Families of Life Distributions Characterized by Two Moments

1988 ◽  
Author(s):  
Manish C. Bhattacharjee ◽  
Jayaram Sethuraman
Keyword(s):  
Life Distributions

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

On classes of life distributions based on the mean time to failure function

2021 ◽  
Vol 58 (2) ◽  
pp. 289-313
Author(s):  
Ruhul Ali Khan ◽  
Dhrubasish Bhattacharyya ◽  
Murari Mitra
Keyword(s):  
Damage Model ◽  
Replacement Policy ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Moment Convergence ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
The Mean ◽  
Age Replacement ◽  
Mean Time

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

Characterizing the Exponential Law Under Laplace Order Domination

1995 ◽  
Vol 45 (3-4) ◽  
pp. 171-178 ◽  
Author(s):  
Murari Mitra ◽  
Sujit K. Basu ◽  
M. C. Bhattacharjee
Keyword(s):  
Exponential Distribution ◽  
Reliability Theory ◽  
Subject Classification ◽  
Exponential Law ◽  
Life Distributions

Interesting characterizations of the exponential distribution have been obtained in classes of life distributions important in reliability theory. The results strengthen some of the analogous conclusions already existing in the literature. AMS (1991) Subject Classification No. Primary 62NOS: Secondaey 90825. 60F99.

New Stochastic Orders Based on Double Truncation

1997 ◽  
Vol 11 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Jorge Navarro ◽  
Felix Belzunce ◽  
Jose M. Ruiz
Keyword(s):  
Likelihood Ratio ◽  
Random Variable ◽  
Stochastic Orders ◽  
Likelihood Ratio Order ◽  
Reliability Measures ◽  
Life Distributions ◽  
The Relationship ◽  
Double Truncation

The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.

Fatigue Reliability Functions in Semilogarithmic Coordinates

1991 ◽  
Author(s):  
Vladimir A. Avakov
Keyword(s):  
Fatigue Life ◽  
Coordinate System ◽  
Strength Distribution ◽  
Fatigue Reliability ◽  
Life Distribution ◽  
Similar Transformation ◽  
Asymptotic Type ◽  
Life Distributions ◽  
Strength Distributions

Abstract In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (lnN-lnS). Here, a similar transformation is established using a semi logarithmic (lnN-S) coordinate system. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smallest value, and three-parameter Weibull strength distributions, respectively. This procedure may be applied to other types of fatigue life distribution.

The Effect of HFPD Thermally Sprayed WC-Co Coatings on the Fatigue Behavior and Deformation of Al 2024-T4

2000 ◽  
Author(s):  
A. Ibrahim ◽  
C.C. Berndt
Keyword(s):  
High Frequency ◽  
High Cycle Fatigue ◽  
Fatigue Behavior ◽  
Cycle Fatigue ◽  
Pulse Detonation ◽  
Deformation Behaviors ◽  
Life Distributions ◽  
Thermally Sprayed ◽  
Al 2024 ◽  
Frequency Pulse

Abstract The effect of high frequency pulse detonation (HFPD) and HVOF thermally sprayed WC-Co coatings on the high cycle fatigue (HCF) behavior of 2024-T4 aluminum was investigated. The fatigue life distributions of specimens in the polished and coated conditions are presented as a function of the probability of failure. The monotonic and cyclic deformation behaviors of the as-received and as-coated specimens were investigated. The conclusions show that, (i) the HFPD sprayed specimens exhibited slightly higher fatigue lives compared to the uncoated specimens, (ii) the HVOF sprayed specimens exhibited significantly higher fatigue lives compared to the uncoated specimens, and (iii) the as-coated specimen was cyclically stable.

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