## A.2 Detailed theoretical methodology

11.213GPPBase Station System (BSS) equipment specificationRadio aspectsRelease 1999TS

The total number of statistical tests indicated in annex C (excluding blocking, intermodulation etc.) are:

GSM 900: 95

DCS 1800: 96

and the rules of the tests are as follows:

‑ in order to pass a BSS it should pass all tests.

‑ a single test which fails should be repeated once. If the BSS fails a 2nd time, the BSS has failed.

This means that the overall probability of passing a good BSS through all the tests is lower than for the individual tests.

Taking into account the total of

GSM 900: 95 tests,

DCS 1800: 96 tests,

assuming that the outcomes of the tests are independent, and requiring that the total probability of passing a "good" BSS should be equal to the total probability of failing a "bad" BSS, the overall confidence requirements in this annex should be as follows on a test by test basis:

P(PASS|Ps) >= 99.9 % (i.e. G = 3.09)

P(FAIL|Pb ) >= 95.0 % (i.e. B = 1.65)

With the above assumptions, the total probabilities of passing a "good" BSS and failing a "bad" BSS will be around 91.0 %.

NOTE 1: If for some reason not all tests are carried out, then the probability of failing a "bad" BSS, P(FAIL|Pb), should be increased accordingly.

Since the test requirement Pt will lie somewhere in between the system requirement Ps and Pb, and that an uncertainty in test equipment resulting from imperfections in the randomness of pseudo‑random generators etc. can be expected to give errors of the order of +/‑ 5 % , the ratio Pb/Ps should be 2.

Under idealized assumptions, the resulting minimum number of samples needed to meet the overall confidence requirements is indicated as a function of the system requirement Ps using (Eq 6) in table A.1.

The ratio of the test requirement Pt to the system requirement Ps will in this case be:

Pt = 1.57 Ps

NOTE 2: It is possible to reduce the needed number of samples. In that case the ratio Pb/Ps should be increased, or the confidence levels should be reduced, see equation (Eq.5). It is preferable to keep the confidence and to increase Pb/Ps. However, the accepted error rate Pt, and Pb, should not deviate too much from the system requirement Ps, especially for high Ps. In order to have meaningful requirements it may even be desirable to reduce Pb/Ps for high Ps.

Table A.1: Minimum number of samples for statistical testing

Error rate Ps | Minimum number of samples |

1.0 E‑1 | 300 |

1.0 E‑2 | 3 000 |

1.0 E‑3 | 30 000 |

1.0 E‑4 | 300 000 |

1.0 E‑5 | 3 000 000 |