Failure Time Research Articles

Imperfect maintenance modelling and estimation for interval-censored data

The paper proposes a new maintenance model for a repairable system. The system is inspected at deterministic times. If a failure occurs between two successive inspections, a minimal repair is performed. At inspection times, two types of maintenance actions can be performed. The first originality of the paper is to consider that the choice between these two types of maintenance depends on the fact that there has been a failure or not since the previous inspection. If no failure has occurred since the last inspection, the maintenance, simply denoted PM, corresponds to a basic preventive maintenance action, whose effect is planned by the initial maintenance plan. If at least one failure has occurred since the last inspection, the maintenance, denoted PCM, includes both the preventive action planned by the initial maintenance plan, and a specific corrective action which aims to fix the defects that have happened since the last inspection. Both types of maintenances are assumed to be imperfect, of the ARA (Arithmetic Reduction of Age) type, with different parameters. Moreover, the paper derives several statistical inference methods for this model. The usual case of complete data is first considered. The second originality of the paper is to analyse interval-censored data in this imperfect maintenance framework. This situation holds when failure times are not observed, and the only information is the fact that failures have occurred or not between two inspections. The quality of the proposed methods is assessed on simulated data. Finally, a real dataset from a gas transmission system operator is provided and analysed with the proposed approach.

How to Perform a Statistical Analysis of Non-Destructive Degradation Data to Study Crack Growth in Wind Blades as a Function of the Number of Cycles

Objective: The aim of this paper is to show the application of the Exponential Regression Model to study the failure time of a system over time. The data was taken from the paper (Wang et al., 2021). Theoretical framework: The linear regression model, where the response is associated with the explanatory variables by means of a linear model, is the best known. To formulate the model, it is necessary to specify a deterministic component and a random (stochastic) component. The exponential model should be used when it is assumed that risk is constant over time. Once the model has been specified, its parameters are estimated. In the absence of normal errors and especially in the presence of censoring, a more appropriate option is the maximum likelihood method. As the equations are non-linear in their parameters and do not have an analytical solution, it is necessary to use the Newton-Raphson numerical method. Due to the simplicity of the exponential regression model, few situations in practice are adequately adjusted by this model. The Weibull regression model is widely used in survival analysis (Bastos Lyra et al., 2008) Method: Data taken from the article (Wang et al., 2021) e foi utilizado a Regressão Exponencial para modelar os dados. Final Considerations: This result indicates that Exponential Regression is a very viable option when the aim is to monitor the number of cracks as a function of time to check whether a system will fail. In this specific Case Study, it is clear that one of the blades is better than the others and that there are some Probability Distribution models that are suitable for the model. Implications of the research: The use cases of Exponential Regression are more restricted in the scientific literature and because of this, this case study is interesting to show that this model is effective for treating data in the area of reliability. Originality/value: Despite being a well-known statistical tool, Exponential Regression has a specific application in monitoring the number of cracks over time in a system.

Improving estimation efficiency of case-cohort studies with interval-censored failure time data.

The case-cohort design is a commonly used cost-effective sampling strategy for large cohort studies, where some covariates are expensive to measure or obtain. In this paper, we consider regression analysis under a case-cohort study with interval-censored failure time data, where the failure time is only known to fall within an interval instead of being exactly observed. A common approach to analyzing data from a case-cohort study is the inverse probability weighting approach, where only subjects in the case-cohort sample are used in estimation, and the subjects are weighted based on the probability of inclusion into the case-cohort sample. This approach, though consistent, is generally inefficient as it does not incorporate information outside the case-cohort sample. To improve efficiency, we first develop a sieve maximum weighted likelihood estimator under the Cox model based on the case-cohort sample and then propose a procedure to update this estimator by using information in the full cohort. We show that the update estimator is consistent, asymptotically normal, and at least as efficient asthe original estimator. The proposed method can flexibly incorporate auxiliary variables to improve estimation efficiency. A weighted bootstrap procedure is employed for variance estimation. Simulation results indicate that the proposed method works well in practical situations. An application to a Phase 3 HIV vaccine efficacy trial is provided for illustration.

