Measurement System Analysis-3rd

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<p>Measurement System Analysis D. J. Wheeler</p> <p> () - Isuzu Motors , Hino Motors , Summit Auto Seat Group Delphi Automotive Systems, Yuasa Battery ,Summit Showa Thai Summit Group. ,Sammitr Motors, Yanmar S.P. Co., Ltd. , Bangchan General Assembly , Toyoda Kosei Vandapac (Max liner), Mitsuboshi Belting , Topy Fastener Auto Alliance, Aichi International, Miyoshi Precision Tel :0-2921-8818 Mobile : 08-1347-5600 Koyo Manufacturing , Toyoda Machine Works e-mail: sopon567@yahoo.com sopon567@hotmail.com JVC Manufacturing , Electrolux , Western Digital Thai Stanley Electric, Lite-On Electronics York Industrial , Star Microelectronics , Kanom and Rayong Electricity Generating Gemba SPC Management Consultant and Manager PTT PLC , GE Plastics (Thailand) , Surapon Foods LVM (Asia) Co., Ltd. Thai Airway International , APL Logistics Consultancy Service Manager Citi bank , Piyavate Hospital , Padang Industry Andersen Consulting Co., Ltd. (Accenture) Thai Caprolactum , Thai Polyacetal , UBE Nylon Quality Controller Thai Shell Exploration and Production , Index Furniture Bangkok Furnitech (Index furniture) , Bangsue Chiameng AT&amp;T Microelectronics (Thai) Co., Ltd. (Agere system) QRA and SPC Engineer South East Asian Packaging and Canning , STB Textile Berli Jucker Cellox , Rubia Industry 08-1347-5600 , PQ Chemical</p> <p> (Tools and Techniques)Management Group ISO 9001 , ISO 14001 ISO/TS 16949 Total Quality Management (TQM) Strategic Management Policy Management Business Plan Balanced scorecard Key Performance Indicator Benchmarking Six sigma Effective Decision Making Time management Daily management Eco-Design , RoHs Clean technology Life cycle analysis Productivity Group Lean Manufacturing Toyota Production System Just In Time Kaizen Productivity Improvement Industrial Engineering Techniques 5S , VFP Poka-Yoke VA-VE Total Productive Maintenance (TPM) P-M Analysis Visual Control OEE Line Balancing Time Management Team Work and Building Managing Waste (Muda Mura Muri) Quality Group Quality control / Assurance APQP and PPAP FMEA and Control Plan Statistical Process Control Measurement System Analysis QCC and 7 QC Tools New QC 7 Tools Problem Solving Methods and 8D Root cause analysis and corrective action Quality Awareness Continuous Improvement Why-Why Analysis (5 why) QFD/QFDE</p> <p>08-1347-5600</p> <p> ...