Generalized Failure Rate Research Articles

A new finite range increasing generalized failure rate distribution and it’s applications

Here we introduce a bounded distribution, bounded by 0 and 1, that has unimodal density function. The distribution function as well as the hazard rate function of the model have closed forms. Structural properties and asymptotic behavior of the distribution are studied and obtained a characterization. Moreover, the distribution is an increasing generalized failure rate distribution and is capable of modeling data with increasing and bathtub failure rates. Two real data sets are analyzed and it is shown that the proposed model fits better than some of the existing models.

Aging notions, stochastic orders, and expected utilities

AbstractThere are some connections between aging notions, stochastic orders, and expected utilities. It is known that the DRHR (decreasing reversed hazard rate) aging notion can be characterized via the comparative statics result of risk aversion, and that the location-independent riskier order preserves monotonicity between risk premium and the Arrow–Pratt measure of risk aversion, and that the dispersive order preserves this monotonicity for the larger class of increasing utilities. Here, the aging notions ILR (increasing likelihood ratio), IFR (increasing failure rate), IGLR (increasing generalized likelihood ratio), and IGFR (increasing generalized failure rate) are characterized in terms of expected utilities. Based on these observations, we recover the closure properties of ILR, IFR, and DRHR under convolution, and of IGLR and IGFR under product, and investigate the closure properties of the dispersive order, location-independent riskier order, excess wealth order, the total time on test transform order under convolution, and the star order under product. We have some new findings.

A generalization of the increasing generalized failure rate unimodality condition

In this paper, we study unimodality conditions for distributions that describe markets with stochastic demand. Such conditions naturally emerge in the analysis of game-theoretic models of market competition (Cournot games) and supply chain coordination (Stackelberg games). We express the price elasticity of expected demand in terms of the mean residual life (MRL) function of the demand distribution and characterize optimal prices or equivalently, points of unitary elasticity, as fixed points of the MRL function. This leads to economic interpretable conditions on the demand distribution under which such fixed points exist and are unique. We find that markets with increasing price elasticity of expected demand that eventually become elastic correspond to distributions with decreasing generalized mean residual life (DGMRL) and finite second moment. DGMRL distributions strictly generalize the widely used increasing generalized failure rate (IGFR) distributions. We further elaborate on the relationship of the two classes, link their limiting behavior at infinity and examine moment and closure properties of DGMRL distributions that are important in economic applications. The DGMRL unimodality condition is useful in the analysis of optimal decisions under uncertainty in settings that are not covered by the widely-used IGFR condition; thus, it can be of broader interest to the game-theory and operations research literature.

Sentinel Lymph Node Biopsy in Breast Cancer Patients Undergoing Neo-Adjuvant Chemotherapy: Clinical Experience with Node-Negative and Node-Positive Disease Prior to Systemic Therapy

Sentinel lymph node biopsy (SLNB) has emerged as the standard procedure to replace axillary lymph node dissection (ALND) in breast cancer (BC) patients undergoing neo-adjuvant chemotherapy (NAC). SLNB is accepted in clinically node-negative (cN0) patients; however, its role in clinically node-positive (cN+) patients is debatable. We performed a retrospective analysis of BC patients undergoing NAC and SLNB. Our aim was to evaluate the clinical significance of SLNB in the setting of NAC. This was accomplished by comparing the characteristics and oncological outcomes between cN0 and cN+ patients prior to NAC and type of axillary surgery. A total of 291 patients were included in the analysis: 131 were cN0 and 160 were cN+ who became ycN0 after NAC. At a median follow-up of 43 months, axillary recurrence occurred in three cN0 (2.3%) and two cN+ (1.3%) patients. However, there were no statistically significant differences in oncological outcomes (disease-free survival, distant disease-free survival, overall survival, and breast-cancer-specific survival) between cN0 and cN+ patients nor between patients treated with SLNB only or ALND. SLNB in the setting of NAC is an acceptable procedure with a general good prognosis and low axillary failure rates for both cN0 and cN+ patients.

Does anterior plus posterior interosseus neurectomy lead to better outcomes than isolated posterior interosseus denervation in the treatment of chronic wrist pain? A systematic review of the literature and meta-analysis.