Assessment of loss of life owing to dam-failure flooding considering population distribution and evacuation

Dam failures pose a serious threat to the safety of downstream populations. Scientifically assessing loss of life (LOL) from dam-failure flooding contributes to the emergency response. Population distribution varies spatially and temporally even within a day, and has different information dissemination and response speeds, which impacts the chances of safe evacuation. This study established an LOL assessment model that considers the initial population distribution and population evacuation process. Shared bike big data and other multi-source data were used to identify daily population activity. The evacuation process includes receiving warnings, responses, and horizontal or vertical evacuation choices, and the evacuation results were then evaluated. This model was applied to a dam in China. During nighttime, commuting, and working hours, the issuance of warnings 214 min, 137 min, and 0 min prior to dam failure, respectively, significantly mitigated LOL. Under the same communication and response speeds, the commuting period poses the highest risk of LOL. Assessments of LOL due to dam failure flooding need to consider the impact of the timing of dam failure and population distribution. The model used in this study proposes varying effective early warning times based on the time of dam failure occurrence, which can contribute to effective dam risk management, helping prevent personnel loss.

Orthostatic Hypotension and Risk of Mild Cognitive Impairment and Dementia in Parkinson's Disease.

Orthostatic hypotension (OH) is a common condition in Parkinson's disease (PD) with a possible link to cognitive decline. The aim was to explore the association between OH and PD-associated mild cognitive impairment (PD-MCI) and dementia (PDD) over 9 years in a population-based incident PD cohort. We prospectively followed up patients from PD diagnosis with serial blood pressure measurements, clinical examinations, and neuropsychological assessments. We defined OH using (1) consensus-based criteria and (2) clinically significant OH by mean arterial pressure (MAP) in standing position ≤75 mmHg. PD-MCI and PDD were diagnosed according to acknowledged criteria. We applied generalized estimating equations models to investigate associations between OH measurements and cognitive impairment over time. Weibull accelerated failure time regression models were used to study if early OH (≤3 years of PD diagnosis) accelerates the time to incident PD-MCI and PDD. Of 186 enrolled patients, consensus-based OH affected 68.8%, clinically significant OH 33.9%, PD-MCI 60.8%, and PDD 31.2%. Consensus-based OH was associated with PD-MCI (odds ratio [OR]: 2.04, 95% confidence interval: 1.44-2.90, P < 0.001), whereas clinically significant OH was associated with both PD-MCI (OR: 1.95, 1.11-3.43, P = 0.020) and PDD (OR: 3.66, 1.95-6.86, P < 0.001). Early clinically significant OH, but not early consensus-based OH, reduced time to incident PD-MCI by 54% (P = 0.021) and time to PDD by 44% (P = 0.003) independently of potential confounders, including supine hypertension and cardiovascular disease. MAP in standing position emerged as a stronger predictor of cognitive decline than OH determined using consensus-based criteria. These findings have implications for both research and clinical practice.

Experimental investigations on the behaviour of structural-sized wood-CFRP composite beams in local fire

AbstractThe study involved combustion of 24 structural-sized beams under three-point bending subjected to substantial loading prior to ignition, reaching 90% of characteristic load-carrying capacity. A localised fire exposure zone was established proximal to the region experiencing the highest bending moment. The specimens were categorised into two groups: the first consisted of tituted by glued-laminated timber (B), and the second comprised wood-CFRP (carbon fibre reinforced polymer) composite (BW). Initial measurements encompassed pre-ignition static deflection and load. Subsequently, the specimens underwent controlled combustion, during which parameters including burning duration and deflection up to failure, were documented. Following cooling with sand, two cross-sectional slices were extracted from each fractured beam, enabling to find vector-based contours of the remaining cross-section. The charring rate and the approximate heat flux density for each test were determined, enabling a direct comparison of the results. A statistically significant number of specimens was examined, facilitating a comparative analysis between reinforced and unreinforced beams concerning failure time and form. Incorporating CFRP tapes among wooden constituents was found to increase the fire resistance of the structure, however, the thickness of the wooden material enveloping the CFRP composite emerges as a pivotal determinant. This issue needs thorough testing under standard fire in the future. Nevertheless, the fact is that adding CFRP tapes engenders a distinct form of beam collapse, transitioning from instantaneous cracking in B-beams to ductile failure in BW-beams.

