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Non conformities

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Calculating non conformities

The number of observations falling within the distributionfrequency curve can be co-related with the area under thecurve.

Finding area ( percentage of non conformities ) under anormal curve requires the use of standard normal distributiontable. It is conventional to use the letter z to denote thestandard normal variate. The table for areas under normal

curve are given at the end of this section.

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Sigma ratings in terms of Z

The z value corresponding to USL or LSL* tells us how manysigma the USL or LSL is from the process setting. Thus the zvalue corresponding to the specification limit gives the sigmarating of the process.

Note 1: As we know that most of the variable data that we come across in theindustry follows normal distribution with certain mean and standard deviation. Wedefine a variate Z( standardized normal variate ) which has a mean value 0 andstandard deviation 1. This is done in order to make use of Standard Normal Tables.

* LSL is the lower specification limit & USL is the upper specification limit

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LSL USL

Nonconformities

Nonconformities

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Illustration for calculating% non conformities

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Normal curve for the population

Spec: 1.6+/- 0.1 mm

50

40

30

20

10

01.465 1.505 1.545 1.585 1.625 1.665 1.705

LSL USL

F r e q u e n c y

%

Thickness

Proportionof defects

Proportionof defects

Mean=1.58SD=0.042

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With respect to LSL,

With respect to USL,

= ( 1.50-1.58 )/0.042 = -1.90

ZU = ( USL-X )/SD = ( 1.70-1.58 )/0.042 = 2.86

ZL = ( LSL - X )/SD

The Percentage of values falling beyond specification limits, corresponding

to the z value can be read from the standard normal table as 0.0287 and0.0021 for ZU and ZL respectively. Total percentage of non conformities=2.87+0.21=3.08. (While referring to Normal distribution table, onlyabsolute value of z should be taken.)

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Areas under normal curve - Normal distribution table

z Area z Area z Area z Area0.00 0.500000 0.20 0.420740 0.40 0.344578 0.60 0.274253

0.01 0.496011 0.21 0.416834 0.41 0.340903 0.61 0.270931

0.02 0.492022 0.22 0.412936 0.42 0.337243 0.62 0.267629

0.03 0.488033 0.23 0.409046 0.43 0.333598 0.63 0.264347

0.04 0.484047 0.24 0.405165 0.44 0.329969 0.64 0.261086

0.05 0.480061 0.25 0.401294 0.45 0.326355 0.65 0.257846

0.06 0.476078 0.26 0.397432 0.46 0.322758 0.66 0.254627

0.07 0.472097 0.27 0.393580 0.47 0.319178 0.67 0.251429

0.08 0.468119 0.28 0.389739 0.48 0.315614 0.68 0.248252

0.09 0.464144 0.29 0.385908 0.49 0.312067 0.69 0.245097

0.10 0.460172 0.30 0.382089 0.50 0.308538 0.70 0.241964

0.11 0.456205 0.31 0.378281 0.51 0.305026 0.71 0.238852

0.12 0.452242 0.32 0.374484 0.52 0.301532 0.72 0.235762

0.13 0.448283 0.33 0.370700 0.53 0.298056 0.73 0.232695

0.14 0.444330 0.34 0.366928 0.54 0.294599 0.74 0.229650

0.15 0.440382 0.35 0.363169 0.55 0.291160 0.75 0.226627

0.16 0.436441 0.36 0.359424 0.56 0.287740 0.76 0.223627

0.17 0.432505 0.37 0.355691 0.57 0.284339 0.77 0.220650

0.18 0.428576 0.38 0.351973 0.58 0.280957 0.78 0.217695

0.19 0.424655 0.39 0.348268 0.59 0.277595 0.79 0.214764

Area

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0.81 0.208970 1.01 0.156248 1.21 0.113140 1.41 0.079270

0.82 0.206108 1.02 0.153864 1.22 0.111233 1.42 0.077804

0.83 0.203269 1.03 0.151451 1.23 0.109349 1.43 0.076459

0.84 0.200454 1.04 0.149170 1.24 0.107488 1.44 0.074934

0.85 0.197662 1.05 0.146859 1.25 0.105650 1.45 0.073529

0.86 0.194894 1.06 0.144572 1.26 0.103835 1.46 0.072145

0.87 0.192150 1.07 0.142310 1.27 0.102042 1.47 0.070781

0.88 0.189430 1.08 0.140071 1.28 0.100273 1.48 0.069437

0.89 0.186733 1.09 0.137875 1.29 0.098525 1.49 0.0681120.90 0.184060 1.10 0.135666 1.30 0.096801 1.50 0.0668072

