Abstract: In this paper we will develop a sequential life test approach applied to a modified low alloy-high strength steel part used in highway overpasses in Brazil.We will consider two possible underlying sampling distributions: the Normal and theInverse Weibull models. The minimum life will be considered equal to zero. We will use the two underlying models to analyze a fatigue life test situation, comparing the results obtained from both.Since a major chemical component of this low alloy-high strength steel part has been changed, there is little information available about the possible values that the parameters of the corresponding Normal and Inverse Weibull underlying sampling distributions could have. To estimate the shape and the scale parameters of these two sampling models we will use a maximum likelihood approach for censored failure data. We will also develop a truncation mechanism for the Inverse Weibull and Normal models. We will provide rules to truncate a sequential life testing situation making one of the two possible decisions at the moment of truncation; that is, accept or reject the null hypothesis H0. An example will develop the proposed truncated sequential life testing approach for the Inverse Weibull and Normal models.
Abstract: Constant upgrading of Enterprise Resource Planning
(ERP) systems is necessary, but can cause new defects. This paper
attempts to model the likelihood of defects after completed upgrades
with Weibull defect probability density function (PDF). A case study
is presented analyzing data of recorded defects obtained for one ERP
subsystem. The trends are observed for the value of the parameters
relevant to the proposed statistical Weibull distribution for a given
one year period. As a result, the ability to predict the appearance of
defects after the next upgrade is described.
Abstract: The aim of this paper is to introduce a parametric
distribution model in fatigue life reliability analysis dealing with
variation in material properties. Service loads in terms of responsetime
history signal of Belgian pave were replicated on a multi-axial
spindle coupled road simulator and stress-life method was used to
estimate the fatigue life of automotive stub axle. A PSN curve was
obtained by monotonic tension test and two-parameter Weibull
distribution function was used to acquire the mean life of the
component. A Pearson system was developed to evaluate the fatigue
life reliability by considering stress range intercept and slope of the
PSN curve as random variables. Considering normal distribution of
fatigue strength, it is found that the fatigue life of the stub axle to
have the highest reliability between 10000 – 15000 cycles. Taking
into account the variation of material properties associated with the
size effect, machining and manufacturing conditions, the method
described in this study can be effectively applied in determination of
probability of failure of mass-produced parts.
Abstract: Wind is among the potential energy resources which
can be harnessed to generate wind energy for conversion into
electrical power. Due to the variability of wind speed with time and
height, it becomes difficult to predict the generated wind energy more
optimally. In this paper, an attempt is made to establish a
probabilistic model fitting the wind speed data recorded at
Makambako site in Tanzania. Wind speeds and direction were
respectively measured using anemometer (type AN1) and wind Vane
(type WD1) both supplied by Delta-T-Devices at a measurement
height of 2 m. Wind speeds were then extrapolated for the height of
10 m using power law equation with an exponent of 0.47. Data were
analysed using MINITAB statistical software to show the variability
of wind speeds with time and height, and to determine the underlying
probability model of the extrapolated wind speed data. The results
show that wind speeds at Makambako site vary cyclically over time;
and they conform to the Weibull probability distribution. From these
results, Weibull probability density function can be used to predict
the wind energy.
Abstract: In this paper, Economic Order Quantity (EOQ) based model for non-instantaneous Weibull distribution deteriorating items with power demand pattern is presented. In this model, the holding cost per unit of the item per unit time is assumed to be an increasing linear function of time spent in storage. Here the retailer is allowed a trade-credit offer by the supplier to buy more items. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This model aids in minimizing the total inventory cost by finding the optimal time interval and finding the optimal order quantity. The optimal solution of the model is illustrated with the help of numerical examples. Finally sensitivity analysis and graphical representations are given to demonstrate the model.
Abstract: A two-parameter fatigue model explicitly accounting for the cyclic as well as the mean stress was used to fit static and fatigue data available in literature concerning carbon fiber reinforced composite laminates subjected tension-tension fatigue. The model confirms the strength–life equal rank assumption and predicts reasonably the probability of failure under cyclic loading. The model parameters were found by best fitting procedures and required a minimum of experimental tests.
Abstract: In this paper, a Dynamic Economic Dispatch (DED) model is developed for the system consisting of both thermal generators and wind turbines. The inclusion of a significant amount of wind energy into power systems has resulted in additional constraints on DED to accommodate the intermittent nature of the output. The probability of stochastic wind power based on the Weibull probability density function is included in the model as a constraint; A Here-and-Now Approach. The Environmental Protection Agency-s hourly emission target, which gives the maximum emission during the day, is used as a constraint to reduce the atmospheric pollution. A 69-bus test system with non-smooth cost function is used to illustrate the effectiveness of the proposed model compared with static economic dispatch model with including the wind power.