Association between cytokines, nitric oxide, hemodynamic and microcirculation in a porcine model of sepsis

Systemic inflammation and hemodynamic or microvascular alterations are a hallmark of sepsis and play a role in organs hypoperfusion and dysfunction. Pimobendan, an inodilator agent, could be an interesting option for inotropic support and microcirculation preservation during shock. The objectives of this study were to evaluate effect of pimobendan on cytokine and nitric oxide (NO) release and investigate whether changes of macro and microcirculation parameters are associated with the release of cytokines and NO in pigs sepsis model. After circulatory failure, induced by intravenous inoculation of live Pseudomonas aeruginosa, eight animals were treated with pimobendan and eight with placebo.Pimobendan did not affect cytokines secretion (TNF-α, IL-6 and IL-10), but decreased time-dependently NO release. Data of macro and microcirculation parameters, NO and TNF- α recorded at the time of circulatory failure (Thypotension) and the time maximum of production cytokines was used for analyses. A positive correlation was observed between TNF-α and cardiac index (r = 0.55, p = 0.03) and a negative with systemic vascular resistance (r = −0.52, p = 0.04). Positive correlations were seen both between IL-10, 30 min after resuscitation (T30min), and systolic arterial pressure (r = 0.57, p = 0.03) and cardiac index (r = 0.67, p = 0.01), and also between IL-6, taken 2 h after resuscitation and systolic arterial pressure (r = 0.53, p = 0.04). Negative correlations were found between IL-10 and lactate, measured resuscitation time (r = −0.58, p = 0.03). Regarding microcirculation parameters, we observed a positive correlation between IL-6 and IL-10 with the microvascular flow index (r = 0.52, p = 0.05; r = 0.84, p = 0.0003) and a negative correlation with the heterogeneity index with TNF-α and IL-10 (r = −0.51, p = 0.05; r = −0.74, p = 0.003) respectively. NO derivatives showed a positive correlation with temperature gradient (r = 0.54, p = 0.04).Pimobendan did not show anti-inflammatory effects in cytokines release. Our results also, suggest changes of macro- and microcirculation are associated mainly with low levels of IL-10 in sepsis.

A hybrid reliability assessment method based on health index construction and reliability modeling for rolling bearing

AbstractThe assessment of rolling bearing reliability is vital for ensuring mechanical operational safety and minimizing maintenance costs. Due to the difficulty in obtaining data on the performance degradation and failure time of rolling bearings, traditional methods for reliability assessment are challenged. This paper introduces a novel hybrid method for the reliability assessment of rolling bearings, combining the convolutional neural network (CNN)‐convolutional block attention module (CBAM)‐ bidirectional long short‐term memory (BiLSTM) network with the Wiener process. The approach comprises three distinct stages: Initially, it involves acquiring two‐dimensional time‐frequency representations of bearings at various operational phases using Continuous Wavelet Transform. Subsequently, the CNN‐CBAM‐BiLSTM network is employed to establish health index (HI) for the bearings and to facilitate the extraction of deep features, serving as input for the Wiener process. The final stage applies the Wiener process to evaluate the bearings’ reliability, characterizing the HI and quantifying uncertainties. The experiment is performed on bearing degradation data and the results indicate the effectiveness and superiority of the proposed hybrid method.

Synergistic effects of graphene oxide, steel wire mesh and fibers on the impact resistance of preplaced aggregate concrete

Graphene Oxide (GO) has become a focal point of interest in civil engineering due to its exceptional mechanical and functional properties, making it a novel and promising carbon-based nanomaterial. However, the improvement in impact resistance of fibrous concrete by incorporating GO has not been explored until now. The novelty of this research is rooted in its pioneering analysis of the impact resistance of preplaced aggregate fibrous concrete, achieved through the combined incorporation of GO and steel wire mesh (SWM). This study uniquely investigates the effects of three different dosages of GO (0.1 %, 0.15 %, and 0.2 %) and three variations in the diameter of the steel wire mesh (50 mm, 100 mm, and 150 mm), alongside a fixed dosage of 3 % for steel fibers. Thirty-two distinct mixtures were prepared, with the steel wire mesh strategically placed at the midpoint of the specimen depth in each case. The specimens underwent drop-weight impact testing, with investigations conducted into their compressive strength, impact numbers related to cracking and failure, ductility index, and failure mode. The specimens incorporating a 0.2 % GO dosage with a 150 mm diameter of SWM displayed the highest observed cracking and failure impact numbers compared to those with 50 mm and 100 mm diameters of SWM. The observed increments ranged from 1.07 to 1.18 times for cracking and from 1.38 to 2.45 times for failure, compared to specimens containing 0.2 % GO without SWM. The identical specimens demonstrated the highest ductility values, ranging from 9.34 to 10.61. It is crucial to emphasize that adding GO does not induce an evolution from brittle to ductile failure of the specimen under impact loading, unlike the effect observed with steel wire mesh and steel fibre.

