Start-Up Demonstration Tests With the Intent of Equipment Classification for Balanced Systems

A start-up demonstration test is a mechanism that is often applied to determine the acceptability of equipment. Two new start-up demonstration tests are derived and demonstrated with the intent of equipment classification based on the testing results. The two new tests are called the CSTSCFTF_AMGC and CS⁽¹⁾CS⁽¹⁾⁽²⁾TF⁽¹⁾⁽²⁾TF⁽²⁾_AMGC start-up demonstration tests. By using the finite Markov chain imbedding approach, several probabilistic indexes are presented for the new start-up demonstration tests based on the assumption that the tests are independent and identically distributed cases. Two types of optimization models are formulated and solved for the new start-up demonstration tests. Numerical examples are then presented to demonstrate the new start-up demonstration tests. This basic idea of equipment classification can be easily extended to other traditional start-up demonstration tests.

Nomenclature

Abbreviations CS

Consecutive successes. Note: Test is ended and unit is accepted if a number of CS are observed.

CSTF

CS total failures. Note: Test is ended and unit is accepted if CS are observed prior to total failures; test is ended and unit is rejected otherwise.

TSCF

Total successes consecutive failures. Note: Test is ended and unit is accepted if total successes are observed prior to consecutive failures; test is ended and unit is rejected otherwise.

CSCF

CS consecutive failures. Note: Test is ended and unit is accepted if CS are observed prior to consecutive failures; test is ended and unit is rejected otherwise.

TSTF

Total successes total failures. Note: Test is ended and unit is accepted if total successes are observed prior to total failures; test is ended and unit is rejected otherwise.

CSDF

CS distant failures. Note: Test is ended and unit is accepted if CS are the first to be observed, while the equipment is rejected if two failures separated by at most successes are observed prior to CS.

TSCSTF

Total successes CSTF. Note: Test is ended and unit is accepted if total successes or CS are observed prior to total failures; test is ended and unit is rejected otherwise.

TSCSTFCF

TSCSTF consecutive failures. Note: Test is ended and unit is accepted if total successes or CS are observed prior to total failures and consecutive failures; test is ended and unit is rejected otherwise.

TSCSTFDF

TSCSTF distant failures. Note: Test is ended and unit is accepted if total successes or CS are observed prior to total failures and the occurrence of two failures that have less than successes between them; test is ended and unit is rejected otherwise.

CS⁽¹⁾CS^(1,2)TF

CS 1, CS 1 or 2, total failures. Note: Test is ended and unit is accepted if a consecutive run of length of type S⁽¹⁾ successes or consecutive run of length of type S⁽¹⁾ or S⁽²⁾ successes occur prior to total failures; test is ended and unit is rejected otherwise.

CS⁽¹⁾CS^(1,2)CF

CS 1, CS 1 or 2, consecutive failures. Note: Test is ended and unit is accepted if a consecutive run of length of type S⁽¹⁾ successes or consecutive run of length of type S⁽¹⁾ or S⁽²⁾ successes occur prior to consecutive failures; test is ended and unit is rejected otherwise.

TS⁽¹⁾TS^(1,2)TF

Total successes 1, total successes 1 or 2, total failures. Note: Test is ended and unit is accepted if a total of successes of type S⁽¹⁾ or total of successes of type S⁽¹⁾ or S⁽²⁾ occur prior to total failures; test is ended and unit is rejected otherwise.

TS⁽¹⁾TS^(1,2)CS⁽¹⁾

Total full successes, total full or degrad-

CS^(1,2)TFCF

ed successes, consecutive full successes, consecutive full or degraded successes, total failures, consecutive failures. Note: Test is ended and unit is accepted if a consecutive run of length of full successes (S⁽¹⁾), or a consecutive run of length of either full and/or degraded successes (S⁽¹⁾, S⁽²⁾), or a total number of full successes , or a total number of full and/or degraded successes , occur prior to a total number of failures and a consecutive run of length of failures; test is ended and unit is rejected otherwise.

CSTSCFTF_AMGC

CSTSCFTF start-up demonstration test aiming at multigrade classification. Note: Detailed model is shown in Section II-A.

CS⁽¹⁾CS⁽¹⁾⁽²⁾TF⁽¹⁾⁽²⁾

CS⁽¹⁾CS⁽¹⁾⁽²⁾TF⁽¹⁾⁽²⁾TF⁽²⁾ start-up demo-

TF⁽²⁾_AMGC

nstration test aiming at multi-grade classification. Note: Detailed model is shown in Section II-B.