Performance evaluation, Capability Analysis and monitoring with Low Level Count data Erwin M. Saniga Dept. of Bus. Admin. University of Delaware Newark, DE 19716 302-831-2555 [email protected]James M. Lucas J.M. Lucas and Associates 302-368-1214 5120 New Kent Road Wilmington, DE 19808 [email protected]Darwin J. Davis Dept. of Bus. Admin. University of Delaware Newark, DE 19716 302-831-2555 [email protected]Presenter: Erwin Saniga
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Performance evaluation, Capability Analysis and monitoring with Low Level Count data
Erwin M. Saniga Dept. of Bus. Admin. University of Delaware Newark, DE 19716 302-831-2555 [email protected] James M. Lucas J.M. Lucas and Associates 302-368-1214 5120 New Kent Road Wilmington, DE 19808 [email protected] Darwin J. Davis Dept. of Bus. Admin. - PowerPoint PPT Presentation
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Performance evaluation, Capability Analysis and monitoring with Low Level Count data
Purpose: To examine the performance of alternative methods to study processes where quality is measured by counts and counts are low.
Example Large Wilmington (DE) area credit card bank Processes credit card applications Four vendors process these applications Wish to implement a vendor certification and
quality improvement program
BankVendorA
VendorD
VendorB
VendorC
We will show in this presentation:
When exploring this type of data for performance evaluation or process capability analysis, four different types of plots can reveal different things about the process A traditional sequence plot Adding a Shewhart UCL and a
method to detect improvements to the traditional sequence plot
A CUSUM plot Adding a “V-mask” to the
CUSUM plot
Actual results for the four vendors
Each point represents the number of defectives resulting from an inspection of 50 random credit card applications that were processed during the day. These were taken at the end of the day.
Each credit card application can be processed correctly or incorrectly.
Vendor Analysis
Average vendor performance Vendor A average p = 0.0246 Vendor B average p = 0.0510 Vendor C average p = 0.0247 Vendor D average p = 0.0294
Analyst questions: What caused the spikes at various points in time for
each vendor? What caused the sequence of “good” (zero
defective) samples for various vendors? Why is Vendor B doing poorly when compared to
Vendors A, C, and D? Are these substantive differences?
If the data were available in real time and we could plan the data collection we might:
Investigate the cause of a spike or run of good points immediately
Keep a diary or log of variables identified during a focus group meeting of employees, managers, etc.
CUSUM SEQUENCE (DIAGNOSTIC) PLOTS
Let Xj = the actual number of defectives observed in the jth sample
The ith CUSUM is then:
where k is the reference value. We use a reference value of
k=1.25 which is the average count of defectives in a sample of 50 for the three “good” vendors.
i
1jji kXC
Process Averages for CUSUM Sequence Plot
The CUSUM sequence plot can identify “good”, “average” or “bad” regimes.
Regime average is determined by the slope (in this case, slope = 0 implies 1.25 defects).
The average count from periods L to M is given by: