摘要:

Assume that the probability density function for the lifetime of a newly designed product has the form:, for some knownH(·). The Exponentialϵ(θ), Rayleigh, and Pareto Pdf's are special cases. A class of continuous-time sequential tests based on the transformed total time on test and the total number of failures is proposed. The use of Steck's (1971) recursions for rectangle probabilities of uniform order statistics simplifies the exact computation for the operating characteristic, the average sample number, and the average failure number. Applications are given to Epstein and Sobel's (1955) continuous-time sequential probability ratio tests (SPRT), Anderson (1960) type of modification to the SPRT, a Bayesian sequential reliability demonstration test (BSRDT) and a predictive sequentila reliability demonstration test (PSRDT). Jeffreys’ prior appears inappropriate for both BSRDT's and PSRDT's. An ad hoc noninformative prior is used for BSRDT's and PSRDT's. Relationship between BSRDT's and PSRDT's is discussed. Numerical examples are given for illustrating the recursion formulas for the OC and ASN functions.

ISSN:0747-4946    

DOI:10.1080/07474949808836403

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Let X(t), 0 ≤ t < ∞ denote a real-valued process with independent and stationary increments. We assume that X has paths which are right-continuous and have left limits and that 0 < EX(1) < ∞. Letgdenote a nonnegative convex function on the real linc which assumes a unique minimum at some pointb. We treat the problem of minimizing Eg(X(T)) over all stopping times T of X. We prove the existence of threshold a*≤ b such that it is optimal to stop as soon as X(t) > a*. Under suitable conditions ongthe threshold a*can be characterized in terms of the size of the jump of X over an infinite barrier. The optimal solution can also be characterized as an infinitesimal look ahead stopping rule. We present an application of our results to tests of power one.

ISSN:0747-4946    

DOI:10.1080/07474949808836404

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

An exact solution of the integral equation for the ARL function of CUSUM schemes in the case of Erlang distributed observations is presented. The results are derived in a direct way similary to Vardeman and Ray (1985) in the case of exponentially distributed random variables.

ISSN:0747-4946    

DOI:10.1080/07474949808836405

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Letbe a stationary stochastic process with distributionP. We consider the problem of detecting a change in distribution fromPto a specifiedQ. We further assume that the process may not be continuously observed; thus we study the relevant design problem of choosing the observational instants.

ISSN:0747-4946    

DOI:10.1080/07474949808836406

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

LetX = (X1, …, Xn)be a sequence of independent, integrable[ai, bi]-valued random variables, wherea1≤ … ≤ an, b1≤ … ≤ bn. Considering the class of all such sequences, a complete comparison is made betweenM(X), the expected gain of a prophet (an observer with complete foresight), andV(X)the maximal expected gain of a gambler (an observer using only non-anticipatory stopping rules). The solution of this problem is a set in, the ‘prophet region’, which is explicitly characterized. This region yields a variety of prophet inequalities, e.g.M(X) ≤ V(X)/2ifbn= 0, bn-1= -1, an= -2andM(X) - V(X) ≤ an/2ifan> 0, bn-1= 2an, bn= 3an.

ISSN:0747-4946    

DOI:10.1080/07474949808836407

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949808836402

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor