Irwin/McGraw-Hill 1 TN7: Basic Forms of Statistical Sampling for Quality Control Acceptance Sampling: Sampling to accept or reject the immediate lot of product at hand. Statistical Process Control (SPC): Sampling to determine if the process is within acceptable limits.

Irwin/McGraw-Hill 2 Acceptance Sampling Purposes Determine quality level Ensure quality is within predetermined level Lot received for inspection Sample selected and analyzed Results compared with acceptance criteria Accept the lot Send to production or to customer Reject the lot Decide on disposition

Irwin/McGraw-Hill 3 Basic Forms of Variation - SPC Assignable variation is caused by factors that can be clearly identified and possibly managed. Common variation is inherent in the production process.

Irwin/McGraw-Hill 4 Control Limits are based on the Normal Curve x z  Standard deviation units or “z” units.

Irwin/McGraw-Hill 5 Control Limits If we establish control limits at +/- 3 standard deviations, then we would expect 99.7% of our observations to fall within these limits x LCLUCL

See Exhibit S6.3 for other evidence prompting investigation Statistical Process Control

UCL LCL Samples over time UCL LCL Samples over time UCL LCL Samples over time Normal Behavior Possible problem, investigate Statistical Process Control (SPC) Charts

Irwin/McGraw-Hill 8 Statistical Sampling--Data Attribute (Go no-go information) Defectives Defects Typically use sample size of Variable (Continuous) Usually measured by the mean and the standard deviation Typically use sample size of 2 to 10

Irwin/McGraw-Hill 9 Statistical Process Control: Attribute Measurements (P-Charts) Where Z is equal to the number of Standard Deviations

1. Calculate the sample proportion, p, for each sample.

2. Calculate the average of the sample proportions. 3. Calculate the sample standard deviation. 4. Calculate the control limits (where Z=3).

Irwin/McGraw-Hill 12 p-Chart (Continued) 5. Plot the individual sample proportions, the average of the proportions, and the control limits

An Example: Calculate sample means, sample ranges, mean of means, and mean of ranges.

Control Limit Formulas Exhibit TN7.6

Irwin/McGraw-Hill 15 x-Bar Chart

Irwin/McGraw-Hill 16 R-Chart

Irwin/McGraw-Hill 17  If you treat special causes like common causes, you lose an opportunity to track down and eliminate something specific that is increasing variation in your process.  If you treat common causes like special causes, you will most likely end up increasing variation (called “tampering”).  Taking the wrong action not only doesn’t improve the situation, it usually makes it worse. Matching Action to the Type of Variation

Irwin/McGraw-Hill 18 Quarterly Audit Scores · · · · · Score Quarter

Irwin/McGraw-Hill 19 Quarterly Audit Scores · · · · · Score Quarter

Irwin/McGraw-Hill 20 Quarterly Audit Scores · · · · Score · · · · · · · · · · · · · · · O O O O O · · · · · · · · · · · · · ·

Irwin/McGraw-Hill 21 Process Capability Process limits (The “Voice of the Process” or The “Voice of the Data”) - based on natural (common cause) variation Tolerance limits (The “Voice of the Customer”) – customer requirements Process Capability – A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits

Irwin/McGraw-Hill 22 Process Capability natural variation specification (a) specification natural variation (b) specification natural variation (c) specification natural variation (d) Evans and Lindsay The Management and Control of Quality, Southwestern Books.

Irwin/McGraw-Hill 23 Process Capability Index, C pk Capability Index - shows how well parts being produced fit into design limit specifications.

Irwin/McGraw-Hill 24 Interpreting the C pk C pk < 1Not Capable C pk = 1Capable at 3  C pk = 1.33Capable at 4  C pk = 1.67Capable at 5  C pk = 2Capable at 6 

Irwin/McGraw-Hill 25 Process Capability Index, C pk Find the C pk for the following: A process has a mean of and a variance of The product has a specification of ± 4.00.

Irwin/McGraw-Hill 26 Is 99% Good Enough? 22,000 checks will be deducted from the wrong bank accounts in the next 60 minutes. 20,000 incorrect drug prescriptions will be written in the next 12 months. 12 babies will be given to the wrong parents each day.

Irwin/McGraw-Hill 27 Motorola’s Initial Six Sigma Measurement Process Cycle time; e.g., 81 minutes  27 minutes  9 minutes  3 minutes  1 minute  20 seconds Defects; e.g., 81 defects  27 defects  9 defects  3 defects 1 defect  0.3 defects REDUCE BOTH SIMULTANEOUSLY!

Irwin/McGraw-Hill 28 Six Sigma Quality The objective of Six Sigma quality is 3.4 defects per million opportunities!

Irwin/McGraw-Hill 29 But is Six Sigma Realistic? · K 10K 100K (66810 ppm) · IRS – Tax Advice (phone-in) Best in Class (3.4 ppm) Domestic Airline Flight Fatality Rate (0.43 ppm) · (233 ppm) Average Company Purchased Material Lot Reject Rate Air Line Baggage Handling Wire Transfers Journal Vouchers Order Write-up Payroll Processing Doctor Prescription Writing Restaurant Bills · · · · · · · Defects Per Million Opportunities (DPMO) SIGMA

Irwin/McGraw-Hill 30 A Partial List of Organizations in Atlanta Implementing Six Sigma Coca-Cola Home Depot SunTrust Banks Bank of America Delta Airlines Atlantic Envelope Company GE Capital Lithonia Lighting