Markov chain modelling of reliability analysis and prediction under mixed mode loading

A new class of distributions with increasing, decreasing, bathtub-shaped and unimodal hazard rate forms called generalized quadratic hazard rate-power series distribution is proposed. The new distribution is obtained by compounding the generalized quadratic hazard rate and power series distributions. This class of distributions contains several important distributions appeared in the literature, such as generalized quadratic hazard rate-geometric, -Poisson, -logarithmic, -binomial and -negative binomial distributions as special cases. We provide comprehensive mathematical properties of the new distribution. We obtain closed-form expressions for the density function, cumulative distribution function, survival and hazard rate functions, moments, mean residual life, mean past lifetime, order statistics and moments of order statistics; certain characterizations of the proposed distribution are presented as well. The special distributions are studied in some details. The maximum likelihood method is used to estimate the unknown parameters. We propose to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. It is observed that the proposed EM algorithm can be implemented very easily in practice. One data set has been analyzed for illustrative purposes. It is observed that the proposed model and the EM algorithm work quite well in practice.

The burr XII and weibull distributions are the most important and the most widely used distributions for the life time distribution as well as the wealth distribution. Burr XII distribution is mainly used to explain the allocation of wealth and wages among the people of the particular society. And weibull distribution is mostly used in the extreme value theory, failure analysis and the reliability engineering. In this paper, the classical properties of the mixture burr XII weibull distribution have been discussed. The estimation of the parameters and the construction of the information matrix are introduced. The var-cov matrix and the interval estimation of the parameters are also proposed in the paper. Cumulative distribution function, hazard rate, failure rate, inverse hazard function, odd function and the cumulative hazard function, rth moment, moment generating function characteristic function, moments, mean and variance, Renyi and Beta entropies, mean deviation from mean and mean time between failures(MTBF)have also been discussed.

There are several reasons why maintenance managers need to ascertain, from time to time, the reliability profile of their production machines that are subject to constant use. This study furnishes the justifications by analyzing a 12-year maintenance data classified under machine time, downtime, idle time, running time, among others. Markov chain model as well as some reliability models – availability, mean time to failure, mean time between failures, hazard rate (λ) – were used to analyze the bulky data obtained from a soft drink bottling company based in Lagos, Nigeria. Our results suggest that the long run maintenance practice of the organization has caused between 87-94% of the machines/equipment to be in idle state while between 6-13% to be due for retirement. It is our candid opinion that if urgent action is not taken to whittle down the lingering trend the company will get to the brink of collapse. Keywords: Transition matrix, Absorbing state, Catastrophic Failure, Matrix Utilization Factors Nigerian Journal of Technological Research

Engineers, economists, hydrologists, social scientists, and behavioural scientists often deal with data belonging to the unit interval. One of the most common approaches for modeling purposes is the use of unit distributions, beginning with the classical power distribution. A simple way to improve its applicability is proposed by the transmuted scheme. We propose an alternative in this article by slightly modifying this scheme with a logarithmic weighted function, thus creating the log-weighted power distribution. It can also be thought of as a variant of the log-Lindley distribution, and some other derived unit distributions. We investigate its statistical and functional capabilities, and discuss how it distinguishes between power and transmuted power distributions. Among the functions derived from the log-weighted distribution are the cumulative distribution, probability density, hazard rate, and quantile functions. When appropriate, a shape analysis of them is performed to increase the exibility of the proposed modelling. Various properties are investigated, including stochastic ordering (first order), generalized logarithmic moments, incomplete moments, Rényi entropy, order statistics, reliability measures, and a list of new distributions derived from the main one are offered. Subsequently, the estimation of the model parameters is discussed through the maximum likelihood procedure. Then, the proposed distribution is tested on a few data sets to show in what concrete statistical scenarios it may outperform the transmuted power distribution.

Influence of Combined Cyclic Fatigue and Torsional Stress on the Fracture Point of Nickel-Titanium Rotary Instruments

A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative semi-line of a phase-type distribution. The density function is defined and the main measures associated, such as the reliability function, hazard rate, cumulative hazard rate and the characteristic function, are also worked out. This new class of distributions enables us to decrease the number of parameters in the estimate when inference is considered. Additionally, the likelihood distribution is built to estimate the model parameters by maximum likelihood. Several applications considering Resistive Random Access Memories compare the adjustment when phase type distributions and one cut-point phase-type distributions are considered. The developed methodology has been computationally implemented in R-cran.

Brittle Fracture of Rounded V-Notches in Isostatic Graphite under Static Multiaxial Loading

This paper provides a survival analysis of End Stage Renal Disease (ESRD) under Kaplan-Meier Estimates and Weibull Distribution. The data were obtained from the records of V. L. MakabaliMemorial Hospital with respect to time t (patient's age), covariates such as developed secondary disease (Pulmonary Congestion and Cardiovascular Disease), gender, and the event of interest: the death of ESRD patients. Survival and hazard rates were estimated using NCSS for Weibull Distribution and SPSS for Kaplan-Meier Estimates. These lead to the same conclusion that hazard rate increases and survival rate decreases of ESRD patient diagnosed with Pulmonary Congestion, Cardiovascular Disease and both diseases with respect to time. It also shows that female patients have a greater risk of death compared to males. The probability risk was given the equation R = 1 — e-H(t) where e-H(t) is the survival function, H(t) the cumulative hazard function which was created using Cox-Regression.

