The random number table is a list of random one digit numbers (from 0 to
9) that have been arbitrarily grouped into sets of 5 digits and divided
into groups of 10 rows. **Note**: *The row number is NOT part of the
table.*

Each entry in the table is equally likely to be one of the values from 0
to 9; each pair of digits in the table is equally likely to be one of
the values from 00 to 99; each triplet in the table is equally likely to
be one of the values 000 to 999; and so on.

For example, if you want to randomly select 10 survey units from a
population that contains 500 units.

-   Label the survey units from 1 to 500.

-   Enter the table at an arbitrary row and position in the row, and
    pick off successive three (3) digit groups. Each three-digit group
    is used to select one of the experimental units. Ignore 000, and
    501-999; these numbers fall out of the sequence of the population.
    For example, suppose that you enter the table at row 48. The random
    digits are:

46499 94631 17985 09369 19009 51848 58794 48921 22845 55264

When this line is grouped into three-digit numbers, the result is:

**464**99 9**463**1 17**985** 093**69 1**900**9** **51**848 **587**94
4**892**1 22**845** 552

(The last two digits, 64, would be discarded in this example.)

Therefore, the three-digit groups from this line are:

464 999 463 117 985 093 691 900 848 587 944 892 122 845 552

The first 10 distinct three-digit groups that are between 001 and 500
(inclusive) are used to select the units for the survey. From the above
example, units 464, 463, 117, 093, and 122 would be selected to sample.
Additional row(s) would be necessary to complete the example of 10
survey units.

**Note:** *[Additional rows might be needed to complete your survey,
depending upon the sample size.]{.underline}*

Table of Uniform Random Numbers

  ---------------------------------------------------------------------------------------------
  **Row**   **Uniform                                                                   
            Random                                                                      
            Numbers**                                                                   
  --------- ----------- ------- ------- ------- ------- ------- ------- ------- ------- -------
  1         57245       39666   18545   50534   57654   25519   35477   71309   12212   98911

  2         42726       58321   59267   72742   53968   63679   54095   56563   09820   86291

  3         82768       32694   62828   19097   09877   32093   23518   08654   64815   19894

  4         97742       58918   33317   34192   06286   39824   74264   01941   95810   26247

  5         48332       38634   20510   09198   56256   04431   22753   20944   95319   29515

  6         26700       40484   28341   25428   08806   98858   04816   16317   94928   05512

  7         66156       16407   57395   86230   47495   13908   97015   58225   82255   01956

  8         64062       10061   01923   29260   32771   71002   58132   58646   69089   63694

  9         24713       95591   26970   37647   26282   89759   69034   55281   64853   50837

  10        90417       18344   22436   77006   87841   94322   45526   38145   86554   42733

                                                                                        

  11        78886       86557   11295   07253   29289   44814   58898   36929   66839   81250

  12        39681       54696   38482   48217   73598   93649   92705   34912   18981   74299

  13        38265       45196   31143   82190   27279   79883   20219   38823   84543   22119

  14        34270       41885   00079   63600   59152   10670   27951   77830   05368   58315

  15        73869       34748   75787   88844   89522   71436   04166   06246   20952   56808

  16        21732       36017   69149   70330   90500   73110   92908   55789   73450   68282

  17        72583       49811   67519   98476   97889   37112   94963   91140   24571   23446

  18        72678       49483   57039   18420   74773   16869   72077   27720   14058   66743

  19        88572       01294   14117   56884   77107   53023   02243   26415   52233   12818

  20        82868       59988   42323   96542   96733   00056   74887   21914   48300   96404

                                                                                        

  21        09949       56572   28104   64281   01217   76250   39511   19059   85172   35273

  22        41942       91440   81609   38147   59406   88491   18079   29786   81499   85390

  23        46777       74928   91290   55022   56629   01335   61379   71134   86187   70717

  24        58280       17867   07990   85055   55279   83390   37598   93350   05666   55402

  25        87042       55080   76185   19947   79551   77594   87381   99430   44251   30896

  26        72183       39856   94385   55160   50680   68443   95437   74302   06204   71004

  27        76768       16066   94109   90685   92058   81744   99133   36354   34292   90092

  28        21703       64616   03431   47610   31968   61593   36259   70600   53491   95542

  29        78269       12087   32204   81177   30333   83630   06026   89308   94179   54907

  30        49285       16579   22109   63651   34778   28631   27285   95751   91704   59819

                                                                                        

  31        90016       10303   81862   41351   88681   76632   15336   91955   38436   43892