</p> <p> . . </p> <p>8</p> <p> = + 9</p> <p> (Common Cause) (Special Cause)10</p> <p> Output</p> <p> 12</p> <p> (Population) (population parameter)13</p> <p> &gt;&gt; &gt;&gt; n &gt;&gt; xn x = n =1 n &gt;&gt; 14</p> <p> 50% &gt;&gt; &gt;&gt; &gt;&gt; 15</p> <p> (Range) &gt;&gt; Range = max min &gt;&gt; (Variance) n (X i X) 2 &gt;&gt; s 2 = i =1 n 1 &gt;&gt; 16</p> <p> (Standard Deviation) &gt;&gt; 2 &gt;&gt; &gt;&gt; n</p> <p>s=</p> <p>(X i X) 2 i =1</p> <p>n 1</p> <p>s = R / d2</p> <p>17</p> <p>()</p> <p> ,19</p> <p> , </p> <p>LSL</p> <p>USL</p> <p>21</p> <p> 22</p> <p>Point of Inflection</p> <p>p(d) 1 p(d)</p> <p>1</p> <p>2</p> <p>3</p> <p>4</p> <p>5</p> <p>6</p> <p>TT</p> <p>USL</p> <p>MSA: 1 2 2</p> <p> 1 2 65</p> <p>MSA: ()</p> <p> 1 2 ():+</p> <p>2 ()</p> <p>=</p> <p>2 ()</p> <p> 2</p> <p>1. 2 ? 2. ? 3. ?66</p> <p> =+</p> <p>69</p> <p> () </p> <p> () </p> <p>........ ...</p> <p>. ........ ..</p> <p>. . . . .. . . . . . . .</p> <p>. . . . .. . . . .</p> <p>70</p> <p>MSA: : = + 71</p> <p>MSA: </p> <p> () = () + ()</p> <p>2</p> <p>() =</p> <p>2</p> <p>() +</p> <p> ()2</p> <p> 72</p> <p> R&amp;R ( , ) 2 2 MSA </p> <p>73</p> <p>Reproducibility</p> <p>Repeatability</p> <p> 74</p> <p> = + R&amp;R</p> <p> 2 2 = 2 + measurement total product </p> <p>75</p> <p> () 76</p> <p>80</p> <p> ? ? ? ? ?</p> <p>81</p> <p> ()</p> <p>Discrimination , Resolution</p> <p>1 2 : ?83</p> <p>? ? , : 10 (6 ) QC 10 </p> <p>84</p> <p> (R Chart) , 4 1 4 Range of Thickness0.020 0.015 0.010 0.005 0.000 5 10 15 20 25 UCL=0.0102 Avg.=0.0048 LCL=0.0000</p> <p>Subgroup#</p> <p>85</p> <p>? ?</p> <p>?1. () (Noise) 2. 86</p> <p>X - R CONTROL CHARTPart Number Part Name Characteristic CL UCL 2.45 LCL 2.40 Department GENERIC Frequency STDW1- 4.76 Flare Length (ISO/F) Specification Q.C. 2 /SHIFT 2.3+0.5/-0.3 Machine Sample Size Unit E/F NO.3 4 mm Judge Tool Note</p> <p>X-Bar CHART</p> <p>CL UCL 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 LCL2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41</p> <p>2.35 2.30 2.25 2.20 2.15</p> <p>CL CL 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 UCL 0.25 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 UCL LCL LCL -</p> <p>R-CHART</p> <p>0.20 0.15 0.10 0.05 0.00</p> <p>n A2 D3 D42.30 2.30 2.30 2.30 2.40 2.40 2.40 2.40 2.30 2.30 2.30 2.30 2.40 2.30 2.30 2.30 2.30 2.40 2.40 2.30 2.40 2.40 2.40 2.30 2.40 2.30 2.30 2.30 2.30 2.40 2.40 2.30 2.40 2.50 2.40 2.30 2.40 2.30 2.40 2.30 2.30 2.30 2.40 2.40 2.40 2.40 2.40 2.40</p> <p>2 1.880 3.267</p> <p>3 1.023 2.575</p> <p>4 0.729 2.282</p> <p>5 0.577 2.115</p> <p>6 0.483 2.004</p> <p>7 0.419 0.076 1.924</p> <p>8 0.373 0.136 1.864</p> <p>9 0.337 0.184 1.816</p> <p>10 0.308 0.223 1.777</p> <p>Avg2.33 2.35</p> <p>Group 1</p> <p>2.36 2.37</p> <p>DATAX - Bar 2.38 