Partial wrist denervation can be performed by isolated posterior interosseous nerve (PIN) or combined PIN plus (+) anterior interosseous nerve (AIN) neurectomy procedures. The purpose of the current systematic review is to investigate any differences in clinical outcomes and failures in patients undergoing AIN + PIN vs isolated PIN neurectomy. A review of the English Literature was performed on Medline, WOS and Scopus according to PRISMA protocol combining 'wrist denervation', 'PIN neurectomy', 'AIN neurectomy', anterior interosseous nerve neurectomy' and 'posterior interosseous nerve neurectomy'. Studies were assessed with a modified Coleman Methodology Score (CMS). The primary outcome for meta-analysis was 'Failures', including all patients who have required a second surgery or those who are left with pain (defined as 'bad'). Overall, 10 studies totalling 347 wrists were included in this systematic review, with a 'moderate' CMS. The isolated PIN neurectomy technique showed a 15.1% pooled failure rate at a median follow-up of 22 months, while the combined AIN+PIN denervation had a pooled failure rate of 23.6% at a follow-up with a median of 29 months. The combined analysis of both procedures did not show significantly better results in favour of either technique, with a general failure rate of 21.6% (P = 0.0501). Partial denervation for chronic wrist pain is a salvage procedure that leads to an overall success of 78.4% for pain relief, with no substantial complications. Apparently, performing the neurectomy also of the AIN does not offer greater advantages compared to the isolated PIN neurectomy.

The Teacher, the Fedathi Sequence and the Failure Indexes of the Subject Differential and Integral Calculus

The failure of students in the discipline of Differential and Integral Calculus is frequent in institutions, whether public or private. It is up to the teacher to reflect on the pedagogical practice, identify how learning is taking place and analyze what changes should be necessary in the planning, conduct and evaluation of the class. The objective of the work is to identify the results of students in the discipline of Differential and Integral Calculus at the Universidade Estadual Vale do Acaraú, over a period of 10 years, presenting the Fedathi Sequence as a possibility of mediation to reduce the low rates in evaluations. The research is exploratory with a quantitative and qualitative approach and indicates that the general failure and dropout rate in the academic periods between 2009.1 to 2019.1 were higher than 50%, reaffirming the national trend. It is concluded that the pedagogical practices based on methodologies that seek to dialogue with the student in the classroom contribute to the evaluation process and also to the final result of the subjects. The Fedathi Sequence is presented as a methodological proposal, supporting the hypothesis that through mediation and evaluation of the knowledge construction process, it is possible to minimize the failure and dropout rates of the discipline.

P611: NEXT-CLL: A NEW NGS-BASED METHOD FOR RAPID ASSESSMENT OF IGHV MUTATIONAL STATUS IN CHRONIC LYMPHOID LEUKEMIA

Background: Chronic Lymphocytic Leukemia (CLL) is a highly heterogeneous disease both in terms of biological landscape and clinical course. Current guidelines recommend IGHV mutation status (MS) determination prior to treatment initiation in order to guide the first-line therapeutic choice between chemoimmunotherapy and novel agents. Currently, the IGHV MS is determined in most routine laboratories by low-throughput Sanger sequencing that allows for the detection of the dominant clone in the majority of CLL cases. However, this technic remains technically challenging despite best practice guidelines, does not provide any insight into subclonal architecture and intraclonal diversity, and has a general failure rate ranging from 10 to 20%. Besides, commercially available NGS solutions have drawbacks (costs) and constraints (as they necessitate mandatorily a MiSeq sequencing machine and are not feasible on other devices) that restrict their use by any laboratory in routine practice. Aims: In this study, we aimed at providing a ready-to-use and rapid strategy to evaluate the IGHV gene MS using NGS in routine practice. We present a new method called Next-CLL, allowing rapid assessment on any NGS device available in routine diagnostic laboratories. Methods: Peripheral blood samples were obtained from 80 patients with typical CLL at diagnosis. Genomic DNA (gDNA) and complementary DNA (cDNA) were used. In order to fully cover the IGHV rearranged gene sequence, 4 mutliplex PCR reactions were designed: [LEADER-FR2R/JHc], [FR1c-JHc], [FR1-JHc] and [FR2-JHc], producing overlapping amplicons. Final products from the 4 PCR reactions were mixed and purified, subjected to A-tailing and ligated to Illumina-single indexed adapters. The library was then sequenced (2x150 bp) on a NextSeq 500 (Illumina). A reassembly of IGHV overlapping amplicons was performed using the BBTools Suite. The outputs were then uploaded on the Vidjil plateform for IGHV clonal analysis. The MS was calculate using the IMGT web interactive tool following ERIC recommendations. IgHV MS was assessed in parallel by Sanger sequencing or the commercial NGS assay IdentiClone® Assay (Invivoscribe) as reference. Gene usage, % identity to the germline and stereotype subsets were compared with the results obtained from Next-CLL. Results: Next-CLL identified a productive clone in 100% of cases (n=80), compared to PCR with Sanger sequencing (15% of failure). All cases that failed using the Sanger sequencing were subjected to a second NGS technique (Invivoscribe) that confirmed the results from Next-CLL, ruling out any possibility of false positive cases. Next-CLL showed 100% concordance with the reference techniques for IGHV gene identification and allowed assessment of the MS from the leader sequence, as recommended by the ERIC consortium. Only 2 cases showed discordant IGHV MS, close to the 98% identity cut-off, between Next-CLL and Sanger sequencing (the latter being unable to capture the leader sequences), thus providing 97% of concordance between the 2 techniques (Figure 1). Moreover, 100% concordant results were obtained between gDNA and cDNA (n=32 cases analysed for both) using Next-CLL. Image:Summary/Conclusion: Our new method Next-CLL allows assessment of the IGHV MS by NGS with an easy and rapid workflow, providing clinically useful information from the IGHV leader sequence and allowing analysis of intra-clonal diversity (not possible with the standard Sanger sequencing). Importantly, it might be used both on gDNA and cDNA and on any sequencing machine, on the contrary to existing commercially available kits.

