No. 935

Title:

Waiting Time Distributions for a Run with Additional Constraints

Author(s):

Aki, S. (Kansai Universiry);
Hirano, K. (The Institute of Statistical Mathematics)

Key words:

run; waiting time; generalized probability generating function; conditional expectation; discreat distribution theory; start-up demonstration tests

Abstract:

    This paper proposes a method for obtaining the exact probability of occurrence of the first success run of specified length with the additional constraint that at every trial until the occurrence of the first success run the number of successes up to the trial exceeds that of failures. For the sake of the additional constraint, the problem can not be solved by the usual method of conditional probability generating functions. An idea of a kind of truncation is introduced and studied in order to solve the problem. Concrete methods for obtaining the probability in the cases of Bernoulli trials and time-homogeneous two-state Markov dependent trials are given. As an application of the results, a modification of the start-up demonstration test is studied. Numerical examples which illustrate the feasibility of the results are also given.