2.30 2.33 2.30 2.33 2.38 2.40 2.35 2.38 2.40 2.38 2.33 R 0.10 0.00 0.10 0.00 0.10 0.10 0.00 0.10 0.10 0.20 0.10 0.10 25 26 Date 4 7 11 12 13 14 MSA 3rd 18 19 20 21 Gemba SPC Management (02)881-3756-7</p> <p>2.35 0.08</p> <p>87</p> <p>X - R CONTROL CHARTPart Number Part Name Characteristic CL UCL 2.45 LCL 2.40 Department GENERIC Frequency STDW1- 4.76 Flare Length (ISO/F) Specification Q.C. 2 /SHIFT 2.3+0.5/-0.3 Machine Sample Size Unit E/F NO.3 4 mm Judge Tool Note</p> <p>X-Bar CHART</p> <p>CL UCL 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 2.26 LCL2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.33 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.41</p> <p>2.35 2.30 2.25 2.20 2.15</p> <p>CL CL 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 UCL 0.25 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 UCL LCL LCL -</p> <p>R-CHART</p> <p>0.20 0.15 0.10 0.05 0.00</p> <p>n A2 D3 D42.36 2.32 2.31 2.31 2.34 2.36 2.40 2.42 2.32 2.30 2.33 2.34 2.36 2.34 2.34 2.32 2.30 2.35 2.40 2.30 2.35 2.40 2.36 2.44 2.38 2.34 2.31 2.32 2.30 2.35 2.36 2.30 2.35 2.45 2.41 2.31 2.39 2.30 2.36 2.33 2.35 2.33 2.40 2.35 2.42 2.40 2.45 2.37</p> <p>2 1.880 3.267</p> <p>3 1.023 2.575</p> <p>4 0.729 2.282</p> <p>5 0.577 2.115</p> <p>6 0.483 2.004</p> <p>7 0.419 0.076 1.924</p> <p>8 0.373 0.136 1.864</p> <p>9 0.337 0.184 1.816</p> <p>10 0.308 0.223 1.777</p> <p>Avg2.34 2.36</p> <p>Group 2</p> <p>2.35 2.37</p> <p>DATAX - Bar 2.37 2.33 2.33 2.32 2.32 2.35 2.39 2.34 2.36 2.39 2.39 2.37 R 0.03 0.04 0.05 0.02 0.05 0.03 0.04 0.12 0.10 0.15 0.12 0.13 25 26 Date 4 7 11 12 13 14 MSA 3rd 18 19 20 21 Gemba SPC Management (02)881-3756-7</p> <p>2.35 0.07</p> <p>88</p> <p> (Bias)</p> <p> (Bias) (Bias) NIST </p> <p> ()</p> <p> ()</p> <p>90</p> <p> = + </p> <p>: () NIST ()</p> <p>91</p> <p>: : (true value) () 1 2</p> <p>92</p> <p> : </p> <p>LSL93</p> <p> n &gt;10 (Reference value) n &gt;10 Histogram Special cuase abnormalities 95</p> <p> Xbar (Repeatability standard deviation, sigma rep.) t statistic , sigma b confidence bound</p> <p>96</p> <p> r r b =n t R d*</p> <p>2</p> <p>=</p> <p>Bias</p> <p>b</p> <p>97</p> <p>Bias -</p> <p>d2</p> <p>b</p> <p>tv, alpha</p> <p>* d2</p> <p>Bias +</p> <p>d2</p> <p>b</p> <p>tv, alpha</p> <p>* d2</p> <p>98</p> <p> r b = rn Max (xi) min (xi) d*2</p> <p>t</p> <p>=</p> <p>Bias</p> <p>b</p> <p> 0 2 Bias d2 b * d2 tv, alpha</p> <p>Bias +</p> <p>d2</p> <p>b</p> <p>tv, alpha</p> <p>* d2</p> <p>99</p> <p>. . . . . .