Abstract: One of the purposes of the robust method of
estimation is to reduce the influence of outliers in the data, on the
estimates. The outliers arise from gross errors or contamination from
distributions with long tails. The trimmed mean is a robust estimate.
This means that it is not sensitive to violation of distributional
assumptions of the data. It is called an adaptive estimate when the
trimming proportion is determined from the data rather than being
fixed a “priori-.
The main objective of this study is to find out the robustness
properties of the adaptive trimmed means in terms of efficiency, high
breakdown point and influence function. Specifically, it seeks to find
out the magnitude of the trimming proportion of the adaptive
trimmed mean which will yield efficient and robust estimates of the
parameter for data which follow a modified Weibull distribution with
parameter λ = 1/2 , where the trimming proportion is determined by a
ratio of two trimmed means defined as the tail length. Secondly, the
asymptotic properties of the tail length and the trimmed means are
also investigated. Finally, a comparison is made on the efficiency of
the adaptive trimmed means in terms of the standard deviation for the
trimming proportions and when these were fixed a “priori".
The asymptotic tail lengths defined as the ratio of two trimmed
means and the asymptotic variances were computed by using the
formulas derived. While the values of the standard deviations for the
derived tail lengths for data of size 40 simulated from a Weibull
distribution were computed for 100 iterations using a computer
program written in Pascal language.
The findings of the study revealed that the tail lengths of the
Weibull distribution increase in magnitudes as the trimming
proportions increase, the measure of the tail length and the adaptive
trimmed mean are asymptotically independent as the number of
observations n becomes very large or approaching infinity, the tail
length is asymptotically distributed as the ratio of two independent
normal random variables, and the asymptotic variances decrease as
the trimming proportions increase. The simulation study revealed
empirically that the standard error of the adaptive trimmed mean
using the ratio of tail lengths is relatively smaller for different values
of trimming proportions than its counterpart when the trimming
proportions were fixed a 'priori'.
Abstract: The paper deals with calculation of the parameters of
ceramic material from a set of destruction tests of ceramic heads of
total hip joint endoprosthesis. The standard way of calculation of the
material parameters consists in carrying out a set of 3 or 4 point
bending tests of specimens cut out from parts of the ceramic material
to be analysed. In case of ceramic heads, it is not possible to cut out
specimens of required dimensions because the heads are too small (if
the cut out specimens were smaller than the normalised ones, the
material parameters derived from them would exhibit higher strength
values than those which the given ceramic material really has). On
that score, a special testing jig was made, in which 40 heads were
destructed. From the measured values of circumferential strains of the
head-s external spherical surface under destruction, the state of stress
in the head under destruction was established using the final elements
method (FEM). From the values obtained, the sought for parameters
of the ceramic material were calculated using Weibull-s weakest-link
theory.
Abstract: The objective of this study is to introduce estimators to the parameters and survival function for Weibull distribution using three different methods, Maximum Likelihood estimation, Standard Bayes estimation and Modified Bayes estimation. We will then compared the three methods using simulation study to find the best one base on MPE and MSE.
Abstract: In order to assess optical fiber reliability in different environmental and stress conditions series of testing are performed simulating overlapping of chemical and mechanical controlled varying factors. Each series of testing may be compared using statistical processing: i.e. Weibull plots. Due to the numerous data to treat, a software application has appeared useful to interpret selected series of experiments in function of envisaged factors. The current paper presents a software application used in the storage, modelling and interpretation of experimental data gathered from optical fibre testing. The present paper strictly deals with the software part of the project (regarding the modelling, storage and processing of user supplied data).
Abstract: Scatter behavior of fatigue life in die-cast AM60B
alloy was investigated. For comparison, those in rolled AM60B alloy
and die-cast A365-T5 aluminum alloy were also studied. Scatter
behavior of pore size was also investigated to discuss dominant
factors for fatigue life scatter in die-cast materials. Three-parameter
Weibull function was suitable to explain the scatter behavior of both
fatigue life and pore size. The scatter of fatigue life in die-cast
AM60B alloy was almost comparable to that in die-cast A365-T5
alloy, while it was significantly large compared to that in the rolled
AM60B alloy. Scatter behavior of pore size observed at fracture
nucleation site on the fracture surface was comparable to that
observed on the specimen cross-section and also to that of fatigue
life. Therefore, the dominant factor for large scatter of fatigue life in
die-cast alloys would be the large scatter of pore size. This
speculation was confirmed by the fracture mechanics fatigue life
prediction, where the pore observed at fatigue crack nucleation site
was assumed as the pre-existing crack.
