1. MOS 3330 Operations Management Professor Burjaw Fall/Winter 2012-2013

2. Learning Objectives: 1.4 stages/levels of quality management 2.Acceptance sampling vs. SPC 3.SPC steps 4.Attributes vs. variables 5.4 SPC charts 6.Pattern tests 7.Process capability basics MOS 3330SPC2 Formula Sheet Formula Sheet

3. Four stages Quality inspection: focus on providing information Quality control: focus on monitoring and controlling  SPC Quality assurance: management programs aimed at ensuring good product quality Total Quality Management (TQM): management philosophy about ensuring and improving product quality throughout the entire organization MOS 3330SPC3

4. When Upon receipt of resources Before transformation operations (especially bottleneck) The first few items coming out of an automated operation Final inspection Customer complaints and returned goods How much and how often Complete inspection vs. sampling Cost of inspection vs. cost of not detecting defects Cost, time and physical possibility MOS 3330SPC4

5. The method of randomly inspecting a sample of goods and deciding whether to accept the entire lot based on the results 1.Take a random sample from a lot (batch) of items 2.Test the sample items for the specified quality characteristics 3.Accept all items in the lot if (Number of defective items in the sample) < (Maximum number of defective items allowed in a sample) Otherwise, reject all items in the lot. Historical mentality: “some degree of poor quality will occur and that is acceptable” MOS 3330SPC5

6. To prevent poor product quality Process improvement tool Method of randomly inspecting a sample of goods and deciding whether the production process is in control –Monitor the production process (data pattern) –Provide a statistical signal when the process (quality) changes MOS 3330SPC6

7. 7 Step 3: Take a random sample and plot the quality measure Step 2: Set up a control chart Step 1: Define the quality characteristic to measure Step 6: The process is out of control; stop the process until the quality problem is identified and fixed Step 4: Is any sample point outside of the control limits? Step 5: Does any pattern exist? No Yes No Yes The process is in control (continue monitoring)

8. Step 1: Define the quality characteristic to measure Attributes: characteristics that are measured qualitatively, thus have discrete values –e.g., defective/non-defective, # of scratches or blemishes –Count both defective and non-defective items  p-chart –Count defective features in an item  c-chart Variables: characteristics that are measured quantitatively, thus have continuous values –e.g, weight, length, volume, temperature –Difference (range) between smallest and largest values  R-chart –Average  x-chart MOS 3330SPC8

9. Step 2: Set up a control chart MOS 3330SPC9 Sample number UCL (Upper Control Limit) Process Average 12345678 9 10 LCL (Lower Control Limit) 3 Sigma Limits

10. Step 3: Take random samples over time. For each sample, measure the quality characteristic and plot the result. MOS 3330SPC10 Sample number UCL Process Average LCL 12345678 9 10

11. Key ideas behind the control limits: In spite of inherent random variation in a production process, the average of the distribution of the quality characteristic should be stable if the process is in control The range between the UCL and LCL allows for random variation Observations falling outside the UCL or LCL indicate the existence of abnormal variation Control limit standard = 3-sigma limits –Control limits too narrow  Type I error: random variation mistaken for an abnormal variation –Control limits too wide  Type II error: abnormal variation may not be detected MOS 3330SPC11

12. Step 4: Is any sample point outside of the control limits? Yes  the process is out of control (step 6) No  go to step 5 Step 5: Does any pattern exist? (Pattern tests) Yes  the process is out of control (step 6) No  the process is in control  continue monitoring (step 3) Step 6: Identify and correct the quality problems Process improvement tools Discard out-of-control sample observations May need to revise the control chart MOS 3330SPC12

13. Quality to be measured: proportion of defective items Sample size (n): 50-100 items per sample (guideline) Center line: p = historical average proportion of defects UCL = p + z [ p (1 – p)/n] 1/2 LCL = p – z [ p (1 – p)/n] 1/2 z = number of standard deviations corresponding to the sigma limit MOS 3330SPC13 Sample standard deviation Formula Sheet Formula Sheet

14. Example 1: A soft drink bottler is concerned about over- and under-filled bottles. Management desires 3-sigma control limits. 10 samples (200 bottles per sample) have been collected. a) Is the process in control? b) The first day on the job, a machine operator takes a sample of 30 units and finds 5 units to be defective. Should you be concerned? Sample ## of defects 112 216 3838 424 520 6464 716 812 928 108 MOS 3330SPC14

15. MOS 3330SPC15 Control chart for Example 1: Sample number 12345678 9 10

16. Quality to be measured: # of defective features per item Sample size: 1 item per sample Used when it is not possible to count non-defective items (i.e., no proportion of defectives can be computed) Center line: c = historical average # of defective features UCL = c + z ( c ) 1/2 LCL = c – z ( c ) 1/2 MOS 3330SPC16 Sample standard deviation Formula Sheet Formula Sheet