</p> <p> 50 6.00/0.18 </p> <p> Reference Value ( mm ) = Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 READING 0.180 0.181 0.181 0.181 0.179 0.179 0.179 0.179 0.179 0.180 0.180 0.180 0.181 0.180 0.179 0.000 0.001 0.001 0.001 -0.001 -0.001 -0.001 -0.001 -0.001 0.000 0.000 0.000 0.001 0.000 -0.001107</p> <p>0.180 Bias</p> <p>Constant Value</p> <p>Mean0.05 1 15</p> <p>0.1799 0.0008 0.18 0.18 0.00</p> <p>-0.0001 0.0008 0.00 0.00 0.00</p> <p>g m</p> <p>Std. Dev. Max Min Range</p> <p>d2 3.47193 d2* 3.55333 n(m) Statiscals Summary</p> <p>Mean,</p> <p>Standard Deviation</p> <p>Standard</p> <p>x=</p> <p>xi =1</p> <p>n</p> <p>i</p> <p>n0.1799</p> <p>Range r = * d20.000562852</p> <p>r b = n</p> <p>Error of Mean</p> <p>Measured value</p> <p>15</p> <p>0.000145328</p> <p>108</p> <p> 0 bias Analysis Summary statistic of freedom t value ( 2-tailed) Lower Interval of the Bias Upper</p> <p>bias t = bMeasured value -0.9175</p> <p>(df) Mean-REF.</p> <p>Bias - [b ( t,1/2)]</p> <p>Bias + [b ( t,1/2)]</p> <p>10.8</p> <p>2.201</p> <p>-0.0001</p> <p>-0.00045</p> <p>0.00018</p> <p>X</p> <p>Acceptable, (0) Lower and upper 95% bias Unacceptable, (0) Lower and upper 95% bias</p> <p>109</p> <p> , , , , , 111</p> <p> (Stability)</p> <p> , , R&amp;R () 1 2</p> <p>113</p> <p> 1 2 , </p> <p>114</p> <p>Step , , ( ) , 115</p> <p>Step 3 Xbar&amp;R chart control limit Out of control Unstable116</p> <p> Control Chart</p> <p>1. ?UCL CL</p> <p>LCL</p> <p>117</p> <p> Control Chart</p> <p>2. 1 UCL</p> <p>CL</p> <p>LCL</p> <p> 2118</p> <p> Control Chart</p> <p>3. (Trend) ?UCL CL</p> <p>LCL</p> <p>119</p> <p> Control Chart</p> <p>4. (Periodicity)?UCL</p> <p>CL</p> <p>LCL</p> <p>120</p> <p> Control Chart</p> <p>5. UCL</p> <p>CL</p> <p>LCL</p> <p>121</p> <p> Control Chart</p> <p>6. UCL</p> <p>CL</p> <p>LCL</p> <p>122</p> <p>_ R chart X chart _ CL = R CL = X _ UCL = _ 2+R UCL = D2 R X+A _ LCL = X - A2R LCL = D3 R</p> <p> Xbar - R Chart X Chart (n) A2</p> <p>R Chart D3 D4 3.267 3.575 2.283 2.115 2.004</p> <p>d2 1.128 1.693 2.059 2.326 2.534</p> <p>2 3 4 5 6</p> <p>1.880 1.023 0.729 0.577 0.483</p> <p>123</p> <p>Stability Control ChartFax 02-744-7201P roduc t nam e P art no. P aram eter</p> <p>S TUD A 0123 D iam ete r1 2 3 4 5 6</p> <p>S pec ific ation Operation M ac hine no.</p> <p>0.75 0 +/- 0.00 5 Mac hining 119 10 11 12 13 14 15 16</p> <p>Chart no. unit of m eas urem ent Frequenc y</p> <p>1 inches every day20 21 22 23</p> <p>date tim e operato r S am ple</p> <p>7</p> <p>8</p> <p>17</p> <p>18</p> <p>19</p> <p>1 2 3 4 5</p> <p>5 5 5</p> <p>5 6 4</p> <p>6 4 3</p> <p>3 4 5</p> <p>4 7 7</p> <p>6 5 6</p> <p>5 5 4</p> <p>4 4 4</p> <p>6 5 6</p> <p>1 5 7</p> <p>5 5 1</p> <p>7 8 7</p> <p>3 4 7</p> <p>6 6 6</p> <p>3 4 4</p> <p>2 2 2</p> <p>5 