HIV-1 subtype-specific drug resistance on dolutegravir-based antiretroviral therapy: protocol for a multicentre study (DTG RESIST)

IntroductionHIV drug resistance poses a challenge to the United Nation’s goal of ending the HIV/AIDS epidemic. The integrase strand transfer inhibitor (InSTI) dolutegravir, which has a higher resistance barrier, was...

A complementary approach to quantify the basic GSI chart considering scale effect on rock structure

Geological strength index (GSI) has been widely used as an input parameter in predicting the strength and deformation properties of rock masses. This study derived a series of equations to satisfy the original GSI lines on the basic GSI chart. Two axes ranging from 0 to 100 were employed for surface conditions of the discontinuities and the structure of rock mass, which are independent of the input parameters. The derived equations can analyze GSI values ranging from 0 to 100 within ±5% error. The engineering dimensions (EDs) such as the slope height, tunnel width, and foundation width were used together with representative elementary volume (REV) in jointed rock mass to define scale factor (sf) from 0.2 to 1 in evaluating the rock mass structure including joint pattern. The transformation of GSI into a scale-dependent parameter based on engineering scale addresses a crucial requirement in various engineering applications. The improvements proposed in this study were applied to a real slope which was close to the time of failure. The results of stability assessments show that the new proposals have sufficient capability to define rock mass quality considering EDs.

Multi‐cohort survival of northern red oak seedlings at a northern hardwood forest transition

AbstractGlobal change has created less stable forest systems and given urgency to understanding limitations to the establishment of tree seedlings beyond current range boundaries. We quantified trends in 13 years of annual northern red oak (QURU) seedling survival data for 1733 marked individuals at a local species distribution boundary within the northern hardwood forest in New Hampshire, USA. Over the study period, the median distance of seedlings into the valley did not change, although there was a net gain of 89 plots (5 m2) occupied. For a subset of seedlings that were marked in their year of birth (N = 937), we examined relationships among terrain, vegetation community, and initial individual seedling traits, and evaluated their effects on time to seedling mortality using a parametric accelerated failure time model. The year of seedling germination had the largest effect on survival with increasing mortality rates for seedlings from more recent cohorts. Seedlings had longer survival times where oak seedling densities were lower, shrub cover was higher, and when the acorn remained attached. Additionally, survival time was increased in higher elevation plots, which were also located further into the valley. Interannual seedling survival (N = 1580) was strongly impacted by seedling condition in the previous year, particularly leaf number and amount of leaf damage. Most seedling deaths occurred over winter, and seedlings failed to break bud the following spring. Interannual variation in seasonal climate, particularly deep, heavy snowpack in 2019 followed by drought conditions in 2020, coincided with recent elevated mortality. Overall, the median survival time of 3–4 years and the rapid turnover of the oak seedling population currently limit ability for expansion, although the net gain of occupied plots and increase in survival at higher elevation plots with lower QURU densities present some mechanisms that could promote expansion if the current suboptimal understory conditions shift to favor QURU.

The survival outcomes of localized low-risk prostate cancer, a population-based study using NCDB.

The optimal treatment approach for low-risk prostate cancer (LRPC) remains controversial. While active surveillance is an increasingly popular option, definitive local treatments, including radical prostatectomy (RP), external beam radiotherapy (EBRT), and prostate seed implantation (PSI), are also commonly used. This study aimed to evaluate the survival outcomes of patients with LRPC using a large patient population from the National Cancer Database (NCDB). We analyzed data from 195,452 patients diagnosed with LRPC between 2004 and 2015 using the NCDB. Patients were classified based on their treatment modalities, including RP, EBRT, PSI, or no local treatment (NLT). Only patients with Charlson-Deyo comorbidity scores of 0 or 1 were included to ensure comparability. Propensity score analysis was used to balance the treatment groups, and the accelerated failure time model was used to analyze the survival rates of the treatment groups. After a median follow-up of 70.8 months, 24,545 deaths occurred, resulting in an all-cause mortality rate of 13%. RP demonstrated a survival benefit compared with NLT, particularly in patients younger than 74 years of age. In contrast, radiation treatments (EBRT and PSI) did not improve survival in the younger age groups, except for patients older than 70 years for EBRT and older than 65 years for PSI. Notably, EBRT in patients younger than 65 years was associated with inferior outcomes. This study highlights the differences in survival outcomes among LRPC treatment modalities. RP was associated with improved survival compared to NLT, especially in younger patients. In contrast, EBRT and PSI showed survival benefits primarily in the older age groups. NLT is a reasonable choice, particularly in younger patients when RP is not chosen. These findings emphasize the importance of individualized treatment decisions for LRPC management.

