AISM 52, 184-196

## Start-up demonstration tests with rejection of units upon observing *d* failures

### N. Balakrishnan^{1} and P.S. Chan^{2}

^{1}Department of Mathematics and Statistics,
McMaster University, Hamilton, Ontario, Canada L8S 4K1

^{2}Department of Statistics, The Chinese
University of Hong Kong, Shatin, Hong Kong, China

(Received November 17, 1997; revised June 30, 1998)

Abstract.
The probability generating function of
number of trials for the start-up demonstration test with
rejection upon *d* failures is derived. The exact
distribution of the number of trials is obtained. Some
recurrence relations for the probabilities are also
established. The average length of the test is derived. Some
illustrative examples are finally presented.

Key words and phrases:
Probability generating
function, runs, start-up demonstration test.

**Source**
( TeX , DVI )