Abstract: In this paper we will develop further the sequential life test approach presented in a previous article by [1] using an underlying two parameter Inverse Weibull sampling distribution. The location parameter or minimum life will be considered equal to zero. Once again we will provide rules for making one of the three possible decisions as each observation becomes available; that is: accept the null hypothesis H0; reject the null hypothesis H0; or obtain additional information by making another observation. The product being analyzed is a new electronic component. There is little information available about the possible values the parameters of the corresponding Inverse Weibull underlying sampling distribution could have.To estimate the shape and the scale parameters of the underlying Inverse Weibull model we will use a maximum likelihood approach for censored failure data. A new example will further develop the proposed sequential life testing approach.
Abstract: This paper presents the possibilities of using Weibull statistical distribution in modeling the distribution of defects in ERP systems. There follows a case study, which examines helpdesk records of defects that were reported as the result of one ERP subsystem upgrade. The result of the applied modeling is in modeling the reliability of the ERP system from a user perspective with estimated parameters like expected maximum number of defects in one day or predicted minimum of defects between two upgrades. Applied measurement-based analysis framework is proved to be suitable in predicting future states of the reliability of the observed ERP subsystems.
Abstract: In this paper, the test purpose will be to assess
whether or not the accelerated model proposed by Eyring will be able
to translate results for the shape and scale parameters of an
underlying Weibull model, obtained under two accelerating using
conditions, to expected normal using condition results for these
parameters. The product being analyzed is a new type of insulate
fluid, and the accelerating factor is the voltage stresses applied to the
fluid at two different levels (30KV and 40KV). The normal operating
voltage is 25KV. In this case, it was possible to test the insulate fluid
at normal voltage using condition. Both results for the two
parameters of the Weibull model, obtained under normal using
condition and translated from accelerated using conditions to normal
conditions, will be compared to each other to assess the accuracy of
the Eyring model when the accelerating factor is only the voltage
stress.
Abstract: A model is presented to find the optimal design of the
mixed renewable warranty policy for non-repairable Weibull life
products. The optimal design considers the conflict of interests
between the customer and the manufacturer: the customer interests
are longer full rebate coverage period and longer total warranty
coverage period, the manufacturer interests are lower warranty cost
and lower risk. The design factors are full rebate and total warranty
coverage periods. Results showed that mixed policy is better than full
rebate policy in terms of risk and total warranty coverage period in all
of the three bathtub regions. In addition, results showed that linear
policy is better than mixed policy in infant mortality and constant
failure regions while the mixed policy is better than linear policy in
ageing region of the model. Furthermore, the results showed that
using burn-in period for infant mortality products reduces warranty
cost and risk.
Abstract: Using a texture database, a statistical estimation of
spring-back was conducted in this study on the basis of statistical
analysis. Both spring-back in bending deformation and experimental
data related to the crystal orientation show significant dispersion.
Therefore, a probabilistic statistical approach was established for the
proper quantification of these values. Correlation was examined
among the parameters F(x) of spring-back, F(x) of the buildup fraction
to three orientations after 92° bending, and F(x) at an as-received part
on the basis of the three-parameter Weibull distribution. Consequent
spring-back estimation using a texture database yielded excellent
estimates compared with experimental values.
Abstract: Protective relays are components of a protection system
in a power system domain that provides decision making element for
correct protection and fault clearing operations. Failure of the
protection devices may reduce the integrity and reliability of the power
system protection that will impact the overall performance of the
power system. Hence it is imperative for power utilities to assess the
reliability of protective relays to assure it will perform its intended
function without failure. This paper will discuss the application of
reliability analysis using statistical method called Life Data Analysis
in Tenaga Nasional Berhad (TNB), a government linked power utility
company in Malaysia, namely Transmission Division, to assess and
evaluate the reliability of numerical overcurrent protective relays from
two different manufacturers.
Abstract: In this paper we will develop further the sequential
life test approach presented in a previous article by [1] using an
underlying two parameter Weibull sampling distribution. The
minimum life will be considered equal to zero. We will again provide
rules for making one of the three possible decisions as each
observation becomes available; that is: accept the null hypothesis H0;
reject the null hypothesis H0; or obtain additional information by
making another observation. The product being analyzed is a new
type of a low alloy-high strength steel product. To estimate the shape
and the scale parameters of the underlying Weibull model we will use
a maximum likelihood approach for censored failure data. A new
example will further develop the proposed sequential life testing
approach.
Abstract: In this paper we propose a mixture of two different
distributions such as Exponential-Gamma, Exponential-Weibull and
Gamma-Weibull to model heterogeneous survival data. Various
properties of the proposed mixture of two different distributions are
discussed. Maximum likelihood estimations of the parameters are
obtained by using the EM algorithm. Illustrative example based on
real data are also given.