A Start-Up Demonstration Test Involving Distant Failures

A new procedure for determining the acceptance or rejection of a system that undergoes a start-up demonstration set of tests is presented. It is a generalization of the recently introduced CSDF model (consecutive successes distant failures). According to the new total successes consecutive successes total failures distant failures (TSCSTFDF) procedure, a unit is accepted when either a total number of successful tests or a specified number of consecutive successes are observed before a total number of failures or the occurrence of near failures which are too close to each other. The practical advantage of this new procedure is the significant reduction in the expected number of required tests together with improved second-order statistics (standard deviation). 1. Introduction Start-up demonstration tests are performed in order to prove the reliability of power generating equipment like lawn mowers, water pumps, car batteries, and many sorts of electronic equipment. An example for an application has been mentioned by Antzoulakos et al. [1] regarding a conference center that wishes to replace its old slide projectors with modern ones. The outcomes of a set of demonstration tests that are carried out on the new projectors are recorded. The requirement may be in form of observing consecutive successes before the occurrence of a certain number of failures or before meeting a consecutive set of failures. As a result, the reliability of the equipment is determined. Various procedures exist for deciding whether the set of tests is successful which imply the decision on accepting or rejecting the unit in question. They are based on the commonly known theory of consecutive -out-of- systems [2]. Among others, there exist the consecutive successes (CS), total successes consecutive successes (TSCS), consecutive failures total failures (CSTF), consecutive successes distant failures (CSDF), and a general TSCSTFCF procedure. According to the simplest CS procedure, the equipment is accepted if there exists a certain run of successes of prespecified length ( ) when performing the set of tests [3, 4]. The combination of the requirement for consecutive successes and/or the total number of successes (TSCS) ( ,？？ ) as a basis for accepting the unit has been presented by Gera [5]. A more advanced procedure (CSTF) has been given by Balakrishnan and Chan [6], Smith and Griffith [7, 8], and Martin [9, 10]. Like before, the unit is accepted if there exists a run of successes ( ). However, it is rejected if a certain number of failures is reached before that run ( ). More general