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

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.

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A MIXTURE OF EXPONENTIAL AND IFR GAMMA DISTRIBUTIONS HAVING AN UPSIDEDOWN BATHTUB-SHAPED FAILURE RATE

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964812000204 ◽

2012 ◽

Vol 26 (4) ◽

pp. 573-580 ◽

Cited By ~ 3

Author(s):

Henry W. Block ◽

Naftali A. Langberg ◽

Thomas H. Savits

Keyword(s):

Exponential Distribution ◽

Failure Rate ◽

Gamma Distribution ◽

Increasing Failure Rate ◽

Bathtub Shape ◽

Gamma Distributions ◽

The Right

We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

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Clinical Evaluation of Bracket Bonding Using Two Different Polymerization Sources

The Angle Orthodontist ◽

10.2319/072807-351.1 ◽

2008 ◽

Vol 78 (5) ◽

pp. 922-925 ◽

Cited By ~ 12

Author(s):

Nikolaos S. Koupis ◽

Theodore Eliades ◽

Athanasios E. Athanasiou

Keyword(s):

Failure Rate ◽

Orthodontic Treatment ◽

Light Emitting Diode ◽

Rank Test ◽

Dental Arch ◽

Halogen Lamp ◽

Failure Rates ◽

Bond Failure ◽

Significant Difference ◽

The Right

Abstract Objective: To comparatively assess clinical failure rate of brackets cured with two different photopolymerization sources after nine months of orthodontic treatment. Materials and Methods: The sample of this study comprised 30 patients who received comprehensive orthodontic treatment by means of fixed appliances. Using the same adhesive, 600 stainless steel brackets were directly bonded and light cured for 10 seconds with the light-emitting diode (LED) lamp or for 20 seconds with the conventional halogen lamp. A split-mouth design randomly alternated from patient to patient was applied. Failure rates were recorded for nine months and analyzed with Pearson χ2 test, and log-rank test at α = .05 level of significance. Results: The overall failure rate recorded with the halogen unit (3.33%) was not significantly different from the failure rate for the LED lamp (5.00%). Significantly more failures were found in boys compared with girls, in the mandibular dental arch compared with the maxillary arch, and in posterior segments compared with anterior segments. However, no significant difference was found between the right and left segments. Conclusion: Both light-curing units showed sufficiently low bond failure rates. LED curing units are an advantageous alternative to conventional halogen sources in orthodontics because they enable a reduced chair-time bonding procedure without significantly affecting bond failure rate.

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Varicocele surgery or embolization: Which is better?

Canadian Urological Association Journal ◽

10.5489/cuaj.295 ◽

2013 ◽

Vol 6 (4) ◽

pp. 266 ◽

Cited By ~ 19

Author(s):

Darby Cassidy ◽

Keith Jarvi ◽

Ethan Grober ◽

Kirk Lo

Keyword(s):

Failure Rate ◽

Attractive Alternative ◽

Published Data ◽

Technical Failure ◽

Failure Rates ◽

Male Factor Infertility ◽

Male Factor ◽

Gonadal Vein ◽

Microsurgical Approach ◽

The Right

Introduction: Varicocele remains the most commonly identifiedcorrectable cause of male factor infertility. Surgical correction isthe most commonly performed technique to treat varicoceles with a technical failure rate of less than 5%. An attractive alternative to surgery is the selective catheterization and embolization of the gonadal vein. This data are limited by small series.Methods: We reviewed a total of 158 patients. These patientsunderwent embolization for clinical varicoceles and male factorinfertility between 2004 and 2008. Of these, 56% underwentattempted bilateral embolization, 43% unilateral left-sided embolization and 1.3% unilateral right-sided embolization.Results: Of these patients who underwent attempted bilateralembolization, 19.3% did not experience a successful obliterationof the right gonadal vein and 2.3% (2/88) experienced a failure rate in the embolization of the left gonadal vein. Of the 2 attempts at unilateral right-sided embolization, there were no failures. Of the 68 unilateral left-sided embolization attempts, there was a 4.4% failure rate. Of all of the right-sided embolization attempts, 18.9% failed, while 3.2% of the left-sided attempts failed.Conclusion: This review represents the largest contemporary series of varicocele embolization outcomes currently in the literature. Our 19.3% technical failure rate for bilateral varicocele embolization is higher than the current published rate of 13% and is largely related to failure to successfully occlude the right gonadal vein. This supports our belief that bilateral varicoceles are best managed with a primary microsurgical approach, where technical failure rates are expected to be less than 5% based on published data. Men withunilateral left-sided varicoceles should be offered both options as they have similar failure rates, but with embolization offering some clear advantages to the patient.

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A multivariate IFR class

Journal of Applied Probability ◽

10.1017/s0021900200029120 ◽

1985 ◽

Vol 22 (01) ◽

pp. 197-204 ◽

Cited By ~ 5

Author(s):

Thomas H. Savits

Keyword(s):

Exponential Distribution ◽

Failure Rate ◽

Random Vector ◽

Increasing Failure Rate ◽

Rate Distribution ◽

Weak Limits ◽

Multivariate Exponential Distribution ◽

Multivariate Exponential

A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.

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A multivariate IFR class

Journal of Applied Probability ◽

10.2307/3213759 ◽

1985 ◽

Vol 22 (1) ◽

pp. 197-204 ◽

Cited By ~ 17

Author(s):

Thomas H. Savits

Keyword(s):

Exponential Distribution ◽

Failure Rate ◽

Random Vector ◽

Increasing Failure Rate ◽

Rate Distribution ◽

Weak Limits ◽

Multivariate Exponential Distribution ◽

Multivariate Exponential

A non-negative random vector T is said to have a multivariate increasing failure rate distribution (MIFR) if and only if E[h(x, T)] is log concave in x for all functions h(x, t) which are log concave in (x, t) and are non-decreasing and continuous in t for each fixed x. This class of distributions is closed under deletion, conjunction, convolution and weak limits. It contains the multivariate exponential distribution of Marshall and Olkin and those distributions having a log concave density. Also, it follows that if T is MIFR and ψ is non-decreasing, non-negative and concave then ψ (T) is IFR.

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PRESERVATION OF PROPERTIES UNDER MIXTURE

Probability in the Engineering and Informational Sciences ◽

10.1017/s026996480317204x ◽

2003 ◽

Vol 17 (2) ◽

pp. 205-212 ◽

Cited By ~ 14

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.

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A New MIFRA Class of Life Distributions

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319880107 ◽

1988 ◽

Vol 37 (1-2) ◽

pp. 67-80 ◽

Cited By ~ 2

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.

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

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800001455 ◽

1990 ◽

Vol 4 (1) ◽

pp. 57-71 ◽

Cited By ~ 5

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.

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Electromigration and Electrochemical Reaction Mixed Failure Mechanism in Gold Interconnection System

ISTFA 1999: Conference Proceedings from the 25th International Symposium for Testing and Failure Analysis ◽

10.31399/asm.cp.istfa1999p0399 ◽

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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