1. Statistical Process Control Operations Management - 5 th Edition Chapter 4 Roberta Russell & Bernard W. Taylor, III

2. 4-2 Basics of Statistical Process Control  Statistical Process Control (SPC) Monitoring production process to detect and prevent poor quality Monitoring production process to detect and prevent poor quality  Sample Subset of items produced to use for inspection Subset of items produced to use for inspection  Control Charts Process is within statistical control limits Process is within statistical control limits UCL LCL

3. 4-3 Variability  Random Inherent in a process Inherent in a process Can be eliminated only through improvements in the system Can be eliminated only through improvements in the system  Non-Random Special causes Special causes Due to identifiable factors Due to identifiable factors Can be modified through operator or management action Can be modified through operator or management action

4. 4-4 SPC in TQM  SPC Tool for identifying problems and making improvements Tool for identifying problems and making improvements Contributes to the TQM goal of continuous improvements Contributes to the TQM goal of continuous improvements

5. 4-5 Quality Measures  Attribute a product characteristic that can be evaluated with a discrete response a product characteristic that can be evaluated with a discrete response good – bad; yes - no good – bad; yes - no  Variable a product characteristic that is continuous and can be measured a product characteristic that is continuous and can be measured weight - length weight - length

6. 4-6  Nature of defect is different in services  Service defect is a failure to meet customer requirements  Monitor times, customer satisfaction Applying SPC to Service

7. 4-7 Applying SPC to Service (cont.)  Hospitals Timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts Timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts  Grocery Stores Waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors Waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors  Airlines Flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance Flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance

8. 4-8 Where to Use Control Charts  Process has a tendency to go out of control  Process is particularly harmful and costly if it goes out of control  Examples At the beginning of a process because it is a waste of time and money to begin production process with bad supplies At the beginning of a process because it is a waste of time and money to begin production process with bad supplies Before a costly or irreversible point, after which product is difficult to rework or correct Before a costly or irreversible point, after which product is difficult to rework or correct Before and after assembly or painting operations that might cover defects Before and after assembly or painting operations that might cover defects Before the outgoing final product or service is delivered Before the outgoing final product or service is delivered

9. 4-9 Control Charts  A graph that establishes control limits of a process  Control limits Upper and lower bands of a control chart Upper and lower bands of a control chart  Types of charts Attributes Attributes p-chart p-chart c-chart c-chart Variables Variables range (R-chart) range (R-chart) mean (x bar – chart) mean (x bar – chart)

10. 4-10 Process Control Chart 12345678910 Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control

11. 4-11 Normal Distribution  =0 1111 2222 3333 -1  -2  -3  95% 99.74%

12. 4-12 A Process Is in Control If … 1.… no sample points outside limits 2.… most points near process average 3.… about equal number of points above and below centerline 4.… points appear randomly distributed

13. 4-13 Control Charts for Attributes  p-charts  uses proportion defective in a sample  c-charts  uses number of defects in an item

14. 4-14 p-Chart UCL = p + z  p LCL = p - z  p z=number of standard deviations from process average p=sample proportion defective; an estimate of process average  p = standard deviation of sample proportion p =p =p =p = p(1 - p) n

15. 4-15 p-Chart Example (p.138) 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE 16.06 20.00 34.04 ::: 2018.18 200

16. 4-16 p-Chart Example (cont.) UCL = p + z = 0.10 + 3 p(1 - p) n 0.10(1 - 0.10) 100 UCL = 0.190 LCL = 0.010 LCL = p - z = 0.10 - 3 p(1 - p) n 0.10(1 - 0.10) 100 = 200 / 20(100) = 0.10 total defectives total sample observations p =

17. 4-17 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Proportion defective Sample number 2468101214161820 UCL = 0.190 LCL = 0.010 p = 0.10 p-Chart Example (cont.)

18. 4-18 c-Chart UCL = c + z  c LCL = c - z  c where c = number of defects per sample  c = c

19. 4-19 c-Chart (cont. – p.141 ) Number of defects in 15 sample rooms 1 12 2 8 3 16 : : 15 15 190 190 SAMPLE c = = 12.67 19015 UCL= c + z  c = 12.67 + 3 12.67 = 23.35 LCL= c + z  c = 12.67 - 3 12.67 = 1.99 NUMBER OF DEFECTS

20. 4-20 3 6 9 12 15 18 21 24 Number of defects Sample number 246810121416 UCL = 23.35 LCL = 1.99 c = 12.67 c-Chart (cont.)

21. 4-21 Control Chart Patterns UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line

22. 4-22 Control Chart Patterns (cont.) LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

23. 4-23 Zones for Pattern Tests UCL LCL Zone A Zone B Zone C Zone B Zone A Process average 3 sigma = x + A 2 R = 3 sigma = x - A 2 R = 2 sigma = x + (A 2 R) = 2323 2 sigma = x - (A 2 R) = 2323 1 sigma = x + (A 2 R) = 1313 1 sigma = x - (A 2 R) = 1313 x = Sample number |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | 10 | 11 | 12 | 13

24. 4-24 Control Chart Patterns  8 consecutive points on one side of the center line  8 consecutive points up or down across zones  14 points alternating up or down  2 out of 3 consecutive points in zone A but still inside the control limits  4 out of 5 consecutive points in zone A or B

25. 4-25 Performing a Pattern Test 14.98B—B 25.00BUC 34.95BDA 44.96BDA 54.99BUC 65.01—UC 75.02AUC 85.05AUB 95.08AUA 105.03ADB SAMPLExABOVE/BELOWUP/DOWNZONE

26. 4-26 Sample Size  Attribute charts require larger sample sizes  50 to 100 parts in a sample  Variable charts require smaller samples  2 to 10 parts in a sample