To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second...To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.展开更多
Rainfall and temperature variability analysis is important for researchers and policy formulators in making critical decisions on water availability and use in communities. The Western Sahel, which comprises Mali is c...Rainfall and temperature variability analysis is important for researchers and policy formulators in making critical decisions on water availability and use in communities. The Western Sahel, which comprises Mali is considered as one of the vulnerable regions to climate change, and also encountered the challenges of climatic shocks such as flood and drought. This research therefore sought to investigate climate change effects on hydrological events and trends in Sahelian rainfall intensity using Bamako (Mali) as a case study from 1991 to 2020, as limited data availability did not allow an extended period of study. Monthly observed data provided by MALI-METEO was used to validate daily rainfalls data from African Rainfall Climatology Version 2 (ARC2) satellite-based rainfall product on monthly basis. The validated model performance used Nash-Sutcliffe Efficiency (NSE) and Percent Bias (PBAIS) and gave results of 0.904 and 1.0506 respectively. Trends in annual maximum temperatures and rainfalls were analyzed using Mann-Kendall trend test. The result indicated that the trend in annual maximum rainfalls was decreasing, while annual total rainfall was increasing but not significant at 5% significance level. The rate of increase in annual total rainfalls was 0.475 mm/year according to the observed annual rainfall series and decreased to 0.68 mm/year in annual maximum. The analysis further found that annual maximum temperatures were increasing at the rate of 0.03°C/year at 5% significance level. To provide more accurate climate predictions, it is recommended that further studies on rainfall and temperature with data sets spanning 60 - 90 years be carried out.展开更多
Rockbursts have become a significant hazard in underground mining,underscoring the need for a robust early warning model to ensure safety management.This study presents a novel approach for rockburst prediction,integr...Rockbursts have become a significant hazard in underground mining,underscoring the need for a robust early warning model to ensure safety management.This study presents a novel approach for rockburst prediction,integrating the Mann-Kendall trend test(MKT)and multi-indices fusion to enable real-time and quantitative assessment of rockburst hazards.The methodology employed in this study involves the development of a comprehensive precursory index library for rockbursts.The MKT is then applied to analyze the real-time trend of each index,with adherence to rockburst characterization laws serving as the warning criterion.By employing a confusion matrix,the warning effectiveness of each index is assessed,enabling index preference determination.Ultimately,the integrated rockburst hazard index Q is derived through data fusion.The results demonstrate that the proposed model achieves a warning effectiveness of 0.563 for Q,surpassing the performance of any individual index.Moreover,the model’s adaptability and scalability are enhanced through periodic updates driven by actual field monitoring data,making it suitable for complex underground working environments.By providing an efficient and accurate basis for decision-making,the proposed model holds great potential for the prevention and control of rockbursts.It offers a valuable tool for enhancing safety measures in underground mining operations.展开更多
Adaptive detection of range-spread targets is considered in the presence of subspace interference plus Gaussian clutter with unknown covariance matrix.The target signal and interference are supposed to lie in two line...Adaptive detection of range-spread targets is considered in the presence of subspace interference plus Gaussian clutter with unknown covariance matrix.The target signal and interference are supposed to lie in two linearly independent subspaces with deterministic but unknown coordinates.Relying on the two-step criteria,two adaptive detectors based on Gradient tests are proposed,in homogeneous and partially homogeneous clutter plus subspace interference,respectively.Both of the proposed detectors exhibit theoretically constant false alarm rate property against unknown clutter covariance matrix as well as the power level.Numerical results show that,the proposed detectors have better performance than their existing counterparts,especially for mismatches in the signal steering vectors.展开更多
Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understan...Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understand the trends of vegetation cover, this research examined the spatial-temporal trends of global vegetation by employing the normalized difference vegetation index(NDVI) from the Advanced Very High Resolution Radiometer(AVHRR) Global Inventory Modeling and Mapping Studies(GIMMS) time series(1982–2015). Ten samples were selected to test the temporal trend of NDVI, and the results show that in arid and semi-arid regions, NDVI showed a deceasing trend, while it showed a growing trend in other regions. Mann-Kendal(MK) trend test results indicate that 83.37% of NDVI pixels exhibited positive trends and that only 16.63% showed negative trends(P < 0.05) during the period from 1982 to 2015. The increasing NDVI trends primarily occurred in tree-covered regions because of forest growth and re-growth and also because of vegetation succession after a forest disturbance. The increasing trend of the NDVI in cropland regions was primarily because of the increasing cropland area and the improvement in planting techniques. This research describes the spatial vegetation trends at a global scale over the past 30+ years, especially for different land cover types.展开更多
In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially acc...In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.展开更多
Partial discharge test on a transformer is carried out according to the items in IEC 60. During the test, unproved measuring system is calibrated by proved system at a voltage no less than 50% the rated testing voltag...Partial discharge test on a transformer is carried out according to the items in IEC 60. During the test, unproved measuring system is calibrated by proved system at a voltage no less than 50% the rated testing voltage. The result is then extrapolated linearly, leading to an error related to the distribution of stray capacitance, which varies with the testing frequency, especially to large transformers. In this paper a factor, named the capacitive rise fact, is introduced to assess the rise. The factor can be adjusted to some extent by changing the reactance that is connected to the LV side of the testing circuit to lower the capacity of the power source. However, the factor changes when the voltage divider on the high voltage side is removed after the voltage ratio has been calculated, and a great error is resulted under unfavorable conditios.展开更多
Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed tha...Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.展开更多
In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear met...In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.展开更多
Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditio...Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.展开更多
Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Mulle...Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.展开更多
We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alte...We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.展开更多
In general,simple subsystems like series or parallel are integrated to produce a complex hybrid system.The reliability of a system is determined by the reliability of its constituent components.It is often extremely d...In general,simple subsystems like series or parallel are integrated to produce a complex hybrid system.The reliability of a system is determined by the reliability of its constituent components.It is often extremely difficult or impossible to get specific information about the component that caused the system to fail.Unknown failure causes are instances in which the actual cause of systemfailure is unknown.On the other side,thanks to current advanced technology based on computers,automation,and simulation,products have become incredibly dependable and trustworthy,and as a result,obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure.Therefore,because of its capacity to produce rapid and adequate failure data in a short period of time,accelerated life testing(ALT)is the most utilized approach in the field of product reliability and life testing.Based on progressively hybrid censored(PrHC)data froma three-component parallel series hybrid system that failed to owe to unknown causes,this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test(SSPALT).Failures of components are considered to follow a power linear hazard rate(PLHR),which can be used when the failure rate displays linear,decreasing,increasing or bathtub failure patterns.The Tempered random variable(TRV)model is considered to reflect the effect of the high stress level used to induce early failure data.The maximum likelihood estimation(MLE)approach is used to estimate the parameters of the PLHR distribution and the acceleration factor.A variance covariance matrix(VCM)is then obtained to construct the approximate confidence intervals(ACIs).In addition,studentized bootstrap confidence intervals(ST-B CIs)are also constructed and compared with ACIs in terms of their respective interval lengths(ILs).Moreover,a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper.Finally,real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.展开更多
基金National Key R&D Program of China(Grant No.2020YFC1512404).
文摘To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.
文摘Rainfall and temperature variability analysis is important for researchers and policy formulators in making critical decisions on water availability and use in communities. The Western Sahel, which comprises Mali is considered as one of the vulnerable regions to climate change, and also encountered the challenges of climatic shocks such as flood and drought. This research therefore sought to investigate climate change effects on hydrological events and trends in Sahelian rainfall intensity using Bamako (Mali) as a case study from 1991 to 2020, as limited data availability did not allow an extended period of study. Monthly observed data provided by MALI-METEO was used to validate daily rainfalls data from African Rainfall Climatology Version 2 (ARC2) satellite-based rainfall product on monthly basis. The validated model performance used Nash-Sutcliffe Efficiency (NSE) and Percent Bias (PBAIS) and gave results of 0.904 and 1.0506 respectively. Trends in annual maximum temperatures and rainfalls were analyzed using Mann-Kendall trend test. The result indicated that the trend in annual maximum rainfalls was decreasing, while annual total rainfall was increasing but not significant at 5% significance level. The rate of increase in annual total rainfalls was 0.475 mm/year according to the observed annual rainfall series and decreased to 0.68 mm/year in annual maximum. The analysis further found that annual maximum temperatures were increasing at the rate of 0.03°C/year at 5% significance level. To provide more accurate climate predictions, it is recommended that further studies on rainfall and temperature with data sets spanning 60 - 90 years be carried out.
基金The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China(Grant Nos.52011530037 and 51904019)the Fundamental Research Funds for the Central Universities and the Youth Teacher International Exchange&Growth Program(Grant No.QNXM20210004).We also greatly appreciate the assistance provided by Kuangou coal mine,China Energy Group Xinjiang Energy Co.,Ltd.
文摘Rockbursts have become a significant hazard in underground mining,underscoring the need for a robust early warning model to ensure safety management.This study presents a novel approach for rockburst prediction,integrating the Mann-Kendall trend test(MKT)and multi-indices fusion to enable real-time and quantitative assessment of rockburst hazards.The methodology employed in this study involves the development of a comprehensive precursory index library for rockbursts.The MKT is then applied to analyze the real-time trend of each index,with adherence to rockburst characterization laws serving as the warning criterion.By employing a confusion matrix,the warning effectiveness of each index is assessed,enabling index preference determination.Ultimately,the integrated rockburst hazard index Q is derived through data fusion.The results demonstrate that the proposed model achieves a warning effectiveness of 0.563 for Q,surpassing the performance of any individual index.Moreover,the model’s adaptability and scalability are enhanced through periodic updates driven by actual field monitoring data,making it suitable for complex underground working environments.By providing an efficient and accurate basis for decision-making,the proposed model holds great potential for the prevention and control of rockbursts.It offers a valuable tool for enhancing safety measures in underground mining operations.
