Chapter 3

1. Chapter 3

2. There are no two things in the world that are exactly the same… And if there was, we would say they’re different. - unknown Measurement concepts

3. Measurement terms Discrimination The smallest unit of measurement on a measuring device. Resolution The capability of the system to detect and faithfully indicate even small changes of the measured characteristic. Maximum error Half of the accuracy. Tolerance, specification limits Acceptable range of a specific dimension. Can be bilateral or unilateral

4. Measurement terms Distribution A graphical representation of a group of numbers based on frequency. Variation The difference between things. Population Set of all possible values. Sample A subset of the population.

5. Measurement terms Randomness Any individual item in a set has the same probability of occurrence as all other items within the specified set. Random Sample One or more samples randomly selected from the population. Biased Sample Any sample that is more likely to be chosen than another.

6. Initial thoughts • It is impossible for us to improve our processes if our gaging system cannot discriminate between parts or if we cannot repeat our measurement values. • Every day we ask “Show me the data” - yet we rarely ask is the data accurate and how do you know?

7. Initial thoughts Success depends upon the ability to measure performance. Rule #1: A process is only as good as the ability to reliably measure. Rule #2: A process is only as good as the ability to repeat. Gordy Skattum, CQE

8. Impact of bad measurements on SPC • Difficult or impossible to make process improvements • Can make our processes worse! • Causes quality, cost, delivery problems • False alarm signals, increases process variation, loss of process stability • Improperly calculated control limits

9. Variation • Some variation can be experienced with natural senses: • The visual difference in height between someone who is 6'7" and someone who is 5'2". • Some variation is so small that an extremely sensitive instrument is required to detect it: • The diametrical difference between a shaft that is ground to ∅.50002 and one that is ground to ∅.50004.

10. Types of variation • Normal variation • running in an expected, consistent manner, we would consider it normal or common cause variation. • Non-normal variation • running in a sudden, unexpected manner, we would consider it non-normal, or assignable cause variation. We only want normal variation in our processes

11. Why only normal variation? • Statistical control - shows if the inherent variability of a process is being caused by normal causes of variation, as opposed to assignable or non-normal causes.

12. What is a distribution? Each unit of measure is a numerical value on a continuous scale Variation common and special causes Pieces vary from each other Size Size Size Size But they form a pattern that, if stable, is called a distribution Normal Distribution Histogram

13. Distributions There are three terms used to describe distributions 1. Shape 2. Spread 3. Location

14. Concept of goal posting Lower Spec Upper Spec Average Capability Specification Tolerance Left Upright Right Upright Goal Post

15. The Taguchi Loss Function Concept Lower Spec Upper Spec Mean (target) Cost at lower spec Cost at upper spec Potential Failures Cost Cost at mean Waste

16. What happens when “Shift Happens?” • Because we are using all of our tolerance, we’re forced to keep the process exactly centered. If the process shifts at all, nonconforming parts will be produced Lower Specification Limit Upper Specification Limit Target

17. Getting started • Using 75% or less of a tolerance will allow processes to shift slightly with little chance of producing any defects • The goal is to improve your process in order to use the least amount of tolerance possible • Reduce the opportunity to produce defects • Reduce the cost of the process We need to calculate process capability

18. Low High Spread Too Large Low High Pictures of “BAD” quality Low High Off Center 65 73.5 75 65 70 75 Off Center & Spread Combination 65 68 75

19. World-class Quality Using only 50% of the tolerance or less Lower Specification Limit Upper Specification Limit 65 70 75 6 s

20. Statistics • What is statistics? • How are statistics used with: • Baseball Scouts • Bankers • Weathermen • Television Networks • Insurance Agents

21. Using statistics

22. Central tendency • Mean - can be found of a group of values by adding them together, and dividing by the number of values. The mean is the average of a group of numbers. We will use it to find out where the center of a distribution lies. ** 100k is the mean because it is the middle weighted value.** Remember - Average and Mean are synonymous!!!

23. Central tendency • Median - The median represents the data value that is physically in the middle when the set of data is organized from smallest to largest. If there are an odd number of data values, there will be just one value in the middle when the data are ordered, and that value is the median. If there is an even number of values, order the values and average the two values that occur in the middle. ** 100k is the median because after the data is arranged in order it is exactly half way to both ends.** • Mode- The mode represents the data value that occurs the most or the class that has the highest frequency in a frequency distribution. ** 100k is the mode because it occurs more than the others in the data table.**

24. Dispersion • Range is a measure that shows the difference between the highest and lowest values in a group. To find range, subtract from the highest value the lowest value. • The formula for range is: R = H - L R = range H = highest value L = lowest value

25. Example #1 Using the following numbers, lets find the range: The data is 4,7,6,1,15,10. R = H - L R = 15 - 1 R = 14 The range is 14. Example #2 Two consecutive parts in an order have the following sizes: .250, .2535 R = H - L R = .2535 - .250 R = .0035 Range examples

26. Standard deviation • Standard Deviation (sigma) is a more descriptive measure of the spread or variability of a group than is range. • It is better defined as the “average deviation from the mean” of any process. • If all of the parts in a group have a large range, the standard deviation will normally be quite high. If the same parts have a small range, the standard deviation will also be small.

27. Estimating sigma – The Shewhart Formula Although the method we just used to calculate standard deviation is accurate, it is also very time consuming. Because time is money in industry, we find that it becomes more cost effective to estimate standard deviation rather than calculate the exact number. This gives us a number very close to the exact number, but in a very short time period. The following formula is used to estimate standard deviation: Where....... = Estimate of Standard Deviation = the average range among the samples in each subgroup and, = a constant based on the number of samples in each subgroup An Individuals X and Moving Range chart, which we will discuss in detail later, uses subgroup sizes of two. The d2 value for subgroups of size two = 1.128. Therefore, we can easily calculate an estimate of standard deviation for IX & MR charts by dividing the average of all range values by 1.128. The numbers are .3472, .3476, .3478, .3479, .3474, .3472: Your book also calls this “s” See Table B.1 for d2 values

28. Estimating standard deviation exercise An operator is running a job on a lathe. The tolerance is .656-.657. The following values were documented. Complete the calculations and answer the questions that follow.

29. Histograms 10 9 8 7 6 5 4 3 2 1 Tally histogram

30. Histograms (cont.....)

31. Histograms (cont.....)

32. Let’s look at how this fits together…

33. Dev. from Heights Avgerage. Total Xbar » Sigma!! (average) Calculate our statistics Let’s practice Find: Mean Median Mode Range Sigma -population -sample -est. of 5’ = 60” 6’ = 72”

34. Xbar = Step 2 Create a Histogram - (Use 2" Scale increments) Sigma Area % Height Span Realistic? (Y/N) +/- 1 Sigma +/- 2 Sigma +/- 3 Sigma +/- 6 Sigma Plot height data and use the statistics Step 3 Add Sigma Limits Step 4 Analyze

35. Population vs. sample Sample Population Low Speed Limit High Speed Limit 65 70 75