4 6</p> <p>5 4 4</p> <p>0 4 2</p> <p>-1 -1 0</p> <p>8 8 4</p> <p>4 6 4</p> <p>4 5 6</p> <p>S um A verag e X -bar R ange R A verag e8.00 6.00</p> <p>15 15 13 12 185.00 5.00 4.33 4.00 6.00</p> <p>17 145.67 4.67</p> <p>12 17 13 11 2 2 14 18 114.00 5.67 4.33 3.67 7.33 4.67 6.00 3.67</p> <p>6 1 5 132.00 5.00 4.33</p> <p>6 419</p> <p>-2 20 1 4 1 56.67 4.67 5.00</p> <p>2.00 -0.67</p> <p>01</p> <p>22</p> <p>33</p> <p>24</p> <p>35</p> <p>16</p> <p>17</p> <p>08</p> <p>19</p> <p>610</p> <p>411</p> <p>112</p> <p>413</p> <p>014</p> <p>115</p> <p>016</p> <p>217</p> <p>118</p> <p>120</p> <p>421</p> <p>222</p> <p>223</p> <p>P owered B y Gem ba S P C M anagem ent</p> <p>4.00 2.00 0.00 -2.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23</p> <p>R angeP owered B y Gem ba S P C M anagem ent</p> <p>7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23</p> <p>124</p> <p> , , , </p> <p>125</p> <p> , , , </p> <p>126</p> <p> (Linearity)</p> <p> () ()</p> <p>130</p> <p> (range) y = x 3: y=x</p> <p> 1: </p> <p>y=x</p> <p> 2: </p> <p>131</p> <p>Step , 5 10 133</p> <p>Step 5 10 134</p> <p>140</p> <p>141</p> <p> (Ho) = &gt; 1994 Dr. Mikel J. Harry V3.0</p> <p>142</p> <p> : </p> <p> . T-test .Ho: . a = 0 Ha:. a = 0143</p> <p>t</p> <p>=</p> <p>a s</p> <p> tgm-2,1-/2 Reject H0, Aacept H1 [ ] [X] tb tgm-2,1-/2 Accept H0, Reject H1 tb &gt; tgm-2,1-/2 Reject H0, Aacept H1</p> <p>Final conclusion Acceptable X Unacceptable Comment:</p> <p>152</p> <p> , , , , , , 156</p> <p> (Repeatability &amp; Reproducibility)</p> <p>: 2meas = 2repeat + 2reprod R&amp;R 2meas :Precision-to-Tolerance Ratio (P/T)</p> <p> 2meas (P/TV):% (%R&amp;R) </p> <p>158</p> <p>2 2 2 2 = + + </p> <p>ndc = number of distinct category </p> <p>159</p> <p>: 2 2 2 2 = + + : () : </p> <p> () 160</p> <p> : </p> <p>2</p> <p>= + + 2 2</p> <p>2</p> <p> , , </p> <p>161</p> <p> : </p> <p>2</p> <p>= + + 2 2 2</p> <p>: </p> <p> 162</p> <p> : , , A B C B A C</p> <p>163</p> <p> P/T 5.15 * meas P/T = Tolerance = USL - LSL</p> <p> 5.15 meas 99% 10% &lt; 30% 164</p> <p>P/TV %R&amp;RP/TVmeas P / TV = Total </p> <p>%R&amp;R P/TV: : 7.7% 2 - 7.7% 0 - 2%</p> <p> 10</p> <p>169</p> <p>Step 5 ( ) 2 ( ) 171</p> <p>Step ( ) 2 172</p> <p>. . . . . 3 10 </p> <p>GAGE REPEATABILITY AND REPRODUCIBILITY DATA SHEET VARIABLE DATA RESULTSDEPARTMENT: ENGINEERING &amp; Q.C. SECTION: Q.C.