Optimal extended warranty length with limited number of repairs in the warranty period

Inherently, the survival function of a distribution converges to zero as time approaches infinity. The medical interpretation of this definition is that all the patient populations are susceptible ...

The Marshall–Olkin generalized defective Gompertz distribution for surviving fraction modeling

We consider in this paper a parallel system consisting of $$\eta $$
 identical components. Each component works independently of the others and has a Weibull distributed inter-failure time. When the system fails, we assume that the repair maintenance is imperfect according to the Arithmetic Reduction of Age models (
 $$ARA_{m}$$
 ) proposed by Doyen and Gaudoin. The purpose of this paper is to generate a simulated failure data of the whole system in order to forecast the behavior of the failure process. Besides, we estimate the maintenance efficiency and the reliability parameters of an imperfect repair following $$ARA_{m}$$
 models using maximum likelihood estimation method. Our method is tested with several data sets available from related sources. The real data set corresponds to the time between failures of a compressor which is tested by Likelihood Ratio Test (LR). An analysis of the importance and the effect of the memory order of imperfect repair classes (
 $$ARA_{m}$$
 ) will be discussed using LR test.

Reliability parameters estimation for parallel systems under imperfect repair

The reliability of repairable systems is important for many engineering applications such as warranty forecasting, maintenance strategies, and durability, among others. A generalized renewal process (GRP) approach, considering the effectiveness of repairs, is commonly used, modeling the concepts of minimal repair, perfect repair, and general repair. The effect of the latter is between the effects of a minimal and a perfect repair. The GRP models the sequence of recurrent failure/repair events for repairable systems by solving the so-called g-renewal equation, which has no analytical solution. This paper proposes a data-driven numerical estimation of the expected number of failures (ENF) for the GRP model without solving the complicated g-renewal equation directly. Instead, it uses an empirical relationship among the cumulative intensity function (CIF) of the GRP, ordinary renewal process (ORP), and nonhomogeneous Poisson process (NHPP). The ORP and NHPP are limiting cases of the generalized renewal process. For practical reasons, it is common to observe only a few units of a repairable system population for only a short time. Using the observed data, the proposed approach creates a reliability metamodel of a renewal process, which is then used to predict the expected number of failures, and assess the average effectiveness of each repair. This increases the usefulness of the method for many practical reliability problems where the collection of a large amount of data is not possible or economical. The good accuracy of the proposed approach is demonstrated with three examples using simulated data, and a real-life example of locomotive braking grids using actual data.

Numerical Estimation of Expected Number of Failures for Repairable Systems using a Generalized Renewal Process Model

Exponentiated Generalized Weibull distribution is a probability
distribution which generalizes the Weibull distribution introducing two more
shapes parameters to best adjust the non-monotonic shape. The parameters of the
new probability distribution function are estimated by the maximum likelihood
method under progressive type II censored data via expectation maximization
algorithm.

/pdf/maximum-likelihood-estimation-of-the-parameters-of-da93rqyxuo.pdf

Maximum Likelihood Estimation of the Parameters of Exponentiated Generalized Weibull Based on Progressive Type II Censored Data

Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.

/pdf/parameter-estimations-for-some-modifications-of-the-weibull-43a6u04ko0.pdf

Soumaya Ghnimi

Papers

Parameter Estimations for Some Modifications of the Weibull Distribution

Reliability parameters estimation for parallel systems under imperfect repair