Supply network design with uncertain demand: Computational cooperative game theory approach using distributed parallel programming

In this work we investigate a supply chain design problem with uncertain final demands for the end products produced by a set of manufacturers. This network of manufacturers has the organizational decisions made internally by pooling resources in a cooperative manner and externally by determining the dominant strategic actors that are characterized by the retailer. A non-linear production game (NLPG) is formulated as a mathematical programming problem to describe coalition formation among the manufacturers based on initial contractual agreements. We show that NLPG is a grand coalition game when demand distribution has an increasing generalized failure rate. The conditions that impact the profit allocation in the game including core set, fairness, stability, superadditivity, least-core and ∊-core are defined. A core allocation solution is generated by using an algorithmic approach. This algorithmic solution is tested in a distributed work station network and resulted in attaining strong computational results for the proposed mathematical programming problem; optimization results with 1000 players are determined in 6 min 40 s on a university computer network using parallel programming with 52 powerful work stations. The numerical results indicated O(log(-N|)) complexity of the algorithmic solution up to 800 players. To the best of our knowledge, this work is the first of its kind in which distributed parallel processing is implemented in a university work station network with distributed parallel programming and processing for solving a production cooperative game.

The Impact of Reducing Mathematics Component in Biology “O” Level Examinations on Student’s Performance in Mathematical Related Biology Courses at Diploma Level in Zambia

Mathematics has played important roles in many fields of biology, and can be a powerful tool for understanding biological observed phenomena which cannot be understood by verbal reasoning alone. Quantitative questions in Zambian Biology O level examinations has kept on reducing irrespective of its importance in higher level biology courses. Therefore, this study aimed at determining the effect of reducing mathematics component in biology “O” Level examinations on students’ performance in mathematical related biology courses at diploma level. Primary data was collected using five point Likert scale questionnaire and assessment test for mathematical biology. Secondary data was collected from Zambian, Cambridge and Edexcel biology “O” Level examination question papers from 1999-2017, Syllabi for Biology and examination results for mathematical biology related courses at diploma Level.The sample size for the study was 200 education and pharmacology students from Mansa School of Nursing and Zambia College of Open and Distance Learning and 50 teachers and examiners from the surrounding schools of Mansa District. The analysis of biology papers for the three examining bodies have revealed that International examinations had more mathematics component and it was consistent from 1999 to 2017 whilst in Zambian had less and kept on reducing from 2008 to 2017. Further, the syllabi for these examining bodies revealed that key aims and objectives are the same except that Zambian (Curriculum Development Centre) had no assessment objective weightings. The assessment test results analyzed using independent sample t-test at 0.05 level of significance revealed that students who did biology with more mathematics component performed better in mathematical related biology courses compared to the one with less mathematics component at diploma level. Further, the comparison of means of the results of pharmacology and biology education at diploma level also agreed with the outcome of the sample test.From the analysis of questionnaires for biology teachers and examiners revealed that pupil’s attitude and performance in mathematics related biology questions and the general failure rate in biology had led to the reducing of mathematics component in Zambian biology. DOI: 10.7176/JEP/12-30-09 Publication date: October 31 st 2021

