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Quality Control

Quality Control. Agenda. - What is quality? - Approaches in quality control - Accept/Reject testing - Sampling (statistical QC) - Control Charts - Robust design methods. What is ‘Quality’. Performance :. - A product that ‘performs better’ than others at same function Example:

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Quality Control

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  1. Quality Control Agenda - What is quality? - Approaches in quality control - Accept/Reject testing - Sampling (statistical QC) - Control Charts - Robust design methods

  2. What is ‘Quality’ Performance: - A product that ‘performs better’ than others at same function Example: Sound quality of Apple iPod vs. iRiver… - Number of features, user interface Examples: Tri-Band mobile phone vs. Dual-Band mobile phone Notebook cursor control (IBM joystick vs. touchpad)

  3. What is ‘Quality’ Reliability: - A product that needs frequent repair has ‘poor quality’ Example: Consumer Reports surveyed the owners of > 1 million vehicles. To calculate predicted reliability for 2006 model-year vehicles, the magazine averaged overall reliability scores for the last three model years (two years for newer models) Best predicted reliability:Sporty cars/Convertibles Coupes Honda S2000 Mazda MX-5 Miata (2005) Lexus SC430 Chevrolet Monte Carlo (2005)

  4. What is ‘Quality’ Durability: - A product that has longer expected service life Nike Air Resolve Plus Mid Men’s Shoe (no warranty) Adidas Barricade 3 Men's Shoe (6-Month outsole warranty)

  5. What is ‘Quality’ Aesthetics: - A product that is ‘better looking’ or ‘more appealing’ Examples? ? or

  6. Defining quality for producers.. Example: [Montgomery] - Real case study performed in ~1980 for a US car manufacturer - Two suppliers of transmissions (gear-box) for same car model Supplier 1: Japanese; Supplier 2: USA - USA transmissions has 4x service/repair costs than Japan transmissions Lower variability  Lower failure rate Distribution of critical dimensions from transmissions

  7. Definitions Quality is inversely proportional to variability Quality improvement is the reduction in variability of products/services. How to reduce in variability of products/services ?

  8. QC Approaches (1) Accept/Reject testing (2) Sampling (statistical QC) (3) Statistical Process Control [Shewhart] (4) Robust design methods (Design Of Experiments) [Taguchi]

  9. Accept/Reject testing - Find the ‘characteristic’ that defines quality - Find a reliable, accurate method to measure it - Measure each item - All items outside the acceptance limits are scrapped Lower Specified Limit Upper Specified Limit target Measured characteristic

  10. Problem with Accept/Reject testing (1) May not be possible to measure all data Examples: Performance of Air-conditioning system, measure temperature of room Pressure in soda can at 10° (2) May be too expensive to measure each sample Examples: Service time for customers at McDonalds Defective surface on small metal screw-heads

  11. Problems with Accept/Reject testing Solution: only measure a subset of all samples This approach is called: Statistical Quality Control What is statistics?

  12. The standard deviation =s= =√( s2) ≈ 0.927. Background: Statistics Average value (mean) and spread (standard deviation) Given a list of n numbers, e.g.: 19, 21, 18, 20, 20, 21, 20, 20. Mean = m =S ai / n = (19+21+18+20+20+21+20+20) / 8 = 19.875 The variance s2 = ≈ 0.8594

  13. Background: Statistics.. Example. Air-conditioning system cools the living room and bedroom to 20; Suppose now I want to know the average temperature in a room: - Measure the temperature at 5 different locations in each room. Living Room: 18, 19, 20, 21, 22. Bedroom: 19, 20, 20, 20, 19. What is the average temperature in the living room? m =Sai / n = (18+19+20+21+22) / 5 = 20. BUT: is m = m ?

  14. Background: Statistics... Example (continued) m =Sai / n = (18+19+20+21+22) / 5 = 20. BUT: is m = m ? If: sample points are selected randomly, thermometer is accurate, … then m is an unbiased estimator of m. - take many samples of 5 data points, - the mean of the set of m-values will approach m - how good is the estimate?

  15. ≈ 1.4142 sn= The unbiased estimator of stdevof a sample = s = Background: Statistics.... Example. Air-conditioning system cools the living room and bedroom to 20; Suppose now I want to know the variation of temperature in a room: - Measure the temperature at 5 different locations in each room. Living Room: 18, 19, 20, 21, 22. BUT: is sn = s? No!

  16. Sampling: Example Soda can production: Design spec: pressure of a sealed can 50PSI at 10C Testing: sample few randomly selected cans each hour Questions: How many should we test? Which cans should we select? To Answer: We need to know the distribution of pressure among all cans Problem: How can we know the distribution of pressure among all cans?

  17. Sampling: Example.. How can we know the distribution of pressure among all cans? Plot a histogram showing %-cans with pressure in different ranges

  18. 30 40 35 45 55 70 60 65 50 pressure (psi) Sampling: Example… Limit (as histogram step-size)  0: probability density function why? pdf is (almost) the familiar bell-shaped Gaussian curve! True Gaussian curve: [-∞ , ∞]; pressure: [0, 95psi]

  19. Why is everything normal? pdf of many natural random variables ~ normal distribution WHY ? Central Limit Theorem Let X random variable, any pdf, mean, m, and variance, s2 Let Sn = sum of n randomly selected values of X; As n  ∞ Sn approaches normal distribution with mean = nSn, and variance = ns2.

  20. -1, with probability 1/3 0, with probability 1/3 1, with probability 1/3 p(S1) X1 = S1 1 0 -1 -2, with probability 1/9 -1, with probability 2/9 0, with probability 3/9 1, with probability 2/9 2, with probability 1/9 X1 X2 X1 + X2 -1 -1 -2 -1 0 -1 -1 1 0 0 -1 -1 0 0 0 0 1 1 1 -1 0 1 0 1 1 1 2 X1 + X2 = p(S2) S2 1 2 0 -2 -1 -3, with probability 1/27 -2, with probability 3/27 -1, with probability 6/27 0, with probability 7/27 1, with probability 6/27 2, with probability 3/27 3, with probability 1/27 Gaussian curve Curve joining p(S3) X1 + X2 + X3 = p(S3) 3 1 2 S3 0 -2 -1 -3 Central limit theorem.. Example

  21. (Weaker) Central Limit Theorem... Let Sn = X1 + X2 + … + Xn Different pdf, same m and s normalized Sn is ~ normally distributed Another Weak CLT: Under some constraints, even if Xi are from different pdf’s, with different m and s, the normalized sum is nearly normal!

  22. Central Limit Therem.... Observation: For many physical processes/objects variation is f( many independent factors) effect of each individual factor is relatively small Observation + CLT  The variation of parameter(s) measuring the physical phenomenon will follow Gaussian pdf

  23. Sampling for QC Soda Can Problem, recalled: How can we know the distribution of pressure among all cans? Answer: We can assume it is normally distributed Problem: But what is the m, s ? Answer: We will estimate these values

  24. Outline

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