PRESERVATION OF PROPERTIES UNDER MIXTURE

2003 ◽  
Vol 17 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Henry W. Block ◽  
Yulin Li ◽  
Thomas H. Savits
Keyword(s):  
Failure Rate ◽  
Failure Rates ◽  
Finite Mixtures ◽  
Mixture Of Distributions ◽  
Lifetime Distributions ◽  
Increasing Failure Rate ◽  
Mixtures Of Distributions

In general, finite mixtures of distributions with increasing failure rates are not increasing. However, conditions have been given by Lynch [8] so that a mixture of distributions with increasing failure rates has increasing failure rate. We establish similar results for other standard classes and also give examples which show that although the assumptions are stringent, continuous mixtures of standard families of lifetime distributions do have increasing failure rates. We also show that the result of Lynch follows from Savits [12] and the techniques of the last-cited paper can be applied to other classes as well.

Mixtures of distributions with increasing linear failure rates

2003 ◽  
Vol 40 (02) ◽  
pp. 485-504 ◽  
Author(s):  
Henry W. Block ◽  
Thomas H. Savits ◽  
Eshetu T. Wondmagegnehu
Keyword(s):  
Failure Rate ◽  
Heterogeneous Population ◽  
Failure Rates ◽  
Mixture Of Distributions ◽  
Statistical Concept ◽  
Mixtures Of Distributions ◽  
Decreasing Failure Rate ◽  
Standard Components

Populations of specific components are often heterogeneous and consist of a small number of different sub-populations. For example there are often two groups: defective components with shorter lifetimes and standard components with longer lifetimes. Another heterogeneous population results when components produced by two different manufacturing lines are combined. In either case a mixture results. The resulting population can be described using the statistical concept of a mixture. It is a well-known result that a mixture of distributions with decreasing failure rates has a decreasing failure rate. However, little is known about the monotonicity of a mixture when the various subpopulations have failure rates which are not necessarily decreasing. In this paper we study and attempt to determine the shape as well as the overall behavior of the failure rate of a mixture from two subpopulations each of which has increasing linear failure rate.

Mixtures of distributions with increasing linear failure rates

2003 ◽  
Vol 40 (2) ◽  
pp. 485-504 ◽  
Author(s):  
Henry W. Block ◽  
Thomas H. Savits ◽  
Eshetu T. Wondmagegnehu
Keyword(s):  
Failure Rate ◽  
Heterogeneous Population ◽  
Failure Rates ◽  
Mixture Of Distributions ◽  
Statistical Concept ◽  
Mixtures Of Distributions ◽  
Decreasing Failure Rate ◽  
Standard Components

Populations of specific components are often heterogeneous and consist of a small number of different sub-populations. For example there are often two groups: defective components with shorter lifetimes and standard components with longer lifetimes. Another heterogeneous population results when components produced by two different manufacturing lines are combined. In either case a mixture results. The resulting population can be described using the statistical concept of a mixture. It is a well-known result that a mixture of distributions with decreasing failure rates has a decreasing failure rate. However, little is known about the monotonicity of a mixture when the various subpopulations have failure rates which are not necessarily decreasing. In this paper we study and attempt to determine the shape as well as the overall behavior of the failure rate of a mixture from two subpopulations each of which has increasing linear failure rate.

Burn-in via shocks for avoiding large risks

2011 ◽  
Vol 226 (3) ◽  
pp. 318-326
Author(s):  
J H Cha ◽  
M Finkelstein
Keyword(s):  
Failure Rate ◽  
Economic Losses ◽  
Failure Rates ◽  
Time Intervals ◽  
Lifetime Distributions ◽  
High Importance ◽  
Heterogeneous Populations ◽  
Mixtures Of Distributions ◽  
Normal Environment ◽  
Early Failures

Burn-in is usually performed for items that have decreasing or bathtub failure rates in order to eliminate early failures. This can be done in either the normal environment or an accelerated environment that uses high environmental stresses, which are often referred to as shocks. Mixtures of distributions present a useful survival model for lifetime distributions in heterogeneous populations. They often result in decreasing failure rates in some time intervals, which can often justify the implementation of the burn-in procedure. This paper considers shocks that eliminate weak items in heterogeneous populations. It is assumed that a larger failure rate of an item corresponds to a larger probability of this elimination. Approaches are developed that can help to minimize the risks of selecting items with large levels of individual failure rates for missions of high importance, where failures can result in substantial economic losses. The optimal burn-in time which minimizes average losses for different criteria is considered using simple examples.

scholarly journals A new Weibull Exponentiated Inverted Weibull Distribution for modelling positively-skewed data

2021 ◽  
Vol 27 (1) ◽  
pp. 43-53
Author(s):  
J.O. Braimah ◽  
J.A. Adjekukor ◽  
N. Edike ◽  
S.O. Elakhe
Keyword(s):  
Weibull Distribution ◽  
Failure Rate ◽  
Real Life ◽  
Rate Function ◽  
Likelihood Method ◽  
Estimation Of Parameters ◽  
Failure Rate Function ◽  
Lifetime Distributions ◽  
Increasing Failure Rate ◽  
Modeling Data