Monopoly pricing in vertical markets with demand uncertainty

Motivation Pricing decisions are often made when market information is still poor. While modern pricing analytics aid firms to infer the distribution of the stochastic demand that they are facing, data-driven price optimization methods are often impractical or incomplete if not coupled with testable theoretical predictions. In turn, existing theoretical models often reason about the response of optimal prices to changing market characteristics without exploiting all available information about the demand distribution. Academic/practical relevance Our aim is to develop a theory for the optimization and systematic comparison of prices between different instances of the same market under various forms of knowledge about the corresponding demand distributions. Methodology We revisit the classic problem of monopoly pricing under demand uncertainty in a vertical market with an upstream supplier and multiple forms of downstream competition between arbitrary symmetric retailers. In all cases, demand uncertainty falls to the supplier who acts first and sets a uniform price before the retailers observe the realized demand and place their orders. Results Our main methodological contribution is that we express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution. This leads to a closed form characterization of the points of unitary elasticity that maximize the supplier’s profits and the derivation of a mild unimodality condition for the supplier’s objective function that generalizes the widely used increasing generalized failure rate (IGFR) condition. A direct implication is that optimal prices between different markets can be ordered if the markets can be stochastically ordered according to their MRD functions or equivalently, their elasticities. Using the above, we develop a systematic framework to compare optimal prices between different market instances via the rich theory of stochastic orders. This leads to comparative statics that challenge previously established economic insights about the effects of market size, demand transformations and demand variability on monopolistic prices. Managerial implications Our findings complement data-driven decisions regarding price optimization and provide a systematic framework useful for making theoretical predictions in advance of market movements.

The Discrete Moment Problem with Nonconvex Shape Constraints

The discrete moment problem aims to find a worst-case discrete distribution that satisfies a given set of moments. This paper studies the discrete moment problems with additional shape constraints that guarantee the worst-case distribution is either log-concave (LC) or has an increasing failure rate (IFR) or increasing generalized failure rate (IGFR). These classes are useful in practice, with applications in revenue management, reliability, and inventory control. The authors characterize the structure of optimal extreme point distributions and show, for example, that an optimal extreme point solution to a moment problem with m moments and LC shape constraints is piecewise geometric with at most m pieces. Using this optimality structure, they design an exact algorithm for computing optimal solutions in a low-dimensional space of parameters. The authors leverage this structure to study a robust newsvendor problem with shape constraints and compute optimal solutions.

Redundancy Dependence in the Context of Competing Risks and Dynamic Degradation

Parallel redundancy is a common approach to increase network availability. As a consequence of providing redundancy, the loading of that component changes, affecting its reliability. In this article, a holistic approach combining two models is introduced to assess both instantaneous and future effects on general failure rates in the context of competing risks and dynamic degradation. Concretely, both are designed to account for the duration of abnormal loading events. First, a per-unit-degradation method is introduced to map the different loading states onto a single normal operation sojourn time variable. Second, a time-inhomogeneous Markov chain is introduced to assess the irreversible degradation following a nondetrimental abnormal loading event. The numerical illustration shows that both models are necessary to correctly assess the effects of redundancy dependence if the underlying failure distribution has a shape parameter exceeding one.

Concavity and Unimodality of Expected Revenue Under Discrete Willingness to Pay Distributions

Most pricing and revenue management models have at their core an optimization problem; one needs to determine the optimal price or quantity to maximize a profit or revenue function. To ensure tractability, conditions that assure the objective function has a unique solution are enormously helpful. So far, several technical assumptions have been proposed for the continuous case, but comparatively little attention has been given to the discrete counterpart despite its prevalence in practice. Thus, this study aims to develop new technical assumptions, built upon relevant economic concepts, to guarantee the tractability of revenue management models in discrete settings. In particular, we present two sufficient conditions for the revenue function to be concave, in terms of quantity or price and propose a condition for the revenue function to be unimodal, called discrete increasing generalized failure rate (IGFR). Our definition has an appropriate economic interpretation and offers comparable properties to those of the continuous version. Finally, we show the discrete IGFR property holds for several discrete distributions.

On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty

AbstractWe revisit the linear Cournot model with uncertain demand that is studied in Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) and provide sufficient conditions for equilibrium uniqueness that complement the existing results. We show that if the distribution of the demand intercept has the decreasing mean residual demand (DMRD) or the increasing generalized failure rate (IGFR) property, then uniqueness of equilibrium is guaranteed. The DMRD condition implies log-concavity of the expected profits per unit of output without additional assumptions on the existence or the shape of the density of the demand intercept and, hence, answers in the affirmative the conjecture of Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) that such conditions may not be necessary.

