BAYESIAN SAMPLING PLANS FOR EXPONENTIAL DISTRIBUTION BASED ON TYPE I CENSORING DATA

YU-PIN LIN^{1}, TACHEN LIANG^{2} AND WEN-TAO HUANG^{1}

1Department of Management Sciences, Tamkang University, Tamsui,Taiwan 251, R.O.C. 2Department of Mathematics and Statistics, Wayne State University, Detroit, MI 48202, U.S.A.

(Received February 14, 2000; revised August 15, 2000)

Abstract. We study variable sampling plans for the exponential distribution based on type I censoring data. Using a suitable loss function, a Bayesian variable sampling plan (n_{B}, t_{B}, δ_{B}) is derived. For certain prior distributions and loss functions, the numerical values of the Bayesian sampling plans and the associated minimum Bayes risks are tabulated. In terms of Bayes risks, comparisons between the proposed Bayesian sampling plans (n_{B}, t_{B}, δ_{B}) and the “Bayesian” variable sampling plans (n_{0}, t_{0}, δ_{T_{0}}^{L}) of Lam (1994, Ann. Statist., 22, 696–711) have been made. The numerical results indicate that under the same conditions, the proposed Bayesian sampling plan is superior to that of Lam in the sense that the Bayes risk of (n_{B}, t_{B}, δ_{B}) is less than that of (n_{0}, t_{0}, δ_{T_{0}}^{L}).

Key words and phrases: Sampling plan, type I censoring, Bayes risk, Bayesian procedure.