A viable explanation to the reliability bathtub curve is presented wherein failure rate is governed by a physical process of component strength decay over time due to a distributed applied stress. In this proposed alternate approach to studying reliability, interdisciplinary boundaries are crossed as links between the fields of reliability engineering, quality control and fracture mechanics are achieved. Further, this physical explanation of hazard rate rejects the traditional and strictly statistical viewpoint that the bathtub curve can be compartmentalized into early, constant and wear-out failures, and instead supports the more recent claim that most failures are due to wear-out. The paper intends to break from strictly statistical reliability approaches and to provide a foundation for the development and application of reliability techniques based on physical science theories. >

In this article, we have introduced a new probability distribution having three parameters using half Cauchy family of distribution named half Cauchy extended exponential distribution. The statistical properties and characteristics of the proposed distribution like the hazard rate function (HRF), cumulative hazard function, and the probability density function (PDF), and the cumulative distribution function (CDF), quantile function and the skewness, kurtosis are provided. The parameters of the proposed distribution are estimated using the Cramer-Von-Mises (CVM) least-square estimation (LSE), and maximum likelihood estimators (MLE) methods. A real data set is analyzed to test the goodness-of-fit of the proposed distribution. It is found that the half Cauchy extended exponential distribution performed well as compared to some competing distributions.

Centrifuge model tests were performed to investigate the torsional behavior of a well-instrumented model pile jacked into loose and dense sand. The whole process of pile jacking, torsional loading, and pile extraction was conducted in-flight at 40g using a four-axis robotic manipulator. The torsional response at the pile head, distributions of torque and shaft friction along the pile shaft, torsional load transfer, and loading rate effects were studied. The shaft resistances along the pile during torsional loading, compression loading, and tension loading were compared. The shear stress – local pile movement curves obtained from the present torsional load tests were found to be approximately hyperbolic and similar to those obtained from axial load tests reported in the literature. The torsional shear stress distribution along the pile shaft was influenced by stress degradation effects, particularly in the loose sand. A criterion was proposed to define pile failure under torsional loading. Torsional loading rates in the range of 1–8°/s had little effect on the torsional resistance of the pile. Depending on the initial state of the soil around the pile, the shaft resistance under torsional loading may be greater than that under axial loading when the horizontal stress is larger than the vertical stress, but smaller when the horizontal stress is smaller than the vertical stress.Key words: centrifuge modeling, compression test, loading rate, load transfer, pile foundations, tension test, torsional test.

<h3>Introduction</h3> Primary PCI studies report 3-year mortality rates of 6–7%, but typically lack external validity or are from historical cohorts. To date, no long-term outcome study has accounted for factors other than primary PCI and variables identified at baseline. This is important because long-term survival is more likely to be influenced by factors not associated with the underlying disease or its early management. In the United Kingdom, continuous whole country PCI data are collected through the British Cardiovascular Intervention Society registry and deaths via the Office for National Statistics, providing a unique opportunity to undertake large scale phenotype and intervention-specific research. In order to address the limitations of previous studies, we utilised the UK national cardiovascular and population databases to report relative survival (RS) and excess mortality after PPCI. <h3>Methods</h3> All individuals in England and Wales with STEMI who received PPCI between 1^st January 2005 and 31^st December 2010 were matched by age, sex, year of procedure and country to English and Welsh population data. Estimates of cumulative relative survival rates (RSRs) and hazard rates were used to calculate expected survival, observed all-cause mortality rate ratios (MRR) and excess mortality rate ratios (EMRR). Crude RS was estimated using the Ederer II method for the whole cohort and cumulative RS estimated by age, sex and biennial year of procedure. <h3>Results</h3> There was a total of 50,181 STEMI treated by PPCI from 109 hospitals, (mean age (SD) 63.2 (13.1) years, 25.9% female, (total time at risk 94997.5 person years). 6 month, 1 and 5 year RSRs were 93.1%, 92.6% and 90.9% and approached the background rate for patients &lt;55 years (Figure 1 a and b). There was a temporal trend towards better outcomes (Figure 2). Excess mortality was evident for females and the elderly (Table 1). <h3>Conclusions</h3> Survival is excellent for young STEMI who receive PPCI. This study highlights long term excess mortality in the elderly and females who could be further stratified for existing and novel therapies to improve cardiovascular outcomes. Relative survival is an accurate, powerful and underused tool that may help identify opportunities to improve longer term cardiovascular outcomes.

The significance of weld imperfections and surface peening on fatigue crack propagation life of butt-welded joints

Improvement in surface fatigue life of hardened gears by high-intensity shot peening: Townsend, D. P. NASA Technical Memorandum NASA TM-105678 1992 8 pp

This paper presents a preventive maintenance policy for wind turbines considering three effects of wind speed: accelerating hazard rate, restricting maintenance implementation, and affecting downtime cost. The effect on the hazard rate is described by a proportional hazards model. The restriction on maintenance actions results in the elongation of maintenance duration. The downtime cost is evaluated based on the power output curve model. Three failure types (i.e., catastrophic failure, critical failure, and minor failure) and multiple maintenance actions (i.e., preventive and corrective replacements, preventive and corrective general repairs, and minimal repair) are integrated into the policy. The objective is to determine the optimal maintenance policy that minimizes the long‐run average cost rate. The optimization problem is formulated and solved in the semi‐Markov decision process (SMDP) framework. A practical example is provided to illustrate the proposed method. The comparison with other policies shows the superiority of the proposed policy as well as the significance of the three effects of wind speed in maintenance decision‐making.