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

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.

1995 ◽  
Vol 9 (2) ◽  
pp. 217-225 ◽  
Author(s):  
Lirong Cui ◽  
Alan G. Hawkes ◽  
Assad Jalali

We prove Hwang and Yao's conjecture about failure of consecutive-k-out-of-n systems whose components have independent and identically distributed increasing failure rate (IFR) lifetimes, namely, that for each k ≥ 2 there exists nk such that for every n ≥ nk the system does not preserve IFR. For the cases k = 4 and 5, we present complete solutions. We present further conjectures.


Author(s):  
Ioannis S. Triantafyllou

In this paper, we study the closure property of the Increasing Failure Rate (IFR) class under the formation of coherent systems. Sufficient conditions for the nonpreservation of the IFR attribute for reliability structures consisting of [Formula: see text] independent and identically distributed ([Formula: see text] components are provided. More precisely, we deal with the IFR preservation (or nonpreservation) under the formation of structures with two common failure criteria by the aid of their signature vectors.


2010 ◽  
Vol 47 (04) ◽  
pp. 899-907 ◽  
Author(s):  
Henry W. Block ◽  
Naftali A. Langberg ◽  
Thomas H. Savits ◽  
Jie Wang

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.


2003 ◽  
Vol 17 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Henry W. Block ◽  
Yulin Li ◽  
Thomas H. Savits

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.


1988 ◽  
Vol 37 (1-2) ◽  
pp. 67-80 ◽  
Author(s):  
S. P. Mukherjee ◽  
A. Chatterjee

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.


2010 ◽  
Vol 47 (4) ◽  
pp. 899-907 ◽  
Author(s):  
Henry W. Block ◽  
Naftali A. Langberg ◽  
Thomas H. Savits ◽  
Jie Wang

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.


Author(s):  
Hide Murayama ◽  
Makoto Yamazaki ◽  
Shigeru Nakajima

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.


2017 ◽  
Vol 45 (9) ◽  
pp. 2098-2104 ◽  
Author(s):  
Jorge Chahla ◽  
Chase S. Dean ◽  
Lauren M. Matheny ◽  
Justin J. Mitchell ◽  
Mark E. Cinque ◽  
...  

Background: Limited evidence exists for meniscal repair outcomes in a multiligament reconstruction setting. Purpose/Hypothesis: The purpose of this study was to assess outcomes and failure rates of meniscal repair in patients who underwent multiligament reconstruction compared with patients who underwent multiligament reconstruction but lacked meniscal tears. The authors hypothesized that the outcomes of meniscal repair associated with concomitant multiligament reconstruction would significantly improve from preoperatively to postoperatively at a minimum of 2 years after the index surgery. Secondarily, they hypothesized that this cohort would demonstrate similar outcomes and failure rates compared with the cohort that did not have meniscal lesions at the time of multiligament reconstruction. Study Design: Cohort study; Level of evidence, 3. Methods: Inclusion criteria for the study included radiographically confirmed skeletally mature patients of at least 16 years of age who underwent multiligamentous reconstruction of the knee without previous ipsilateral osteotomy, intra-articular infections, or intra-articular fractures. Patients were included in the experimental group if they underwent inside-out meniscal suture repair with concurrent multiligament reconstruction. Those included in the control group (multiligament reconstruction without a meniscal tear) underwent multiligament reconstruction but did not undergo any type of meniscal surgery. Lysholm, Western Ontario and McMaster Universities Osteoarthritis Index, Short Form–12 physical component summary and mental component summary, Tegner activity scale, and patient satisfaction scores were recorded preoperatively and postoperatively. The failure of meniscal repair was defined as a retear of the meniscus that was confirmed arthroscopically. Results: There were 43 patients (16 female, 27 male) in the meniscal repair group and 62 patients (25 female, 37 male) in the control group. Follow-up was obtained in 93% of patients with a mean of 3.0 years (range, 2.0-4.7 years). There was a significant improvement between all preoperative and postoperative outcome scores ( P < .05) for both groups. The meniscal repair group had significantly lower preoperative Lysholm and Tegner scores ( P = .009 and P = .02, respectively). There were no significant differences between any other outcome scores preoperatively. The failure rate of the meniscal repair group was 2.7%, consisting of 1 symptomatic meniscal retear. There was no significant difference in any postoperative outcome score at a minimum 2-year follow-up between the 2 groups. Conclusion: Good to excellent patient-reported outcomes were reported for both groups with no significant differences in outcomes between the cohorts. Additionally, the failure rate for inside-out meniscal repair with concomitant multiligament reconstruction was low, regardless of meniscus laterality and tear characteristics. The use of multiple vertical mattress sutures and the biological augmentation resulting from intra-articular cruciate ligament reconstruction tunnel reaming may be partially responsible for the stability of the meniscal repair construct and thereby contribute to the overall improved outcomes and the low failure rate of meniscal repair, despite lower preoperative Lysholm and Tegner scores in the meniscal repair group.


2008 ◽  
Vol 78 (5) ◽  
pp. 922-925 ◽  
Author(s):  
Nikolaos S. Koupis ◽  
Theodore Eliades ◽  
Athanasios E. Athanasiou

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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