Manish C. Bhattacharjee

New Jersey Institute of Technology

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Sujit Basu

The Ohio State University

Sunil Dhar

Nazareth Hospital

Sundarraman Subramanian

New Jersey Institute of Technology

Jayaram Sethuraman

Florida State University

A. M. Abouammoh

King Saud University

Ali Ahmed

Gulf University for Science & Technology

A. M. Barry

University of the District of Columbia

Rudrani Banerjee

GlaxoSmithKline (India)

Pranab Kumar Sen

Tata Institute of Fundamental Research

Ritwik Bhattacharya

The University of Texas at El Paso

Cooperative Institutions

Indian Statistical Institute

New Jersey Institute of Technology

University of Mysore

Indian Institute of Management Calcutta

King Saud University

Indian Institute of Engineering Science and Technology, Shibpur

University of Arizona

University of North Carolina at Chapel Hill

Florida State University

The Ohio State University

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Kolmogorov-Smirnov type tests for NB(W)UE alternatives under censoring schemes

Lecture notes-monograph series (1995)

Manish C. Bhattacharjee Pranab K. Sen

For testing the null hypothesis that a life distribution is exponential against the NBUE (or NWUE) class, the structure of progressively censored TTT statistics is critically examined and incorporated in the study of some linear and Kolmogorov-Smirnov type tests essentially proposed by Koul (1978b) and Kumazawa (1989).Their distributionfreeness property under the null hypothesis (conditionally, under some censoring schemes) is established, and related asymptotics are presented. Introduction.Nonparametric notions of aging have been popular and useful for modeling degradation in performance in a wide variety of contexts ranging from reliability engineering to biomedίcal applications.Correspondingly, the development and investigation of statistical tests, based on complete or censored life-test observations, for testing the null hypothesis of exponentiality against various aging alternatives has been an active area of research.In particular, the need for statistical inference with censored data occur when observing all units in the sample is not feasible.Among the standard aging notions (viz., Barlow and Proschan 1991), the NBUE (New Better than Used in Expectation) is a relatively weak form of aging assumption, often made when one is unwilling to invoke a stronger assumption such as IFR, IFRA or NBU.A continuous life d.f.F on R + = [0, oo), with a finite mean μ and survival function F = 1 -F, is said to be (strictly) NBUE if (1.1) Γ F{x)dx{<) < μF(t), VI > 0. Jt

Censoring (clinical trials)

10.1214/lnms/1215452211

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Citations (8)

Dynamic Programming Methods in Repair and Replacement

Encyclopedia of Statistics in Quality and Reliability (2007)

Manish C. Bhattacharjee

Abstract Applications of dynamic programming to problems in reliability, with a specific emphasis on repair and replacement are surveyed. A brief summary of early classic work on such uses of dynamic programming is followed by a review of later approaches adopted by different researchers toward the problem of modeling plausible and pragmatic notions of imperfect repairs. We then provide a synthesis of how such different approaches for the study of repairable systems can be subsumed within a unified setting of a stochastic dynamic programming framework with some illustrative applications of such a formulation.

10.1002/9780470061572.eqr481

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Families of life distributions characterized by two moments

Journal of Applied Probability (1990)

Manish C. Bhattacharjee Jayaram Sethuraman

We consider several classical notions of partial orderings among life distributions which have been used to describe ageing properties and tail domination. We show that if a distribution G dominates another distribution F in one of these partial orderings introduced here, and if two moments of G agree with those of F , including the moment that describes this partial ordering, then G = F. This leads to a characterization of the exponential distribution among HNBUE and HNWUE life distribution classes, and thus extends the results of Basu and Bhattacharjee (1984) and rectifies an error in that paper.

Characterization

10.2307/3214556

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Citations (31)

Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

Journal of Applied Probability (2000)

Manish C. Bhattacharjee A. M. Abouammoh Ali Ahmed A. M. Barry

We investigate some preservation properties of two nonparametric classes of survival distributions and their duals, under appropriate reliability operations. The aging properties defining these nonparametric classes are based on comparing the mean life of a new unit to the mean residual life function of the asymptotic remaining survival time of the unit under repeated perfect repairs. They are motivated from a point of view that realistic notions of degradation, applicable to repairable systems, should be based on contrasting some aspect of the remaining life of a repairable unit (under a given repair strategy, such as renewals) to the life of a new unit.

Survival function

Dual polyhedron

Renewal theory

10.1239/jap/1014843079

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Ordering Policies for Perishable Items with Unknown Shelf Life⁄Variable Supply Distribution

Calcutta Statistical Association Bulletin (1985)

Manish C. Bhattacharjee

Many inventory problems of practical significance deal with perishable commodities and uncertainty in the amount received against order under conditions of relative scarcity. In addition the statistical profile of such uncertainties in supply or shelf life may not be completely known. For perishable items, we incorporate these departures from the standard inventory model to allow for variable supply or random shelf life, having NBUE distributions with given mean but which are otherwise unknown. The NBUE hypothesis, which is a nonparametric specification only, is invoked as a description of the relative scarcity of supply and deterioration in quality of aging items. Minimax inventory policies under these assumptions are developed. The relationship of our findings to the earlier results of Silver and Panda, stability properties of the minimax solution as the shelf life increases and an approach when both supply and shelf life are random are indicated.

Scarcity

10.1177/0008068319850302

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BACK MATTER

Manish C. Bhattacharjee Sunil Dhar Sundarraman Subramanian

10.1142/9789814329804_bmatter

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Citations (0)

Dynamic Programming Methods in Repair and Replacement

Wiley StatsRef: Statistics Reference Online (2014)

Manish C. Bhattacharjee

10.1002/9781118445112.stat04185

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Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

Journal of Applied Probability (2000)

Manish C. Bhattacharjee A. M. Abouammoh Ali Ahmed A. M. Barry

Survival function

Dual polyhedron

Renewal theory

10.1017/s0021900200018180

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Citations (4)

New results for the Brown-Proschan model of imperfect repair

Journal of Statistical Planning and Inference (1987)

Manish C. Bhattacharjee

10.1016/0378-3758(87)90083-8

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The Class of Mean Residual Lives and Some Consequences

SIAM Journal on Algebraic and Discrete Methods (1982)

Manish C. Bhattacharjee

The class of mean residual life functions and sequences is characterized. Apart from the utility of such characterizations for modelling life distributions through empirically determined mean residual lives, it is shown that such functions arise naturally in many areas such as branching processes. Several additional consequences regarding various nonparametric classes of life distributions are derived, including some characterizations of the exponential and uniform distributions.

Branching (polymer chemistry)

10.1137/0603006

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Citations (50)