 7 and 8. Running average of DPPM does not indicate any control violations based on att rules set when using internal control limits. However, if Site #3 were to implement UCL from Sites 1,2 and 4, essentially all points are in violation.

Figure 6

Figure7

Figure 8

Conclusion

When using Statit e-QC as the centralized core of a web-enabled data analysis infrastructure that acquires data from distributed sources, the SQE can rapidly distribute and communicate supplier analysis results back to the source of origin. A common knowledge base enables business discussion pertinent to addressing and highlighting of both real excursions and non-conformance, as well as more subtle shifts in data (e.g. the dataset 'fingerprint'). The drilldown analysis, automated over a set of indicators, can also be manipulated by a wide range of literacy/skill levels. Trivial data export on concise datasets (per chart level) allows users to step back into their own tools and native languages/compute platforms, for further presentation if needed. More time spent on control & improvements, less time spent rearranging and reformatting results, managing permissions and chasing after spreadsheet files.

References

1. Christoph Schroth, Till Janner, Alexander Schmidt & Gunther Stuhec, From EDI to UN/CEFACT: An Evolutionary Path Towards a Next Generation e-Business Framework,The 5th International Conference on e-Business 2006 (NCEB 2006) (Bangkok, Thailand)

2. EugeneGrant, Richard S. Leavenworth, Statistical Quality Control, 7th ed., pp. 76-82

3. Statit Software, Inc. Statit e-QC Product Guide. Please refer to http://www.statit.com/statiteqc/Statit_e-QC.pdf

*Two types of published/mountable data sources are Linux Samba smb daemon running on Fedora 7 and Microsoft share. Both implemented under restricted/secure login. Additional details available upon request.

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