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Capability indices

Capability indices use estimated sigma.

Cp

Cp for one-sided specifications

If you are using one sided specifications, use the following formulas to determine the Cp:

Upper specification

Lower specification

Cr

Cpk

f-cpk

Where:

Zmin is the smaller of Zupper and Zlower.

Using estimated sigma:

Cpm

Where: sigma for cpm

T = specification target (nominal)

Xi = a given individual reading of ” i ”

n = total number of individual readings

= symbol for summation

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t-chart formula

The t-chart formula:

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g-chart formula

The g-chart formula:

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c-chart formulas

The c-chart formula (for number of nonconformities, from subgroups of a constant size):

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u-chart formula

The u-chart formula (for number of nonconformities from subgroups that can vary in size):

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p-chart formulas

The p formula (for the proportion of nonconforming units from subgroups that can vary in size):

f-p-bar

To calculate control limits for the p-chart:

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np-chart formulas

The np-chart formula (for number of nonconforming units from subgroups with a constant size):

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Standard normal table

z x.x0 x.x1 x.x2 x.x3 x.x4 x.x5 x.x6 x.x7 x.x8 x.x9
4.0 .00003
3.9 .00005 .00005 .00004 .00004 .00004 .00004 .00004 .00004 .00003 .00003
3.8 .00007 .00007 .00007 .00006 .00006 .00006 .00006 .00005 .00005 .00005
3.7 .00011 .00010 .00010 .00010 .00009 .00009 .00008 .00008 .00008 .00008
3.6 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011
3.5 .00023 .00022 .00022 .00021 .00020 .00019 .00019 .00018 .00017 .00017
3.4 .00034 .00032 .00031 .00030 .00029 .00028 .00027 .00026 .00025 .00024
3.3 .00048 .00047 .00045 .00043 .00042 .00040 .00039 .00038 .00036 .00035
3.2 .00069 .00066 .00064 .00062 .00060 .00058 .00056 .00054 .00052 .00050
3.1 .00097 .00094 .00090 .00087 .00084 .00082 .00079 .00076 .00074 .00071
3.0 .00135 .00131 .00126 .00122 .00118 .00114 .00111 .00107 .00104 .00100
2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014
2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019
2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026
2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036
2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048
2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064
2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084
2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110
2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143
2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183
     
z x.x0 x.x1 x.x2 x.x3 x.x4 x.x5 x.x6 x.x7 x.x8 x.x9
1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233
1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294
1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367
1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455
1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559
1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681
1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823
1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985
1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170
1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379
0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611
0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867
0.7 .2420 .2389 .2358 .2327 .2297 .2266 .2236 .2206 .2177 .2148
0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451
0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776
0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121
0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483
0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859
0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247
0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641

Formulas and Tables

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Target Z, Zupper, and Zlower formulas

Target Z

Zupper

Zlower

Where:

= the mean of the X-bars
T = specification target
Sigma is an estimated sigma or sigma of the individual values, depending on how the histogram
is configured or whether you are calculating Cpk (estimated) or Ppk (actual).