  32        63651       93677   08027   80384   71134   79937   23322   10577   21413   86688

  33        02780       37186   74076   33376   03782   64199   77333   12812   78027   89926

  34        49414       09022   38644   53038   34634   36565   01984   88477   83879   60943

  35        53861       74046   04778   08365   83104   79004   88335   54047   99675   41864

  36        78677       55123   73447   00158   61482   02808   83475   59932   19044   27318

  37        74550       84403   56850   83780   88847   65591   03859   58670   60057   25225

  38        22866       64152   35023   35701   98228   53388   82321   34392   09589   97340

  39        17601       32926   06120   27626   48687   42885   25858   53920   95764   84716

  40        20862       64222   96951   19524   15866   52508   03763   98033   87268   71167

                                                                                        

  41        71490       83428   78903   81931   24345   37331   03971   38118   01065   36010

  42        21050       12825   28217   99510   86900   09987   91244   06520   81108   87266

  43        91632       96199   54191   77480   33049   00849   96668   65865   25164   98330

  44        46988       84607   55711   43874   26532   76307   38846   55961   83227   16069

  45        72200       24023   55848   09162   44976   15663   34697   83365   82930   63392

  46        88621       25822   78463   72191   00625   85945   72522   29613   46473   51177

  47        15384       03326   32091   20199   70046   64343   20566   79050   43837   15831

  48        46499       94631   17985   09369   19009   51848   58794   48921   22845   55264

  49        13520       96795   79714   66338   79836   44430   89290   06167   69090   29476

  50        24323       00280   73922   43447   00319   92899   75411   91840   39594   17621

                                                                                        

  51        99090       55543   87734   80685   74261   70848   87196   59085   28471   74971

  52        97585       33311   68919   33189   49987   24081   79404   45363   46920   94760

  53        97622       85282   58594   83977   25002   39124   58350   67845   17771   58031

  54        24260       21646   75111   41560   90082   57613   93807   04060   94811   60124

  55        65250       83876   34806   08796   53719   94310   94363   55289   81226   18190

  56        45817       37470   73508   84200   73933   80187   26207   69917   58064   95000

  57        48898       28088   77723   81458   18981   35389   17199   85718   18019   66290

  58        23900       87304   91349   27541   42047   23002   47976   99586   96453   06861

  59        38635       66539   55139   56894   01608   05068   21910   41858   15382   98701

  60        58095       49005   59108   12315   35856   19651   55545   79711   42424   67008

                                                                                        

  61        76474       40345   47744   45224   42903   86698   09851   87819   81523   34272

  62        03535       70021   61645   84268   65636   94414   06266   12237   43147   16894

  63        14364       82782   07176   53522   06834   46016   42758   04753   00023   15300

  64        91751       29817   90578   31800   13393   35965   41128   92983   61660   50106

  65        56151       59329   22926   66357   41724   68645   04327   27543   18723   11957

  66        57881       15295   43246   47103   15977   84216   78875   06677   77219   50803

  67        36126       70899   51669   79958   93311   62555   70694   16626   35623   18758

  68        73389       33283   66929   73444   31434   10263   16868   74346   84838   82770

  69        77383       40683   84063   45412   21358   84024   88935   77583   33522   53090

  70        62798       96248   60474   36149   21187   23194   03696   74445   54525   12869

                                                                                        

  71        12283       00561   29955   05775   34520   47217   26059   35414   65998   49766

  72        78433       49762   41177   80949   32843   64714   40450   15064   11389   78409

  73        26348       29480   65497   34615   12888   19977   17597   25914   36394   79315

  74        26078       36705   83043   61592   12459   61255   40550   59892   66163   97848

  75        40115       70829   00654   12791   85668   19015   82785   92889   35041   18949

  76        81560       62666   77627   09123   63484   49481   60451   88073   71000   63511

  77        34074       51484   59356   20301   22365   95862   46995   26284   45273   35706

  78        42176       81350   05941   09754   16987   98248   90319   33116   39120   34765

  79        63288       62381   58461   13225   57138   19619   30877   82640   24888   02600

  80        88820       33240   78977   98928   41160   29671   33299   95592   38493   05321

                                                                                        

  81        63532       20433   25690   09557   90207   95808   57383   68622   13359   25371

  82        39033       68857   74705   91718   77485   32496   30737   28551   69056   95615

  83        46964       90715   01804   14953   97658   71613   90353   78189   03195   73795

  84        03528       92683   29740   31679   22941   92131   69021   21325   70930   19548

  85        67027       36641   74347   54500   80074   94364   10164   99309   66272   24925