Microcracking Process Characterization and Failure Time Prediction of Three Typical Rocks upon Uniaxial Compression Based on Acoustic Emission Activity

Microcracking Process Characterization and Failure Time Prediction of Three Typical Rocks upon Uniaxial Compression Based on Acoustic Emission Activity

Using the Non-Homogeneous Poisson Process (Duane's Model) to Analyze the Number of Failures in Industrial Equipment

Objective: The aim of this paper is to show the application of Duane's Chart to analyze the time between failures in a company in the South of Rio de Janeiro. Theoretical framework: A Duane chart is a scatter plot of the cumulative failure rate versus time. Use a Duane chart to do the following: •Assess whether the data follows a power-law process or a homogeneous Poisson process. •Determine whether a repairable system is improving, getting worse or remaining stable. The fitted line on the Duane chart plots the best fitted line when the power-law process assumption is valid and the shape and scale are estimated using the least squares method. The Duane plot should be approximately linear if the power-law process or homogeneous Poisson process is appropriate. A negative slope shows an improvement in reliability, a positive slope shows a deterioration in reliability and no slope (a horizontal line) shows a stable system (Zanin et al., 2010). Method: Data was taken from a company in the South of Rio de Janeiro and a case study was carried out using Duane's Chart. Final Considerations: This result indicates that Duane's Model is a very viable option when the aim is to monitor the failure rate as a function of time to check whether a system is improving or not. In this specific Case Study, it is clear that there is a significant improvement in the system over time and that the work carried out in this company is being very effective in reducing and even eliminating failures in the long term. Implications of the research: The use cases of Duane's Chart are multiplying in scientific literature and are proving to be highly effective for interpreting data in the area of reliability. Originality/value: Despite being a well-known Statistical Tool, Duane's Chart has a specific application in monitoring the number of failures over time in a system.

Effect of ARB process on the plane stress fracture toughness, creep properties and forming limit diagram of Aluminum/BN/Copper composite strips

Abstract In the present study, Al/BN/Cu bimetal composite strips were fabricated via the accumulative roll bonding (ARB) process. Then, fracture toughness, mechanical properties, bonding strength, forming limit diagram (FLD), and creep properties have been studied via experimental techniques. The study of creep behavior and mechanical properties showed a formation of a 17 μm atomic diffusion layer at the interface during ARB under three creep loading conditions namely 35 MPa at 225 °C, 35 MPa at 275 °C, and 30 MPa at 225 °C. The tensile strength of samples improved to 144 MPa which was about 234% in comparison with the primary Al monolithic sample. It was observed by the SEM that the fracture types changed to shear kind after higher passes including prominent effects on the fracture morphology. FLD curve dropped severely after the first ARB pass and then began to enhance at higher passes. The fracture toughness value of 30 MPa m1/2 was achieved after ten ARB passes. An intermetallic composition was created near Al. The creep failure time did decline by 44% and the stress level decreased by 13% at a constant temperature. It can be concluded that applied temperature and stress effect on creep properties especially leads to increasing the slope of creep curves with higher stresses. This trend was opposite for the creep temperature at higher temperature levels. Moreover, dynamic recrystallization was observed through the crystalline structure of samples.

Frailty model for multiple repairable systems hierarchically represented subject to competing risks

In this paper, we propose a statistical model to describe the behaviour of failure times associated with groups of repairable systems hierarchically represented, under a competing risks framework, considering the existence of unobserved heterogeneity that acts individually on systems of each group, as well as the possibility of imperfect repairs whose initial failure rate is in the form of the power law. In this context for the unobserved heterogeneity in the groups, we consider the multiplicative frailty. To illustrate the use of the proposed model, we consider a database with the failures of 38 agricultural machines categorized into five different groups. We understand that the tractor fleet corresponds to the farm's agricultural system, therefore the need for intervention in this system occurs with the failure of any unit, individually, in a serial structure, of competing risks.e On the other hand, the understanding of the time in which all the machinery that makes up the fleet will have required some intervention is obtained by analysing the results under a parallel structure.