17. Example 2: An airline company wishes to set up a control chart to monitor the number of misplaced luggage. One flight is selected at random each hour, and the cases of misplacement are counted. a) Is there any concern regarding misplaced luggage? Use 3 sigma limits. b) The 7th flight had 11 cases of misplacement. Should you be concerned? Flight# of misplacement 1616 2323 3939 4646 5959 6363 MOS 3330SPC17

18. MOS 3330SPC18 Control chart for Example 2: Sample number 12345678 9 10

19. Quality to be measured: R = (Largest value in the sample) – (Smallest value) Sample size (n): 2-10 items per sample Center line: R = historical average of R values UCL = D 4 R LCL = D 3 R D 3 and D 4 = range value constants based on sample size –Specifically developed to determine control limits for R-chart MOS 3330SPC19 Formula Sheet Formula Sheet

20. Quality to be measured: sample average Sample size (n): 2-10 items per sample Center line: x = historical average of x values UCL = x + A 2 R LCL = x – A 2 R A 2 = mean value constant based on sample size –Specifically developed to determine control limits for x-chart R-chart and x-chart should be used together - why? MOS 3330SPC20 Formula Sheet Formula Sheet

21. Control Limit Factors for R-chart and x-chart with 3-sigma limits MOS 3330SPC21 Formula Sheet

22. Example 3: University Food Services uses SPC to monitor the length of time from when an order is placed with a supplier to when the goods arrive at the receiving dock (“order cycle time”). When the process is in control, x = 1.13 days and R = 0.5 days based on samples of size 5. Is the process in control? Use 3 sigma limits. MOS 3330SPC22 Sample1 1.1 1.2 1.1 1.0 Sample2 1.2 1.1 1.2 1.1 1.0 Sample3 1.0 1.8 1.0 Sample4 0.8 1.1 1.2 1.9 Sample5 1.1 1.0 1.2

23. MOS 3330SPC23 Control charts for Example 3: Sample number 12345 12345

24. To detect a non-random pattern within the control limits Run tests: check for the runs –Run: a sequence of observations with a certain characteristic –Pattern 1: 8 consecutive points on one side of the center line –Pattern 2: 8 consecutive points up (or down) –Pattern 3: 14 points alternating up or down Zone Tests: check for the zones –3 zones for 3 sigma limit control charts –Pattern 4: 2 out of 3 consecutive points in zone A –Pattern 5: 4 out of 5 consecutive points in zone A or B MOS 3330SPC24 Zone A Zone B Zone C Zone B Zone A UCL LCL Center Formula Sheet Formula Sheet Formula Sheet Formula Sheet Formula Sheet

25. MOS 3330SPC25 LCL UCL Consistently below  pattern 1? LCL UCL Upward trend  pattern 2? LCL UCL Close to boundary  patterns 4&5? UCL LCL Alternating up&down  pattern 3?

26. Example 4: Is the process in control? x=1.47, UCL=2.05, LCL=0.89 SamplexAbove/BelowUp/DownZone MOS 3330SPC26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1.4 1.3 1.2 1.36 1.56 1.6 1.7 1.53 1.66 1.43 1.87 1.65 1.4 1.78 1.9 1.7 1.83 1.5 1.88 1.1 BBBBAAAAABAABAAAAAABBBBBAAAAABAABAAAAAAB --- D U D U D U D U D U D U D CCBCCCBCCCACCBABBCABCCBCCCBCCCACCBABBCAB

27. SPC monitors natural vs. non-random variation within a process  producer’s perspective Process capability: The ability of a process to satisfy a product’s or service’s tolerances –Tolerances: Design specifications that reflect customer requirements –Not statistically determined –Not a result of production process Production process must be in control (check SPC) and must meet design specifications (check process capability) MOS 3330SPC27

28. Control chart data can be used to determine process capability –UCL  Upper Tolerance Limit (UTL) –LCL  Lower Tolerance Limit (LTL) Rough guideline –Process is capable of meeting specifications if (UCL  LCL) = (UTL  LTL) –Process is capable of exceeding specifications if (UCL  LCL) < (UTL  LTL) –Process is not capable of meeting specifications if (UCL  LCL) > (UTL  LTL) MOS 3330SPC28

29. A youtube video about SPC, showing the case of Honda.) http://www.youtube.com/watch?v=F7LJqOt59IQ An article explaining the concept of statistical process control http://ezinearticles.com/?What-is-Statistical-Process- Control-%28SPC%29?&id=3520371http://ezinearticles.com/?What-is-Statistical-Process- Control-%28SPC%29?&id=3520371 29