Statistical Process Control

1. Statistical Process Control

2. Statistical Process Control Why do we Need SPC?

3. To Help Ensure Quality Quality means fitness for use - quality of design - quality of conformance Quality is inversely proportional to variability.

4. What is Quality? • Transcendentdefinition: excellence • Excellence in every aspect • PERFORMANCE How well the output does what it is supposed to do. • RELIABILITY The ability of the output (and its provider) to function as promised

5. What is Quality • CONVENIENCE and ACCESSIBILITY How easy it is for a customer to use the product or service. • FEATURES The characteristics of the output that exceed the output’s basic functions. • EMPATHY The demonstration of caring and individual attention to customers.

6. What is Quality • CONFORMANCE The degree to which an output meets specifications or requirements. • SERVICEABILITY How easy it is for you or the customer to fix the output with minimum downtime or cost. • DURABILITY How long the output lasts.

7. What is Quality • AESTHETICS How a product looks, feels, tastes, etc. • CONSISTENCY The degree to which the performance changes over time. • ASSURANCE The knowledge and courtesy of the employees and their ability to elicit trust and confidence.

8. What is Quality • RESPONSIVENESS Willingness and ability of employees to help customers and provide proper services. • PERCEIVED QUALITY The relative quality level of the output in the eyes of the customers.

9. What is Quality • Product-based definition: quantities of product attributes • Attributes are non-measurable types of data • What are all the different features

10. What is Quality • User-based definition: fitness for intended use • How well does the product meet or exceed the expected use as seen by the user

11. What is Quality • Value-based definition: quality vs. price • How much is a product or service going to cost and then how much attention to quality can we afford to spend. • Cheap product, little quality

12. What is Quality • Manufacturing-based definition: conformance to specifications • The product has both variable specifications (measurable) and attributable specifications (non-measurable) that manufacturing monitors and ensures conformance

13. What is Statistical Process Control?

14. What is SPC • SPC, Statistical Process Control, is a process that was designed in the 1930’s to characterize changes in process variation from a standard. • It can be used for both attributes and variables

15. The basic tool used in SPC is the control chart • There are various types of control charts • Mean chart • Range chart • Median chart • Mean and range chart (X and R) • c chart • p chart, etc.

16. Control charts • a graphical method for detecting if the underlying distribution of variation of some measurable characteristic of the product seems to have undergone a shift • monitor a process in real time • map the output of a production process over time and signals when a change in the probability distribution generating observations seems to have occurred • are based on the Central Limit Theory

17. Central Limit Theorem says that the distribution of sums of Independent and Identically Distributed (IID) random variables approaches the normal distribution as the number of terms in the sum increases. • Things tend to gather around a center point • As they gather they form a bell shaped curve

18. The center of things are described in various ways • Geographical center • Center of gravity • In statistics, when we look at groups of numbers, they are centered in three different ways • Mode • Median • Mean

19. Mode • Mode • Mode is the number that occurs the most frequently in a group of numbers • 7, 9, 11, 6, 13, 6, 6, 3,11 • Put them in order • 3, 6, 6, 6, 7, 9, 11, 11, 13 • 3, 6, 6, 6, 7, 9, 11, 11, 13 • The mode is 6

20. Median ~ • Median (X) is like the geographical center, it would be the middle number • 7, 9, 11, 6, 13, 6, 6, 3,11 • Put them in order • 3, 6, 6, 6, 7, 9, 11, 11, 13 • 3, 6, 6, 6, 7, 9, 11, 11, 13 • 7 is the median

21. Mean • Mean is the average of all the numbers and is designated by the symbol μ for population mean and for sample mean • The mean is derived by adding all the numbers and then dividing by the quantity of numbers • X1 + X2 + X3 + X4 + X5 + X6 + X7 +…+Xn n _X

22. n Σ _X 1n = Xi i = 1 … to the nth number … … multiplied by 1 over n The sum of … The mean … … all the numbers … … is equal to … … from the first number …

23. 1 2 3 6 8 If we had the numbers, 1,2,3,6 and 8, you can see below that they “balance” the scale. The mean is not geometric center but like the center of gravity

24. As the numbers are accumulated, they are put in order, smallest to largest, and the number or each number can then be put into a graph called a Histogram

25. 45 40 35 30 25 20 15 10 5 40 45 50 55 60

26. 45 40 35 30 25 20 15 10 5 40 45 50 55 60

28. A normal curve is considered “normal” if the following things occur • The shape is symmetrical about the mean • The mean, the mode and the median are the same

29. _ X Variation

30. _ X

31. Workshop I Central Tendency

32. Variation • The numbers that were not exactly on the mean are considered “variation” • When weighing the candy, the manufacturer is targeting a specific weight • Those that do not hit the specific weight are variations. • Will there always be variation? • There are two types of variation • Common cause variation • Special cause variation

33. Common Cause • Common cause variation is that normal variation that exists in a process when it is running exactly as it should • eg. In the production of that candy • When the operator is running the machine properly • Within cycle time allotted for each drop of candy • Candy is properly placed on trays • Temperatures are where they need to be • Mixture is correct

34. When the machine is running properly • Tooling is sharp and aligned correctly • All components are properly maintained • Voltage is correct • Safety interlocks are properly set • When the material is correct • Hardness • Size • Thickness • Blend

35. When the method is correct • Right tonnage machine • Proper timing • When the environment is correct • Ambient temperature • Ambient humidity • Dust and dirt • Corrosives • When the original measurements are correct • Die opening dimensions

36. As we have just reviewed, common cause variation cannot be defined by one particular characteristic • It is the inherent variation of all the parts of the operation together • Voltage fluctuation • Looseness or tightness of bearings

38. Common cause variation must be optimized and run at a reasonable cost • Don’t spend a dollar to save a penny

39. Special Cause • Special cause is when one or more of the process specifications/conditions change • Temperatures • Tools dull • Voltage drops drastically • Material change • Stops move • Bearings are failing

40. Special cause variations are the variations that need to be corrected • But how do we know when these problems begin to happen? Statistical Process Collection and Control!

41. Workshop II Range and Mean Variation

42. Variation in the process occurs two major ways. • The range changes • The mean changes

43. Range is the smallest data point subtracted from the largest data point • It represents the total data spread that has been sampled • If the range gets smaller, or more significantly if it gets larger, something has changed in the process.

44. _ X Changed Process Normal Process Changed Range Normal Range

45. _ X Normal Process Changed Process Changed Range Normal Range

46. Give me some examples that you would think would cause the range to tighten up • How about loosen up?

47. If you remember, the mean is the point around which the data is centered • If the mean changes, then it would mean that the central point has changed

48. Now lets see what the curve would look like if the mean changed

49. _ X

50. _ X _ X’