By Mark Schnittker

1. Manufacturing Statistics and project management By Mark Schnittker

2. Section 1: Manufacturing Statistics

3. What is statistics? • Statistics is a mathematical technique which uses probabilities. • Statistics are used to assist in decision making when there is not enough data. • We use statistics to: • Try to predict the future using sample data from the past. • Try to evaluate a situation and find correlations.

4. Job of statistics in decision making • Humans have intuition, but also have bias • Statistics has no bias, but also has no intuition. Ultimately, the human must evaluate the information and make a decision Statistical techniques help convert data into information. Humans evaluate Decision (Always by a human) Analysis JMP, minitab, Excel Information Graphs or numbers Data Incorrect data analysis leads to bad information. Use simple techniques so that the nature of the data is not obscured in the technique.

5. Don’t be fooled by fancy numbers. There are lies, there are outrageous lies, and then there are statistics. • -Sir Robert Giffen 1837-1910

6. Definitions: Precision and Accuracy • Accuracy is a measure of Typical Value associated with Calibration. • Precision is a measure of data spread associated with Reproducibility. Precise, but not Accurate Accurate but not precise Not Precise or Accurate Accurate and precise

7. We try to describe data with two numbers: • Typical Value: • Mean, μ, Xbar, Average: The average of all values in a data set. • Median: The 50th percentile. The value at which half of the population has higher values, and half has lower. • Average Quartile: The average of the 0.25 and 0.75 percentile • Mode: The histogram bin value with the largest population count. • Spread: • Range: The Maximum minus the Minimum. • Minimum: the lowest value in a data set • Maximum: The highest value in a data set • Standard Deviation: A complex metric to describe the spread of a “normal” data set. • Delta Quartiles: The difference between the 0.25 and 0.75 percentile divided by 1.35. Used for “normal” data that has outliers.

8. Example of typical value and spread A “Histogram” shows the data distribution Here we use “Mean” to find the typical value, and “Standard Deviation” to describe the spread.

9. Populations: Concept of “distribution” A “distribution” is a probability that a part in a population will have a certain value There are many types of distributions. Most of the statistical techniques are designed for “Normal” distributions.

10. Cpk checks if a process is “Good Enough” Something is “Good enough” when it is good relative to the requirements. Tolerance Cpk = Precision Cpk is a ratio to compare performance against specs

11. High Cpk gives high yield • The better your process Cpk, the better your output yield. • Less scrap!

12. Tolerance: Compare specs to a typical value T=Tolerance = distance from typical value to closest spec

13. How Tolerance gets small when close to the specs • Have you ever heard any one say “this process has tight tolerances”? • A small tolerance means that the specs are tight, and so the process control must be very good. When a typical value is outside of the specs, then the Tolerance becomes negative.

14. Process and Gauge Precision • P=Precision • For a one sided precision, P=3σ • For a process, σ is the standard deviation measured across the population. • For a gauge, σ is the standard deviation across multiple measurements of the same part. Measure multiple parts, 3-10 times each to get a typical σ

15. Example: Cpk for Process • In this example, the standard deviation can be from the process of the gauge Choose the smaller value

16. Example: Gauge P/T, real data with absolute specs Standard Deviation Median Median Median Example data with specs from 0.2 to 1.5

17. How to calculate Precision for correlation Paired data matches the same part to the same data • Calculate the “residual” of each part, which is just value “B” minus the reference value “A”. • Take the Median residual • Use the median residual as the “Precision” in a Cpk calculation. • Spec: Residual Ratio >30 Median B-A

18. Correlation: Residual Analysis (Unpaired) Use Unpaired data when it is not possible to take paired data. Un-Paired data has different parts with different population sizes in each data set. Unpaired data needs large data sets to give good information for decision making. Median • Calculate the typical value (median) for each population. • Take the “residual” of the two medians (Btypical-Atypical). • Use the residual of the medians as the “Precision” in a Cpk calculation. • Spec: Residual Ratio> 30 B-A

19. Caution on “Typical Value” Some populations have no clear “Typical value” For a distribution like this, its usually best to use a graphical approach. In the distribution above, a typical value can be calculated, but the meaning has been lost. This requires more advanced statistical techniques, or simply to switch to graphical techniques.

20. What do you do when data is not normal? For non-normal data, a histogram or scatter plot may be the best way to convert the data into information. Histogram with specs to show capability. Scatter plot with specs to show correlation. The data rides the diagonal

21. Remember this Summary • Statistics converts data into information to help the human make decisions. • “Typical Value”: Look at the data. If Normal, use Median • If data is not Normal, switch to graphical approach. • Tolerance (T): Distance from typical value to nearest spec. • Precision (P): Uncertainty in a process or gauge. • Capability: • |Cpk| (T/P)> 1 for a process. Use 3*product sigma for P • P/T<0.3 for a gauge. Use 3*median tool sigma for P • Correlation: • Make a scatter plot. Line fit only if data is clean. • Residual Ratio >=30. Use median residual for “P”

22. SPC monitors the accuracy and precision of a system Xbar is the Average of a set of values. This shows the Accuracy, which is the calibration of the system. Range R, or Standard Deviation S charts show the variation across the parts. This shows the Precision of the system.