  86        65462       73352   17392   09552   74361   46123   13020   63169   98318   91666

  87        55797       95254   84279   88885   65569   96791   66118   05817   17867   88254

  88        58697       56009   20438   06653   93978   51961   97609   97367   02795   04718

  89        97876       76551   19215   87623   55326   85282   86292   18328   55016   84126

  90        72443       02607   13183   06156   76680   62398   79369   77374   78292   41027

                                                                                        

  91        96152       80526   62087   12197   59252   68312   39759   63535   23675   47358

  92        10277       64926   33378   48335   35488   47577   85954   97588   75873   31350

  93        77557       25011   86663   97410   99845   42709   48407   63841   14727   00484

  94        68784       85951   54232   30976   48666   15927   73072   00907   76237   56914

  95        67778       30262   16944   36130   77604   34923   92336   66565   94490   68039

  96        94104       06985   81837   53674   36266   21688   68769   18492   12242   34164

  97        70107       17900   53497   71908   18186   59909   00400   53236   23016   70860

  98        07847       64852   37719   68837   60757   92158   80433   17687   08916   01706

  99        33167       35411   27473   13393   17714   59680   30888   98213   93364   03219

  100       84527       88986   01665   23547   74666   25487   34977   59681   38520   57293
  ---------------------------------------------------------------------------------------------

Inspection Sample Sizes

> To determine the sample size for a given service and/or product, use
> Table below. Determine the lot size to survey, and choose the sample
> size from the 'Normal Sample Size' column.
>
> **Note:** Use the 'Small Sample Size' column only if there are a
> limited number of QAEs, or if the cost of inspection makes Normal
> Inspection levels cost prohibitive.

  ----------------- ----------------- ----------------- -----------------
  Lot Size          Normal Inspection Reduced           Small Sample Size
                    Sample Size       Inspection Sample 
                                      Size              

  2-8               2                 2                 2

  9-15              3                 2                 2

  16-25             5                 2                 3

  26-50             8                 3                 5

  51-90             13                5                 5

  91-150            20                8                 8

  151-280           32                13                13

  281-500           50                20                13

  501-1,200         80                32                20

  1,201-3,200       125               50                32

  3,201-10,000      200               80                32

  10,001-35,000     315               125               50

  35,001-150,000    500               200               80

  150,001-500,000   800               315               80

  500,001-Over      1250              500               125
  ----------------- ----------------- ----------------- -----------------

## **Choosing SampleS**

[]{.mark}

> Once the sample size has been determined, all the items designated in
> a lot must be numbered beginning with 1 through the total of all items
> in the lot. Once all items in a lot are numbered, the actual sample
> must be selected.
>
> Select the sample using the random number table. The random numbers
> are arranged in groups of five numbers (e.g., 58651, 25480, etc.) To
> use the table, begin by picking at random a group of numbers on any
> line on the table. This can be done by a process as simple as closing
> the eyes and pointing with a pencil or finger to some initial group of
> numbers.
>
> The use of variety in the random number table ensures that detectable
> patterns do not occur. In addition to starting at different points and
> alternating the patterns used, the use of the first non-zero digits
> and last non-zero digits of the selected numbers will provide
> additional variety.
>
> Once the total number of random numbers is selected, the numbered
> items in the lot which match the selected random number table numbers
> must be inspected. Based upon the fixed AQL, the sample size, and the
> inspection of the sampled items, the QAE should assess whether or not
> the SP has met or exceeded the AQL.

### [Reduced Inspection]{.underline}

> When a SP's QC program works, the result is good performance. If the
> result of surveillance shows consistently good performance, the amount
> of the surveillance can be decreased for those services surveyed using
> random sampling.
>
> Reduced inspection can only be implemented when all of the following
> conditions have been met for a sampling guide/specific task:

-   The preceding four lots (i.e., last four performance periods) have
    been acceptable.

-   The number of defects in each of the preceding four lots is less
    than one-half of the acceptable number of defects. For example, with
    an AQL of 10% and a sample size of 50, the acceptance number of
    defects is five. If two or fewer defects were found in each of the
    last four lots, reduced inspection could be used.

-   The normal sample size is being used.

> To implement reduced inspection, the following procedures should be
> initiated:

-   Using the reduced lot size, find the new sampling size using the
    sample size table.

-   Apply the AQL in the Surveillance Plan to the new reduced sample
    size identified. If the AQL is met, continue using Reduced
    Inspection. If the AQL is not met, return to normal inspection for
    the next performance period.