Age replacement policy: a multi-attribute value model

The classical optimal maintenance model associated with the age replacement policy is a cost model. The effectiveness of preventive maintenance should be evaluated from multiple aspects, which reflect the main maintenance objectives. The cost model just reflects one of the objectives. This paper provides a multiple attribute value model. Four attributes are considered. They are cost, availability, reliability and lifetime. The performance measures associated with reliability and lifetime objectives are first developed. The overall performance is represented by the overall value. The model is illustrated by a numerical example.     

Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data

Estimation of the Weibull shape parameter is important in reliability engineering. However, commonly used methods such as the maximum likelihood estimation (MLE) and the least squares estimation (LSE) are known to be biased. Bias correction methods for MLE have been studied in the literature. This paper investigates the methods for bias correction when model parameters are estimated with LSE based on probability plot. Weibull probability plot is very simple and commonly used by practitioners and hence such a study is useful. The bias of the LS shape parameter estimator for multiple censored data is also examined. It is found that the bias can be modeled as the function of the sample size and the censoring level, and is mainly dependent on the latter. A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data. Simulation results are also presented. The bias correction methods proposed are very easy to use and they can typically reduce the bias of the LSE of the shape parameter to less than half percent.     

A new approach to MLE of Weibull distribution with interval data

We study the two-parameter maximum likelihood estimation (MLE) problem for the Weibull distribution with consideration of interval data. Without interval data, the problem can be solved easily by regular MLE methods because the restricted MLE of the scale parameter β for a given shape parameter α has an analytical form, thus α can be efficiently solved from its profile score function by traditional numerical methods. In the presence of interval data, however, the analytical form for the restricted MLE of β does not exist and directly applying regular MLE methods could be less efficient and effective. To improve efficiency and effectiveness in handling interval data in the MLE problem, a new approach is developed in this paper. The new approach combines the Weibull-to-exponential transformation technique and the equivalent failure and lifetime technique. The concept of equivalence is developed to estimate exponential failure rates from uncertain data including interval data. Since the definition of equivalent failures and lifetimes follows EM algorithms, convergence of failure rate estimation by applying equivalent failures and lifetimes is mathematically proved. The new approach is demonstrated and validated through two published examples, and its performance in different conditions is studied by Monte Carlo simulations. It indicates that the profile score function for α has only one maximum in most cases. Such good characteristic enables efficient search for the optimal value of α.     

Weighted least‐squares estimation of the shape parameter of the Weibull distribution

The purpose of this paper is to propose the weighted least‐squares procedure for estimating the shape parameter of the Weibull distribution. Results from simulation studies illustrate the mean‐squared error of the weighted least‐squares estimator is smaller than competing procedures in all cases considered. Copyright © 2001 John Wiley & Sons, Ltd.     

A study of Weibull shape parameter: Properties and significance

The two-parameter Weibull distribution has been widely used for modelling the lifetime of products and components. In this paper we study the effect of the shape parameter on the failure rate and three variables of importance in the context of maintenance and reliability improvement. These variables are (i) time to failure, (ii) age at replacement based on risk and (iii) residual life. We propose a classification scheme for the distribution based on the shape parameter and discuss the application of the results.     

A study of two estimation approaches for parameters of Weibull distribution based on WPP

Least-squares estimation (LSE) based on Weibull probability plot (WPP) is the most basic method for estimating the Weibull parameters. The common procedure of this method is using the least-squares regression of Y on X, i.e. minimizing the sum of squares of the vertical residuals, to fit a straight line to the data points on WPP and then calculate the LS estimators. This method is known to be biased. In the existing literature the least-squares regression of X on Y, i.e. minimizing the sum of squares of the horizontal residuals, has been used by the Weibull researchers. This motivated us to carry out this comparison between the estimators of the two LS regression methods using intensive Monte Carlo simulations. Both complete and censored data are examined. Surprisingly, the result shows that LS Y on X performs better for small, complete samples, while the LS X on Y performs better in other cases in view of bias of the estimators. The two methods are also compared in terms of other model statistics. In general, when the shape parameter is less than one, LS Y on X provides a better model; otherwise, LS X on Y tends to be better.     