0.91 0.181411 1.11 0.133500 1.31 0.095098 1.51 0.0655217

0.92 0.178786 1.12 0.131357 1.32 0.093418 1.52 0.0642555

0.93 0.176185 1.13 0.129238 1.33 0.091759 1.53 0.0630084

0.94 0.173609 1.14 0.127143 1.34 0.090123 1.54 0.0617802

0.95 0.171056 1.15 0.125072 1.35 0.088508 1.55 0.0605708

0.96 0.168528 1.16 0.123024 1.36 0.086915 1.56 0.0593799

0.97 0.166023 1.17 0.121001 1.37 0.085343 1.57 0.0582076

0.98 0.163543 1.18 0.119000 1.38 0.083793 1.58 0.05705340.99 0.161087 1.19 0.117023 1.39 0.082264 1.59 0.0559174

Area

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1.61 0.0536989 1.81 0.0351478 2.01 0.0222155 2.21 0.0135525

1.62 0.0526161 1.82 0.0343794 2.02 0.0216916 2.22 0.0132093

1.63 0.0515507 1.83 0.0336249 2.03 0.0211782 2.23 0.0128736

1.64 0.0505026 1.84 0.0328841 2.04 0.0206751 2.24 0.0125454

1.65 0.0494714 1.85 0.0321567 2.05 0.0201821 2.25 0.0122244

1.66 0.0484572 1.86 0.0314427 2.06 0.0196992 2.26 0.0119106

1.67 0.0474597 1.87 0.0307419 2.07 0.0192261 2.27 0.0116038

1.68 0.0464786 1.88 0.0300540 2.08 0.0187627 2.28 0.0113038

1.69 0.0455139 1.89 0.0293789 2.09 0.0183088 2.29 0.0110106

1.70 0.0445654 1.90 0.0287165 2.10 0.0178643 2.30 0.0107241

1.71 0.0436329 1.91 0.0280665 2.11 0.0174291 2.31 0.0104440

1.72 0.0427162 1.92 0.0274289 2.12 0.0170029 2.32 0.0101704

1.73 0.0418151 1.93 0.0268034 2.13 0.0165858 2.33 0.0099031

1.74 0.0409295 1.94 0.0261898 2.14 0.0161773 2.34 0.0096418

1.75 0.0400591 1.95 0.0255880 2.15 0.0157775 2.35 0.0093867

1.76 0.0392039 1.96 0.0249978 2.16 0.0153863 2.36 0.0091375

1.77 0.0383635 1.97 0.0244191 2.17 0.0150034 2.37 0.0088940

1.78 0.0375379 1.98 0.0238517 2.18 0.0146286 2.38 0.0086563

1.79 0.0367269 1.99 0.0232954 2.19 0.0142621 2.39 0.0084242

Area

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2.41 0.00797623 2.61 0.00452715 2.81 0.00247711 3.10 0.00096660

2.42 0.00776023 2.62 0.00439650 2.82 0.00240123 3.20 0.00068714

2.43 0.00754941 2.63 0.00426930 2.83 0.00232744 3.30 0.00048342

2.44 0.00734365 2.64 0.00414532 2.84 0.00225574 3.40 0.00033693

2.45 0.00714284 2.65 0.00402462 2.85 0.00218600 3.50 0.00023263

2.46 0.00694686 2.66 0.00390708 2.86 0.00211829 3.60 0.00015911

2.47 0.00675565 2.67 0.00379258 2.87 0.00205243 3.70 0.00010780

2.48 0.00656915 2.68 0.00368118 2.88 0.00198847 3.80 0.00007235

2.49 0.00638717 2.69 0.00357264 2.89 0.00192630 3.90 0.00004810

2.50 0.00620967 2.70 0.00346702 2.90 0.00186586 4.00 0.00003167

2.51 0.00603658 2.71 0.00336421 2.91 0.00180721 4.10 0.000020662.52 0.00586778 2.72 0.00326413 2.92 0.00175023 4.20 0.00001355

2.53 0.00570315 2.73 0.00316679 2.93 0.00169486 4.30 0.00000854

2.54 0.00554264 2.74 0.00307202 2.94 0.00164115 4.40 0.00000541

2.55 0.00538617 2.75 0.00297282 2.95 0.00158894 4.50 0.00000340

2.56 0.00523365 2.76 0.00289011 2.96 0.00153828 4.60 0.00000211

2.57 0.00508493 2.77 0.00280285 2.97 0.00148904 4.70 0.00000130

2.58 0.00494003 2.78 0.00271803 2.98 0.00144130 4.80 0.00000079

2.59 0.00479883 2.79 0.00263548 2.99 0.00139493 4.90 0.00000048

5.00 0.00000029

Area

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z Area

5.10 0.000001805.20 0.00000107

5.30 0.00000063

5.40 0.00000037

5.50 0.00000021

5.60 0.00000012

5.70 0.000000070

5.80 0.000000040

5.90 0.000000022

6.00 0.000000012

Area

Note: Only absolute values of z should be taken while referring to this table.

Non ties

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