Lieberman, G. J.
Overview
Works:  10 works in 23 publications in 1 language and 23 library holdings 

Roles:  Author 
Publication Timeline
.
Most widely held works by
G. J Lieberman
On the Consecutive kofn System by
Cyrus Derman(
Book
)
3 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
The consecutive kofn system is considered in which there are n components linearly ordered. Each component either functions or fails and the system is said to be failed if any k consecutive components are failed. Let r(p) = r(p sub 1 ..., p sub n) denote the probability that the system does not fail given that the components are independent, component i functions with probability p sub i, i = l ..., n. The function r(p) is called the reliability function. The above system is studied both when the components are linearly ordered and also when they are arranged in a circular order. In Section 2, the case is considered where all p sub i are identical and present a recursion for obtaining the reliability of a consecutive kofn in terms of the reliability of a consecutive k  1 on n system. This yields simple explicit formulas when k is small and differs from the recursion obtained. In Section 3, we show how upper and lower bounds on r(p) can be simply obtained. In Section 4, we consider a dynamic version in which each component independently functions for random time having distribution F. We show that when F is increasing failure rate (IFR), then system lifetime is also IFR only in the circular case when k = 2. In Section 5, we consider a sequential optimization model in the linear k = 2 case. In this model, components are put in place one at a time with complete knowledge as to whether the previous component has worked or not. We show that the optimal policy is such that whenever a success occurs we follow it with the worst of the remaining components and whenever a failure occurs we follow it with the best of the remainder
3 editions published in 1980 in English and held by 2 WorldCat member libraries worldwide
The consecutive kofn system is considered in which there are n components linearly ordered. Each component either functions or fails and the system is said to be failed if any k consecutive components are failed. Let r(p) = r(p sub 1 ..., p sub n) denote the probability that the system does not fail given that the components are independent, component i functions with probability p sub i, i = l ..., n. The function r(p) is called the reliability function. The above system is studied both when the components are linearly ordered and also when they are arranged in a circular order. In Section 2, the case is considered where all p sub i are identical and present a recursion for obtaining the reliability of a consecutive kofn in terms of the reliability of a consecutive k  1 on n system. This yields simple explicit formulas when k is small and differs from the recursion obtained. In Section 3, we show how upper and lower bounds on r(p) can be simply obtained. In Section 4, we consider a dynamic version in which each component independently functions for random time having distribution F. We show that when F is increasing failure rate (IFR), then system lifetime is also IFR only in the circular case when k = 2. In Section 5, we consider a sequential optimization model in the linear k = 2 case. In this model, components are put in place one at a time with complete knowledge as to whether the previous component has worked or not. We show that the optimal policy is such that whenever a success occurs we follow it with the worst of the remaining components and whenever a failure occurs we follow it with the best of the remainder
Optimal selling when the price distribution is unknown by
Cyrus Derman(
Book
)
3 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
This paper reconsiders the classical model for selling an asset in which offers come in daily and a decision must then be made as to whether or not to sell. For each day the item remains unsold a continuation (or maintenance cost) c is incurred. The successive offers are assumed to be independent and identically distributed random variables having an unknown distribution F. The model is considered both in the case where once an offer is rejected it may not be recalled at a later time, and in the case where such recall of previous offers is allowed
3 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
This paper reconsiders the classical model for selling an asset in which offers come in daily and a decision must then be made as to whether or not to sell. For each day the item remains unsold a continuation (or maintenance cost) c is incurred. The successive offers are assumed to be independent and identically distributed random variables having an unknown distribution F. The model is considered both in the case where once an offer is rejected it may not be recalled at a later time, and in the case where such recall of previous offers is allowed
A sequential stochastic assignment problem by
Stanford University(
Book
)
3 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a p man is assigned to an X = x job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if p1 <or = p2 <or = ... <or = pn the optimal choice in the initial stage of an n stage assignment problem is to use pi if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected) reward if a 'p' man is assigned to an x job is given by a function r(p, x). (Author)
3 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a p man is assigned to an X = x job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if p1 <or = p2 <or = ... <or = pn the optimal choice in the initial stage of an n stage assignment problem is to use pi if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected) reward if a 'p' man is assigned to an x job is given by a function r(p, x). (Author)
Prematurely Terminated Sequential Tests for MILSTD 781C by
Stanford University(
Book
)
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
Formulas and tables are provided making it possible for users of the truncated sequential probability ratio tests of MILSTD 781C to make acceptance or rejection decisions when the test procedure is prematurely tuncated. (Author)
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
Formulas and tables are provided making it possible for users of the truncated sequential probability ratio tests of MILSTD 781C to make acceptance or rejection decisions when the test procedure is prematurely tuncated. (Author)
A Sampling Procedure and Public Policy by
Stanford University(
Book
)
3 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
Confidence intervals for independent exponential series systems by
G. J Lieberman(
Book
)
3 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
Suppose X1,X2 ..., Xn are independent identically distributed exponential random variables with parameter lambda 1. Let Y1,Y2 ..., Ym also be independent identically distributed exponential random variables with parameter lambda 2, and assume that X's and Y's are independent. The problem is to estimate R(t) = e to the power ( (lambda 1 + lambda 2)t). The motivation behind this is that if one has a series system with two independent exponential components then R(t) represents the reliability of the system at time t, i.e., the probability that the system survives until time t. A procedure for determining an exact (1alpha) level lower confidence bound for R(t) is presented. In doing so an interesting characterization of the minimum of two independent gamma random variables is obtained. The suggested procedure is then compared with others presented in the literature. (Author)
3 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
Suppose X1,X2 ..., Xn are independent identically distributed exponential random variables with parameter lambda 1. Let Y1,Y2 ..., Ym also be independent identically distributed exponential random variables with parameter lambda 2, and assume that X's and Y's are independent. The problem is to estimate R(t) = e to the power ( (lambda 1 + lambda 2)t). The motivation behind this is that if one has a series system with two independent exponential components then R(t) represents the reliability of the system at time t, i.e., the probability that the system survives until time t. A procedure for determining an exact (1alpha) level lower confidence bound for R(t) is presented. In doing so an interesting characterization of the minimum of two independent gamma random variables is obtained. The suggested procedure is then compared with others presented in the literature. (Author)
Unlimited simultaneous discrimination intervals in regression by
G. J Lieberman(
Book
)
3 editions published in 1966 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1966 in English and held by 2 WorldCat member libraries worldwide
A note on Dodge's continuous inspection plan by
Stanford University(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
On sampling inspection in the presence of inspection errors by
Stanford University(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
Reduced inspection for characteristics with infrequent defects by
Stanford University(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
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