1. Statistical Process Control (SPC) Chapter 6

2. MGMT 326 Foundations of Operations Introduction Strategy Quality Assurance Capacity, Facilities, & Work Design Planning & Control Products & Processes Product Design Process Design Managing Quality Statistical Process Control Project Manage- ment

3. Statistical Process Control (SPC) Mean charts Range charts  and  known ,  unknown Capable Processes  = target Variation Basic SPC Concepts Objectives First steps Types of Measures Attributes Variables SPC for Variables

4. Variation in a Transformation Process Variation in inputs create variation in outputs Variations in the transformation process create variation in outputs Inputs Facilities Equipment Materials Energy Transformation Process Outputs Goods & Services

5. Variation All processes have variation. Common cause variation is random variation that is always present in a process. A ssignable cause variation results from changes in the inputs or the process. The cause can and should be identified. Assignable cause variation shows that the process or the inputs have changed, at least temporarily.

6. Objectives of Statistical Process Control (SPC) Find out how much common cause variation the process has Find out if there is assignable cause variation. A process is in control if it has no assignable cause variation Being in control means that the process is stable and behaving as it usually does. It does not mean that we have conformance quality and meet customer requirements.

7. First Steps in Statistical Process Control (SPC) Measure characteristics of goods or services that are important to customers Make a control chart for each characteristic The chart is used to determine whether the process is in control

8. Variable Measures Continuous random variables Measure does not have to be a whole number. Examples: time, weight, miles per gallon, length, diameter

9. Attribute Measures Good/bad evaluations Good or defective Correct or incorrect Number of defects per unit – always a whole number Number of scratches on a table Opinion surveys of quality Customer satisfaction surveys Teacher evaluations

10. SPC for Variables The Normal Distribution  = the population mean  = the standard deviation for the population 99.74% of the area under the normal curve is between  - 3  and  + 3 

11. SPC for Variables The Central Limit Theorem Samples are taken from a distribution with mean  and standard deviation . k = the number of samples n = the number of units in each sample The sample means are normally distributed with mean  and standard deviation when k is large.

12. Control Limits for the Sample Mean when  and  are known x is a variable, and samples of size n are taken from the population containing x. Given:  = 10,  = 1, n = 4 Then A 99.7% confidence interval for is

13. Control Limits for the Sample Mean when  and  are known (2) The lower control limit for is

14. Control Limits for the Sample Mean when  and  are known (3) The upper control limit for is

15. Control Limits for the Sample Mean when  and  are unknown If the process is new or has been changed recently, we do not know  and  Excel table, page 180 Given: 25 samples, 4 units in each sample  and  are not given k = 25, n = 4

16. Control Limits for the Sample Mean when  and  are unknown (2) 1. Compute the mean for each sample. For example, 2. Compute

17. Control Limits for the Sample Mean when  and  are unknown (3) For the i th sample, the sample range is R i = (largest value in sample i ) - (smallest value in sample i ) 3. Compute R i for every sample. For example, R 1 = 16.02 – 15.83 = 0.19

18. Control Limits for the Sample Mean when  and  are unknown (4) 4. Compute, the average range We will approximate by, where A 2 is a number that depends on the sample size n. We get A 2 from Table 6.1, page 182

19. Control Limits for the Sample Mean when  and  are unknown (5) 5. n = the number of units in each sample = 4. From Table 6.1, A 2 = 0.73. The same A 2 is used for every problem with n = 4.

20. Control Limits for the Sample Mean when  and  are unknown (6) 6. The formula for the lower control limit is 7. The formula for the upper control limit is

21. Control Chart for The variation between LCL = 15.74 and UCL = 16.16 is the common cause variation.

22. Control Limits for R 1. From the table, get D 3 and D 4 for n = 4. D 3 = 0 D 4 = 2.28

23. Control Limits for R (2) 2. The formula for the lower control limit is 2. The formula for the upper control limit is

24. fig_ex06_03

25. Statistical Process Control (SPC) Capable Processes  = target Mean charts Range charts  and  known ,  unknown Variation Basic SPC Concepts Objectives First steps Types of Measures Attributes Variables SPC for Variables

26. Capable Transformation Process Inputs Facilities Equipment Materials Energy Outputs Goods & Services that meet specifications a specification that meets customer requirements + a capable process (meets specifications) = Satisfied customers and repeat business

27. Review of Specification Limits The target for a process is the ideal value Example: if the amount of beverage in a bottle should be 16 ounces, the target is 16 ounces Specification limits are the acceptable range of values for a variable Example: the amount of beverage in a bottle must be at least 15.8 ounces and no more than 16.2 ounces. The allowable range is 15.8 – 16.2 ounces. Lower specification limit = 15.8 ounces or LSL = 15.8 ounces Upper specification limit = 16.2 ounces or USL = 16.2 ounces

28. Control Limits vs. Specification Limits Control limits show the actual range of variation within a process What the process is doing Specification limits show the acceptable common cause variation that will meet customer requirements. Specification limits show what the process should do to meet customer requirements

29. Process is Capable: Control Limits are within or on Specification Limits UCL LCL X Lower specification limit Upper specification limit

30. Process is Not Capable: One or Both Control Limits are Outside Specification Limits UCL LCL X Lower specification limit Upper specification limit

31. Capability and Conformance Quality A process is capable if It is in control and It consistently produces outputs that meet specifications. This means that both control limits for the mean must be within the specification limits A capable process produces outputs that have conformance quality (outputs that meet specifications).

32. Process Capability Ratio Use to determine whether the process is capable when  = target. If, the process is capable, If, the process is not capable.

33. Example Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is 16. The allowable range is 15.8 – 16.2. The standard deviation is 0.06. Find and determine whether the process is capable.

34. Given:  = 16,  = 0.06, target = 16 LSL = 15.8, USL = 16.2 The process is capable. Example (2)

35. Process Capability Index C pk  If C pk > 1, the process is capable.  If C pk < 1, the process is not capable.  We must use C pk when  does not equal the target.

36. C pk Example Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is 15.9. The allowable range is 15.8 – 16.2. The standard deviation is 0.06. Find and determine whether the process is capable.

37. C pk Example (2) Given:  = 15.9,  = 0.06, target = 16 LSL = 15.8, USL = 16.2 C pk < 1. Process is not capable.

38. Statistical Process Control (SPC) Capable Processes  = target Mean charts Range charts  and  known Variation Basic SPC Concepts Objectives First steps Types of Measures Attributes Variables SPC for Variables ,  unknown