START-UP DEMONSTRATION TESTS WITH REJECTION OF UNITS UPON OBSERVING d FAILURES

N. BALAKRISHNAN^{1} AND P. S. CHAN^{2}

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

2Department 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.