Optimal maintenance strategy for Technology‐enhanced classrooms: a case study

The purpose of the study was to collect data and evaluate an age‐based bulb replacement policy for projectors used in Technology‐enhanced classrooms in a university campus.The Office of Information Technology (OIT) had instituted a policy to replace bulbs in these projectors after either failure or 1800h of operation without failure. However, databases maintained by OIT included the time to bulb failure, the average number of times the bulbs were turned on and off per week, and the number of thermal events. Modeling the failure data with a Weibull proportional hazards model revealed that probability of bulb failure was a function of the number of hours a bulb was used and the frequency at which it was turned on and off. Combining this information with a cost model led to the recommendation for an improved condition‐based replacement policy. Copyright © 2009 John Wiley & Sons, Ltd.     

On the validity of the Weibull failure model for brittle particles

The Weibull theory of material strength and fracture assumes that the Weibull modulus m is a material parameter, which does not depend on shape and size of the loaded object. Based on large data sets from single-particle fracture experiments with brittle materials (glass, clinker cement, limestone), the authors show that the Weibull modulus of nearly spherical particles seems to decrease with increasing particle diameter. A possible explanation is that the inner structure of the particles depends on their size so that small particles are much stronger than large ones. Received: 9 December 1999     

Estimation of mixed Weibull distribution parameters using the SCEM-UA algorithm: Application and comparison with MLE in automotive reliability analysis

The shuffled complex-evolution metropolis algorithm (SCEM-UA) is used to estimate mixed Weibull distribution parameters in automotive reliability analysis. The results are compared with maximum likelihood estimation (MLE) results. The comparison shows that, in the examples given, SCEM-UA can deliver more accurate results than MLE overall.     

The effect of the threshold stress on the determination of the Weibull parameters in probabilistic failure analysis

In the analysis of brittle materials and components the probability of failure is commonly modelled using a two-parameter Weibull distribution. Occasionally, a three-parameter model is used when the material shows significant threshold behaviour. In this paper two methods for determining the three-parameter constants are discussed. Two theoretical two- and three-parameter distributions are then analysed to examine the number of samples needed to determine the parameters accurately. The two-parameter models are the best fits of the three-parameter models and their failure distributions are very similar to the three-parameter distributions. It is concluded that far more specimens need to be tested than is usually the case to be confident that the correct distribution has been found.     

Estimation of the Shape Parameter of the Weibull Distribution Using Linear Regression Methods: Non‐Censored Samples

The two‐parameter Weibull distribution is one of the most widely applied probability distributions, particularly in reliability and lifetime modelings. Correct estimation of the shape parameter of the Weibull distribution plays a central role in these areas of statistical analysis. Many different methods can be used to estimate this parameter, most of which utilize regression methods. In this paper, we presented various regression methods for estimating the Weibull shape parameter and an experimental study using classical regression methods to compare the results of the methods. A complete list of the parameter estimators considered in this study is as follows: ordinary least squares (OLS), weighted least squares (WLS, Bergman, F&T, Lu), non‐parametric robust Theil's (Theil) and weighted Theil's (WeTheil), robust Winsorized least squares (WinLS), and M‐estimators (Huber, Andrew, Tukey, Cauchy, Welsch, Hampel and Logistic). Estimator performances were compared based on bias and mean square error criteria using Monte‐Carlo simulations. The simulation results demonstrated that for small, complete, and non‐outlier data sets, the Bergman, F&T, and Lu estimators are more efficient than the others. When the data set contains one or two outliers in the X direction, Theil is the most efficient estimator. Copyright © 2012 John Wiley & Sons, Ltd.     

The effect of melt quality and quenching temperature on the Weibull distribution of tensile properties in aluminium alloys

In this study, the effect of melt quality and quenching temperature on the mechanical properties of 2024, 6063 and 7075 was investigated. The alloys were produced by Strain Induced Melt Activated (SIMA) method. T6 heat treatment was carried out by quenching in two different temperatures: 20 °C and 80 °C. Scanning electron microscope analyses were carried out on the fracture surfaces. In addition, reduced pressure tests were carried out to correlate the mechanical test results with metal quality. The results were analysed by Weibull statistics. It was found that samples quenched at 80 °C showed better mechanical properties and there was a good correlation between bifilm index and Weibull distributions.     

Availability and cost-centered preventive maintenance scheduling of continuous operating series systems using multi-objective genetic algorithm: A case study

This article presents a multi-objective (maximization of availability and minimization of maintenance cost) preventive maintenance (PM) scheduling model for a continuous operating series system (COSS) which do not provide an off-working period for PM. The objective functions are optimized by using a Multi-Objective Genetic Algorithm (MOGA). The effectiveness of the model is demonstrated through a coal-fired boiler-tube. The case study shows that the model can improve the availability along with profound reduction of the maintenance cost, i.e., increases the profit of the plant.     