An Exponentiated Inverted Weibull Distribution (EIWD) has a hazard rate (failure rate) function that is unimodal, thus making it less efficient for modeling data with an increasing failure rate (IFR). Hence, the need to generalize the EIWD in order to obtain a distribution that will be proficient in modeling these types of dataset (data with an increasing failure rate). This paper therefore, extends the EIWD in order to obtain Weibull Exponentiated Inverted Weibull (WEIW) distribution using the Weibull-Generator technique. Some of the properties investigated include the mean, variance, median, moments, quantile and moment generating functions. The explicit expressions were derived for the order statistics and hazard/failure rate function. The estimation of parameters was derived using the maximum likelihood method. The developed model was applied to a real-life dataset and compared with some existing competing lifetime distributions. The result revealed that the (WEIW) distribution provided a better fit to the real life dataset than the existing Weibull/Exponential family distributions.

scholarly journals Continuous Mixtures of Exponentials and IFR Gammas Having Bathtub-Shaped Failure Rates

2010 ◽  
Vol 47 (04) ◽  
pp. 899-907 ◽  
Author(s):  
Henry W. Block ◽  
Naftali A. Langberg ◽  
Thomas H. Savits ◽  
Jie Wang
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Gamma Distribution ◽  
Failure Rates ◽  
Increasing Failure Rate ◽  
Continuous Mixture ◽  
Mixtures Of Exponentials ◽  
The Right

It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In this paper we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped failure rate.

A New MIFRA Class of Life Distributions

1988 ◽  
Vol 37 (1-2) ◽  
pp. 67-80 ◽  
Author(s):  
S. P. Mukherjee ◽  
A. Chatterjee
Keyword(s):  
Failure Rate ◽  
Failure Rates ◽  
Component Failure ◽  
Increasing Failure Rate ◽  
Bivariate Case ◽  
Multivariate Generalization ◽  
Life Distributions ◽  
Component Failure Rates

A new multivariate generalization of the increasing failure rate average (IFRA) class which can be intutively supported in terms of some averaging of the component failure rates is proposed. A piecewise approximability of the class in the bivariate case and an inequality characterizing the proposed class have been established. It has been further shown that the proposed class possesses some desirable properties which should hold for any multivariate ageing class.

scholarly journals Continuous Mixtures of Exponentials and IFR Gammas Having Bathtub-Shaped Failure Rates

2010 ◽  
Vol 47 (4) ◽  
pp. 899-907 ◽  
Author(s):  
Henry W. Block ◽  
Naftali A. Langberg ◽  
Thomas H. Savits ◽  
Jie Wang
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Gamma Distribution ◽  
Failure Rates ◽  
Increasing Failure Rate ◽  
Continuous Mixture ◽  
Mixtures Of Exponentials ◽  
The Right

It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In this paper we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped failure rate.

On the Failure Rates of Consecutive−k−out−of−n Systems

1990 ◽  
Vol 4 (1) ◽  
pp. 57-71 ◽  
Author(s):  
F.K. Hwang ◽  
Y.C. Yao
Keyword(s):  
Failure Rate ◽  
Failure Rates ◽  
Increasing Failure Rate ◽  
N Cycle ◽  
Independent And Identically Distributed

It is known that the lifetime of a k−out−of−n system has increasing failure rate (IFR) if all of its components have independent and identically distributed IFR lifetimes. Derman, Lieberman, and Ross raised the same question for consecutive−k−out−of−n systems. But the scarcity of results gives no clue as to whether most of such systems have IFR's. In this paper, we completely solve the k = 2 and k = 3 cases. We prove that these systems, with a handful of exceptions, do not have IFR's (contradicting the result of Derman, Lieberman, and Ross that a consecutive-2-out-of-n cycle has IFR for any n). Our result suggests the conjecture that for every fixed k there exists nk such that for every n ≧ nk a consecutive-k−out−of−n system does not have IFR. We also prove that for every fixed d there exists nd large enough such that for all n ≧ nd a consecuive.(n – d)−out−of−n system has IFR. In particular, if the system is a line, then nd = 3d +1 for d ≧ 1.

Electromigration and Electrochemical Reaction Mixed Failure Mechanism in Gold Interconnection System

1999 ◽  
Author(s):  
Hide Murayama ◽  
Makoto Yamazaki ◽  
Shigeru Nakajima
Keyword(s):  
Failure Mechanism ◽  
Failure Rate ◽  
Electrochemical Reaction ◽  
Dielectric Films ◽  
Failure Rates ◽  
Interlayer Dielectric ◽  
Bipolar Devices ◽  
Gold Metallization

Abstract Power bipolar devices with gold metallization experience high failure rates. The failures are characterized as shorts, detected during LSI testing at burn-in. Many of these shorted locations are the same for the failed devices. From a statistical lot analysis, it is found that the short failure rate is higher for devices with thinner interlayer dielectric films. Based upon these results, a new electromigration and electrochemical reaction mixed failure mechanism is proposed for the failure.

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