Association Between Greater Social Vulnerability and Delayed Glaucoma Surgery

PurposeTiming of surgical intervention in glaucoma is crucial to preserving sight. While ocular characteristics that increase surgical risk are known, the impact of neighborhood-level social risk factors such as the Social Vulnerability Index (SVI) and Area Deprivation Index (ADI) on time to glaucoma surgery is unknown. The objective of this study was to evaluate the association between SVI or ADI scores and the timing of glaucoma surgical intervention. DesignRetrospective cohort study. MethodsAdult subjects with open-angle glaucoma were identified from the Bascom Palmer Glaucoma Repository using International Classification of Disease-10 codes. Subject demographics, ocular characteristics, and standard automated perimetry (SAP) data were extracted. Geocoded data were obtained using subject residences and American Community Survey data. Univariable and multivariable time-to-event survival analyses using accelerated failure time (AFT) models were completed to evaluate whether geocoded SVI and ADI scores accelerated or delayed time to glaucoma surgery from initial glaucoma diagnosis in the electronic health record. ResultsA total of 10,553 eyes from 6,934 subjects were evaluated, of which 637 eyes (6.0%) from 568 subjects (8.2%) underwent glaucoma surgery. Mean age was 68.3±13.5 years, with 57.9% female, 21.5% Black, and 34.5% Hispanic subjects. Mean follow-up time was 5.0±2.1 years, with time to surgery of 3.2±1.9 years. Multivariable AFT models demonstrated that higher mean intraocular pressure (time ratio (TR) 0.27 per 5 mmHg higher; 95% CI: 0.23-0.31, p<0.001), faster SAP rate of progression (TR 0.74 per 0.5 dB/year faster; 95% CI: 0.69-0.78, p<0.001), moderate (TR 0.69; 95% CI: 0.56-0.85, p<0.001) or severe baseline severity (TR 0.39; 95% CI: 0.32-0.47, p<0.001), and thinner central corneal thickness (TR 0.85 per 50µm thinner; 95% CI: 0.77-0.95, p=0.003) all accelerated time to surgery. In contrast, overall SVI delayed surgery (TR 1.11 per 25% increase; 95% CI: 1.03-1.20, p=0.006). Specifically, SVI Themes 1 (TR 1.08; 95% CI: 1.01-1.17, p=0.037) and 4 (TR 1.11; 95% CI: 1.03-1.19, p=0.006) were significant. Patients from the most deprived neighborhoods (highest national ADI quartile) had a 68% increase in time to surgery compared to the least deprived quartile (TR 1.68; 95% CI: 1.20-2.36, p=0.002). ConclusionsResidence in areas with higher SVI or ADI scores was associated with delayed glaucoma surgery after controlling for demographic and ocular parameters. Awareness of such disparities can guide initiatives aimed at achieving parity in health outcomes.

Semiparametric varying-coefficient additive hazards model for informatively interval-censored failure time data

The analysis of interval-censored data with informative observation processes has recently attracted much attention and a few methods have been developed. However, all of the existing methods assume that covariate effects are constant and this may not be true sometimes in practice. To address this, in this paper, we propose a varying-coefficient additive hazards model and in the proposed method, frailty variables are used to describe the dependence between the failure time and the informative observation process. For inference, a Bernstein polynomials-based, two-step sieve maximum likelihood method is developed and the proposed method can be easily implemented. Furthermore, the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed approach works well for practical situations. The proposed method is applied to a cardiac allograft vasculopathy (CAV) study that motivated this investigation.

Dependent censoring with simultaneous death times based on the Generalized Marshall–Olkin model

In this paper, we consider the problem of dependent censoring models with a positive probability that the times of failure are equal. In this context, we propose to consider the Marshall–Olkin type model and studied some properties of the associated survival copula in its application to censored data. We also introduce estimators for the marginal distributions and the joint survival probabilities under different schemes and show their asymptotic normality under appropriate conditions. Finally, we evaluate the finite-sample performance of our approach relying on a small simulation study with synthetic data real data applications.