基金supported by the National Natural Science Foundation of China(61971432)Taishan Scholar Project of Shandong Province(tsqn201909156)the Outstanding Youth Innovation Team Program of University in Shandong Province(2019KJN031)。
文摘Adaptive detection of range-spread targets is considered in the presence of subspace interference plus Gaussian clutter with unknown covariance matrix.The target signal and interference are supposed to lie in two linearly independent subspaces with deterministic but unknown coordinates.Relying on the two-step criteria,two adaptive detectors based on Gradient tests are proposed,in homogeneous and partially homogeneous clutter plus subspace interference,respectively.Both of the proposed detectors exhibit theoretically constant false alarm rate property against unknown clutter covariance matrix as well as the power level.Numerical results show that,the proposed detectors have better performance than their existing counterparts,especially for mismatches in the signal steering vectors.
基金Under the auspices of National Natural Science Foundation of China(No.41771179,41871103,41771138)the National Key Research and Development Project(No.2016YFA0602301)
文摘Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understand the trends of vegetation cover, this research examined the spatial-temporal trends of global vegetation by employing the normalized difference vegetation index(NDVI) from the Advanced Very High Resolution Radiometer(AVHRR) Global Inventory Modeling and Mapping Studies(GIMMS) time series(1982–2015). Ten samples were selected to test the temporal trend of NDVI, and the results show that in arid and semi-arid regions, NDVI showed a deceasing trend, while it showed a growing trend in other regions. Mann-Kendal(MK) trend test results indicate that 83.37% of NDVI pixels exhibited positive trends and that only 16.63% showed negative trends(P < 0.05) during the period from 1982 to 2015. The increasing NDVI trends primarily occurred in tree-covered regions because of forest growth and re-growth and also because of vegetation succession after a forest disturbance. The increasing trend of the NDVI in cropland regions was primarily because of the increasing cropland area and the improvement in planting techniques. This research describes the spatial vegetation trends at a global scale over the past 30+ years, especially for different land cover types.
基金Supported by National Natural Science Foundation of China(11271039)
文摘In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.
文摘Partial discharge test on a transformer is carried out according to the items in IEC 60. During the test, unproved measuring system is calibrated by proved system at a voltage no less than 50% the rated testing voltage. The result is then extrapolated linearly, leading to an error related to the distribution of stray capacitance, which varies with the testing frequency, especially to large transformers. In this paper a factor, named the capacitive rise fact, is introduced to assess the rise. The factor can be adjusted to some extent by changing the reactance that is connected to the LV side of the testing circuit to lower the capacity of the power source. However, the factor changes when the voltage divider on the high voltage side is removed after the voltage ratio has been calculated, and a great error is resulted under unfavorable conditios.
基金supported by the National Natural Science Foundation of China(71401134 71571144+1 种基金 71171164)the Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province(2016KW-033)
文摘Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.
文摘In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.
基金This work was funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under Grant No.FP-190-42.
文摘Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.
文摘Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.
文摘We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.
文摘In general,simple subsystems like series or parallel are integrated to produce a complex hybrid system.The reliability of a system is determined by the reliability of its constituent components.It is often extremely difficult or impossible to get specific information about the component that caused the system to fail.Unknown failure causes are instances in which the actual cause of systemfailure is unknown.On the other side,thanks to current advanced technology based on computers,automation,and simulation,products have become incredibly dependable and trustworthy,and as a result,obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure.Therefore,because of its capacity to produce rapid and adequate failure data in a short period of time,accelerated life testing(ALT)is the most utilized approach in the field of product reliability and life testing.Based on progressively hybrid censored(PrHC)data froma three-component parallel series hybrid system that failed to owe to unknown causes,this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test(SSPALT).Failures of components are considered to follow a power linear hazard rate(PLHR),which can be used when the failure rate displays linear,decreasing,increasing or bathtub failure patterns.The Tempered random variable(TRV)model is considered to reflect the effect of the high stress level used to induce early failure data.The maximum likelihood estimation(MLE)approach is used to estimate the parameters of the PLHR distribution and the acceleration factor.A variance covariance matrix(VCM)is then obtained to construct the approximate confidence intervals(ACIs).In addition,studentized bootstrap confidence intervals(ST-B CIs)are also constructed and compared with ACIs in terms of their respective interval lengths(ILs).Moreover,a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper.Finally,real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.