23. Box plots for trending or comparison Using JMP Using Excel Median and quartiles are drawn as a function of time or other grouping

24. Additional Statistical Techniques

25. Percentiles: What are they? A percentile is a method of simplifying distributions. Percentiles ignore outliers First sort the data in ascending order. Then find the value part way down the list so that “X” percent of the parts are above that value. If the percentile falls between individual parts, then take the weighted average.

26. Use Percentile to calculate Typical value and Spread. For data that has a normal distribution, but has outliers, we can use Quartiles to calculate typical value and spread using only the middle half of the data. Typical value = average of the first and third quartile. Spread= (third quartile-first quartile)/1.35

27. T-test logic: Used for Correlations • Start by declaring that the two populations are the same. • A null hypothesis of a mean difference =0 is the same as declaring that you think that the two populations have the same mean, meaning that they are the same. • The t-test tries to disprove the null hypothesis. • The t-test will try to show that the null hypothesis is incorrect using statistics. The t-test will show how different it thinks that the two means are, and then show a number of its lack of confidence. • If the t-test has more than 5% in-confidence in trying to disprove the null hypothesis, then we say that the t-test failed to disprove that the two populations are different. • The t-test does not prove that two populations are the same. The t-test only fails at trying to disprove that the two populations are different, and then we conclude that the populations are the same.

28. Different types of t-tests • Un-paired: “Two sample, assuming un-equal variances” • To compare two population which do not have the same standard deviations. • Un-Paired: “Two sample assuming equal variances” • To compare two populations with similar standard deviations. • Paired: “Paired two sample for means” • To compare the exact same population measured twice, and the data is indexed properly.

29. How to read an Excel t-test If P (T<=t) >0.05, then the two populations are considered statistically equivalent • Observations= the number of measurements in each population. • Hypothesized mean difference of 0 states the null hypothesis is that the two populations are the same. • df =degrees of freedom • t Stat = your Calculated t value (T) • t-Critical refers to the table value against which your t-Critical is tested • P(T<=t) reads “the probability that your Calculated T is less than or equal to the critical t” • in order to reject the null hypothesis at 95% confidence that the two means are the same, you would need a two tailed P(T<=t) less than or equal to 0.05

30. Paired and Un-paired data: Definition • Paired data means that there are a “pair” of measurements for each part. Design your experiments to use paired data when possible. If you must use un-paired data, then increase your population size.

31. Section 2: Project Management

32. What is project management • Project management is the practice of starting and completing a project as effectively as possible using available resources • Project owners use project management to successfully complete projects.

33. Why use project management? • Because it saves time and money. • Project management sometimes feels like additional work, but in the long run, it is the most efficient way to complete projects

34. Section 2 Project Management, Step by step

35. Quick Overview. 7steps 1) Define the project scope 2) Make General description and identify risk 3) Define the stakeholders 4) Define specifications 5) Do the project 6) Verification- Project owner compare project results to specifications. 7) Validation- All stakeholders review data and decide if the project scope is met.

36. Step 1, Define Project scope • Define what the project will accomplish. • Define what the project will NOT accomplish. • Though this sounds simple, it is the most overlooked part of a project. If the project scope is not clearly defined, then the project has not clear end point. Different stakeholders have different perspectives of what is needed to complete the project, and items are often added near the end of a project. This is called scope creep. A good project owner avoids scope creep. • If you are a project owner, do not accept a project unless the scope can be clearly defined.

37. Example: Project scope • Project scope • Install a new tool in the CM manufacturing line • Give training to operators and technicians to allows use of the tool • Outside of project scope • Retire the old tool • Build and qualify a new fixture to hold back fill gases. • Order spare parts for the new cap seal tool • Find a new electrode source

38. Step 3: Stakeholders • A Stakeholder is any one that contributes to, or is affected by the project. • Stakeholders are the ones that must agree on the project specs, and project outcome. • Stakeholders that are customers of the results of the project must have sign off authority in the tech review of the ECO which will complete the project. • Stakeholders which contribute to the project, but are not customers of the project will be notified, but their signature is not required.

39. Step 5: Do the project, review the data • Show all relevant collected data to support the statements made on the specifications sheet. • The project owner will be checking the data against the project specifications. This is “Verification”

40. Step 6: Verification • Project owner compares all project data to the project specification, and fills in the “Actual” results of the project. • Project owner creates a “Validation Report” for the stakeholders to review. • Validation report includes: • Scope • General Points and Risk • Stakeholders • Specifications • Project Data • Sing off action slide • Validation notes slide

41. Step 7: Validation-Project Completion • The project owner reviews the validation report with all the stakeholders, fills out “Validation notes” slide and does any additional work needed. • Validation meetings or email exchanges are optional. • The project owner Submits an ECO which reflects the changes that result from the project completion. • Attach Validation report to ECO. • All Stakeholders with signature required are to be in tech review of the ECO. • When Stakeholders sign the ECO, they are agreeing that the project is complete with in the scope of their interest. • The project is complete when the ECO is complete