The price of anarchy in closed‐loop supply chains

AbstractThis paper measures the worst‐case efficiency of price‐only contracts in closed‐loop supply chains (CLSCs) with the price of anarchy (PoA). We model a single‐period Stackelberg game in which a manufacturer sells new products to a retailer and collects used products with exogenous retail price and collection price via three alternative reverse channels: (a) the manufacturer collects directly from customers, (b) the retailer collects for the manufacturer, and (c) a third party is awarded a collection subcontract from the manufacturer. We carry out a comprehensive investigation under push–pull configurations to observe how reverse channel structures with different gaming sequences of CLSC members influence the worst‐case performance when the demand distribution is over the set of increasing generalized failure rate distributions. From our PoA analysis, we find that the pull system does not always outperform the push system, especially when the retailer is the leader, in contrast to the results for forward supply chains. While the PoA of the push system is dramatically sensitive to the quality condition of used products, the pull system has a constant efficiency loss that is independent of the quality condition. Instead, the PoA of the pull system solely changes with the gaming sequence of the manufacturer. We also find that manufacturer's direct collection is a better reverse channel choice compared to retailer's collection. Additional managerial insights are summarized for discussion.

Connection of Generalized Failure Rate and Generalized Reversed Failure Rate with Inequality Curves

The purpose of this paper is to introduce some properties of generalized failure rate (GFR) and generalized reversed failure rate (GRFR), study their connection with inequality measures and then apply it to make comparisons of some reliability models. In the second part of our paper, we obtain the properties for the GRFR based on the properties of the GFR and weighted distributions. The importance of such a study lies in the usefulness of using. Finally, we present two examples to illustrate the applications of the relationships outlined in this paper. A real dataset is used for clarifying presented concepts.

Optimal upper bounds on expected kth record values from IGFR distributions

ABSTRACTThe paper concerns the optimal upper bounds on the expectations of the kth record values () centred about the sample mean. We consider the case, when the records are based on the infinite sequence of the independent identically distributed random variables, which distribution function is restricted to the family of distributions with the increasing generalized failure rate (IGFR). Such a class can be defined in terms of the convex orders of some distribution functions. Particularly important examples of IGFR class are the distributions with the increasing density and increasing failure rate. Presented bounds were obtained with use of the projection method, and are expressed in the scale units based on the standard deviation of the underlying distribution function.

A logistic regression investigation of the relationship between the Learning Assistant model and failure rates in introductory STEM courses

BackgroundLarge introductory STEM courses historically have high failure rates, and failing such courses often leads students to change majors or even drop out of college. Instructional innovations such as the Learning Assistant model can influence this trend by changing institutional norms. In collaboration with faculty who teach large-enrollment introductory STEM courses, undergraduate learning assistants (LAs) use research-based instructional strategies designed to encourage active student engagement and elicit student thinking. These instructional innovations help students master the types of skills necessary for college success such as critical thinking and defending ideas. In this study, we use logistic regression with pre-existing institutional data to investigate the relationship between exposure to LA support in large introductory STEM courses and general failure rates in these same and other introductory courses at University of Colorado Boulder.ResultsOur results indicate that exposure to LA support in any STEM gateway course is associated with a 63% reduction in odds of failure for males and a 55% reduction in odds of failure for females in subsequent STEM gateway courses.ConclusionsThe LA program appears related to lower course failure rates in introductory STEM courses, but each department involved in this study implements the LA program in different ways. We hypothesize that these differences may influence student experiences in ways that are not apparent in the current analysis, but more work is necessary to support this hypothesis. Despite this potential limitation, we see that the LA program is consistently associated with lower failure rates in introductory STEM courses. These results extend the research base regarding the relationship between the LA program and positive student outcomes.

Parameter estimates of general failure rate model: A Bayesian approach

The failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models. A study of the general failure rate model r ( t ) = a + b t θ − 1 , under squared error loss function, taking a and b independent exponential random variables, has been performed in the literature. In this article, we consider a and b not necessarily independent. The estimates of the parameters a and b under squared error loss, linex loss and entropy loss functions are obtained, and further examined using simulated and real data sets. • A general failure rate model r ( t ) = a + b t θ − 1 has been studied when a and b are not necessarily independent. • Bayes’ estimators of the parameters a and b, under symmetric and asymmetric loss functions, have been obtained. • The monotonicity of the estimators has been studied through simulated as well as real data sets

Characterization of Lifetime Distribution Based on Generalized Interval Entropy

In this paper, we introduce the concept of generalized interval entropy measure of order alpha and type beta for the doubly truncated random variable. A characterization problem for the generalized interval entropy measure has been studied. The exponential, the pareto and finite range distributions have been characterized in terms of the proposed entropy measure and generalized failure rate function. A lower bound to generalized interval entropy has also been derived. Finally some stochastic comparison based on generalized interval entropy are presented.