- LABAPPROVED CHECKED REPORTED</p> <p>WORKING CONDITIONS:</p> <p>Humidity:Part Number GENERIC</p> <p>40%</p> <p>Temp:</p> <p>20'C Appraiser A Appraiser B Appraiser C Appraisers Date Performed 1.SEP .03</p> <p>Part Name BRAKE TUBE - STDW1 Characteristics WEIGHT Specification / Classification 71 g/m</p> <p>Gage Name BALANCE - 400g Gage Number KCW - 002 Gage Type WEIGHT SYSTEM Trials Parts</p> <p>3</p> <p>10</p> <p>3</p> <p>174</p> <p>APPRAI SER/ TRI AL # 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. C B A 1 2 3 AVE R 1 2 3 AVE R 1 2 3 R</p> <p>PART 10.290 0.410 0.640</p> <p>AVERAGE 6 70.590 0.750 0.660</p> <p>2-0.560 -0.680 -0.580</p> <p>31.340 1.170 1.270</p> <p>40.470 0.500 0.640</p> <p>5-0.800 -0.920 -0.840</p> <p>8-0.310 -0.200 -0.170</p> <p>92.260 1.990 2.010</p> <p>10-1.360 -1.250 -1.310</p> <p>0.020 -0.110 -0.210</p> <p>0. 1940 0. 1660 0. 2110 XA = RA = 0. 1903 0. 1840 0. 0010 0. 0170 0. 0890 XB = RB = 0. 0357 0. 4300 -0. 2230 -0. 2560 -0. 2840 XC = RC = X = Rp = R= -0. 2543 0. 3280 -0. 0094 3. 5111 0. 3140 0. 4447 0. 8102175 0. 0000</p> <p>0. 447 0. 350.080 0.250 0.070</p> <p>-0. 607 0. 12-0.470 -1.220 -0.680</p> <p>1. 260 0. 537 0. 171.190 0.940 1.340</p> <p>-0. 853 -0. 100 0. 12-0.560 -1.200 -1.280</p> <p>0. 667 0. 160.470 0.550 0.830</p> <p>-0. 227 0. 14-0.630 0.080 -0.340</p> <p>2. 087 -1. 307 0. 271.800 2.120 2.190</p> <p>0. 170.010 0.050 0.200</p> <p>0. 23-0.200 0.220 0.060</p> <p>0. 11-1.680 -1.620 -1.500</p> <p>0. 133 0. 180.040 -0.110 -0.150</p> <p>-0. 790 0. 75-1.380 -1.130 -0.960</p> <p>1. 157 0. 087 0. 400.880 1.090 0.670</p> <p>-1. 013 0. 72-1.460 -1.070 -1.450</p> <p>0. 027 0. 42-0.290 -0.670 -0.490</p> <p>0. 617 0. 360.020 0.010 0.210</p> <p>-0. 297 0. 71-0.460 -0.560 -0.490</p> <p>2. 037 -1. 600 0. 391.770 1.450 1.870</p> <p>0. 190.140 0.200 0.110</p> <p>0. 18-1.490 -1.770 -2.160</p> <p>AVE -0. 073 0. 19 0. 169</p> <p>-1. 157 0. 42 -0. 851</p> <p>0. 880 0. 150 0. 42 0. 09</p> <p>-1. 327 -0. 483 0. 39 0. 38</p> <p>0. 080 0. 20 0. 454</p> <p>-0. 503 0. 10 -0. 342</p> <p>1. 697 -1. 807 0. 42 0. 67</p> <p>16. PART AVE( Xp) 17. 18. 19. 20.</p> <p>1. 099 0. 258</p> <p>-1. 064 -0. 186</p> <p>1. 940 -1. 571</p> <p>( RA + RB + RC) / ( # OF APPRAI SERS) = (M X - M n X ) = ax i R x D4* = R x D3* =</p> <p>XDI FF = UCLR = LCLR =</p> <p>M easur em ent Uni t Anal ysi sRepeat abi l i t y - Equi pm ent Var i at i on ( EV) EV = = = AV = = = R x K1 Tr i al s 2 3 K1 0.8862 0.5908</p> <p>% Tot al Var i at i on ( TV)% EV = 100 ( EV/TV) = 100( 0. 18551/1. 14346) = 16.22% % AV = 100 ( AV/TV) = 100( 0. 23013/1. 14346) = 20.13% n = num ber of par t s r = num ber of t r i al s Par t s 2 3 4 5 6 7 8 9 10 K3 0.7071 0.5231 0.4467 0.4030 0.3742 0.3534 0.3375 0.3429 0.3146 ndc % PV = 100 ( PV/TV) = 100( 1. 10460/1. 14346) = 96.60% = 1. 41 ( PV/GRR) = 1. 41( 1. 10460/0. 29559) = 5.269 % R&amp;R = 100 ( R&amp;R...</p>