The epidemiology and cost of falls requiring hospitalisation in children in Western Australia: a study using linked administrative data

OBJECTIVE: The aim of this study was to examine the epidemiology and health system cost of children's falls resulting in hospitalisation in 2003 in Western Australia. METHODS: The Injury Cost Database was used to identify children who were admitted to hospital with a falls related injury. Adjusted incidence rate ratios (IRR) of hospitalisation were modelled using Poisson regression. In-patient hospital costs were assigned using the published DRG costs for Western Australia. These costs were then extrapolated to health system costs based on previously published relative proportions. RESULTS: When adjusted for other covariates in the model males had a 53% higher incidence of falls requiring hospitalisation compared with females. Aboriginal children had a 36% higher incidence compared with their non-Aboriginal counterparts, and the incidence of falls reduced with increasing age. The total cost of in-patient hospitalisation associated with children's falls in Western Australia was A$4,554,000 with an average cost of A$1876 per case. In children aged 0-4 years and 10-14 years the highest cost resulted from falls on the flat (slips and trips). However, in children aged 5-9 years injuries resulting from falls from playground equipment resulted in both the highest cost group (A$539,000) and the highest cost per case (A$1917). The total cost to the health system of children's falls in Western Australia in 2003 were estimated to be A$21.5 million, with the total cost to the community estimated at A$108.5 million. CONCLUSION: Children's falls impose a considerable burden and cost to both the health care system and the community. This study has provided information on where the burden of risk and the majority of costs lie, namely males, Aboriginal children and for children aged 5-9 years, unlike their younger and older peers, playground equipment.     

Analyzing the effect of introducing a kurtosis parameter in Gaussian Bayesian networks

Gaussian Bayesian networks are graphical models that represent the dependence structure of a multivariate normal random variable with a directed acyclic graph (DAG). In Gaussian Bayesian networks the output is usually the conditional distribution of some unknown variables of interest given a set of evidential nodes whose values are known. The problem of uncertainty about the assumption of normality is very common in applications. Thus a sensitivity analysis of the non-normality effect in our conclusions could be necessary. The aspect of non-normality to be considered is the tail behavior. In this line, the multivariate exponential power distribution is a family depending on a kurtosis parameter that goes from a leptokurtic to a platykurtic distribution with the normal as a mesokurtic distribution. Therefore a more general model can be considered using the multivariate exponential power distribution to describe the joint distribution of a Bayesian network, with a kurtosis parameter reflecting deviations from the normal distribution. The sensitivity of the conclusions to this perturbation is analyzed using the Kullback-Leibler divergence measure that provides an interesting formula to evaluate the effect.     

Estimations of parameters in Pareto reliability model in the presence of masked data

Estimations of parameters included in the individual distributions of the life times of system components in a series system are considered in this paper based on masked system life test data. We consider a series system of two independent components each has a Pareto distributed lifetime. The maximum likelihood and Bayes estimators for the parameters and the values of the reliability of the system's components at a specific time are obtained. Symmetrical triangular prior distributions are assumed for the unknown parameters to be estimated in obtaining the Bayes estimators of these parameters. Large simulation studies are done in order: (i) explain how one can utilize the theoretical results obtained; (ii) compare the maximum likelihood and Bayes estimates obtained of the underlying parameters; and (iii) study the influence of the masking level and the sample size on the accuracy of the estimates obtained.     

Exploring the social dimensions and complexity of cumulative impacts: a case study of forest policy changes in Western Australia

Social impacts resulting from policy changes and other interventions interact and aggregate, and are influenced by additional interventions and exogenous factors, leading to cumulative social impacts. We explored these complex impacts through a case study of forest policy changes introduced in the state of Western Australia between 1999 and 2004. In this process, we both drew on and modified the recently-proposed Cumulative Effects Assessment and Management (CEAM) framework, to improve its utility as an analytical tool for exploring cumulative social impacts that arise from policy changes in natural resource sectors. Our findings highlight the complexity of the pathways that lead to social impacts and the significant influence of individuals' responses. The findings also demonstrate the importance of considering cumulative impacts - negative and positive, and intended and unintended – when designing and implementing mitigation strategies, emphasizing the value of adaptive management approaches. Our results suggest that the CEAM framework, appropriately contextualized and adapted, is relevant to the assessment of social impacts associated with interventions in complex natural resource management cases, and probably more widely.