UnitManufacturingProcessesAssembly and Joiningi 1 2.008 QUALITY Manufacture Manufacturing Research Factory, ••••••••Stamping •Conceptual Manufacture 2.008 - Sprng 2004 Unit Processes Assembly and Joining Market Systems & Enterprise Welding Bolting Bonding Soldering Machining Injection molding Casting Chemical Vapor Deposition Design Design for i 3 Outline i 4 What is quality? 2.008 - Sprng 2004 1. What is quality? 2. Variations 3. Statistical representation 4. Robustness Read Chapter 35 & 36 2.008 - Sprng 2004 i 5 Variations i 6 Variable Outcome ials 1 2 3 4 5 6 7 ) ) ) i () i i ) i ) 2.008 - Sprng 2004 1. Part and assembly variations 2. Variations in conditions of use 3. Deterioration 2.008 - Sprng 2004 Results from measuring intermediate or final process outcome Men Machines Mater Methods Outcome is measured • Unit of measure (mm, kg, etc.•The measurement method must produce accurate and precise results over time • Shaft O.D. (inches• Hole distance from reference surface (mm• Circuit res stance ohms) • Heat treat temperature (degrees• Railcar trans t t me (hours• Engineering change processing t me (hoursOutcome examples 1Technological Development • Physical masters • Engineering drawings • Go / No-Go gage • Statistical measurement • Continuous on-line measurement Engineered Part • Design specification +/- 0.004” • Process specification 4.5” 1.5” 1.00” +/- 0.1” +/- 0.1” +/- 0.004” 2.008 - Spring 2004 7 2.008 - Spring 2004 8 2.008 - Spring 2004 9 Engineered Part (cont’d) 1.0013 0.9986 1.0015 0.9996 1.0060 0.9997 1.0029 0.9977 1.0042 0.9955 1.0019 0.9970 0.9992 1.0034 0.9995 1.0022 1.0020 0.9960 1.0013 1.0020 • Raw data, n = 20 • 6 Buckets .994 - .996 2 .996 - .998 2 .998 - 1.000 5 1.000 - 1.002 6 1.002 - 1.004 3 1.004 - 1.006 2 2.008 - Spring 2004 10 Engineered Part • Design specification +/- 0.004” • Process specification 4.5” 1.5” 1.00” 0 1 2 3 4 5 6 7 .996 .998 1.000 1.002 1.004 1.006 Diameter, in. F requenc y +/- 0.1” +/- 0.1” +/- 0.004” .994 - .996 - .998 - 1.000 - 1.002 - 1.004 -Manufacturing Outcome: Central Tendency Falling balls hit 12 Central Tendency Halloween M&M mass histograms: n = 100 0 5 10 15 20 25 30 35 40 45 0.7167 - 0.75058 0.75058 - 0.78446 0.78446- 0.81834 0.81834 - 0.85222 0.85222- 0.8861 0.8861- 0.91998 0.91998 - 0.95386 0.95386 - 0.98774 Mass , g Frequency 8 buckets these pins and go either left or right 2.008 - Spring 2004 11 Ball part way through row of pins 2.008 - Spring 2004 20.71670 Dispersion Mean 0.89876 Median 0.90183 Std. Dev. Minimum 0.04255 Maximum 0.98774 0.7000 0.7580 0.8160 0.8740 0.9320 0.9900 Mass of Halloween M&M/ g, n=100 2.008 - Spring 2004 13 Statistical Distribution n• Central tendency ∑ xi – Sample mean (arithmetic): x = i =1 n – Sample median n• Measures of dispersion ∑( x − x )2 i s = i =1– Standard deviation n n 2 i 2 i =1– Variance s =∑( x − x ) n – Range 2.008 - Spring 2004 14 Normal Probability Density Function 2 ⎞ 1 ⋅ e ⎜⎝⎜⎛−( x 2 − sx 2 ) ⎠⎟⎟ (x f ) = 2 πs f( x) bProbability a P ≤ x ≤ b }= x f ) dx{ (∫ a ∞ x (P {≤ ∞ − x ∞ ≤ }=∫ x f ) dx = 1 For allx , s ab ∞ − PNormalized x − x z = s 2z 2 2{z P 1 ≤ z ≤ z 2 }= ∫ 1 e − z dz z2 πz 1 2.008 - Spring 2004 15 Areas under the Normal Distribution Curve P Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 z-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 1 0 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 2.008 - Spring 2004 16 Areas under the Normal Distribution Curve P 0.6141 Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948