Thisarticleconcernstheinverse problem of the recoveryof unknown potential coefficient for the Schrödinger equation, in a bounded domain of Rn with non-homogeneous Neumann boundary condition from a time-dependent Dirich let boundary measurement. We prove uniqueness and Lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the spatial domain and under weak regularity requirements on the data. The proof is based on aCarleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality. Mathematics Subject Classification. 35R30, 35Q40, 49K20.

Thisarticleconcernstheinverse problem of the recoveryof unknown potential coefficient for the Schrödinger equation, in a bounded domain of Rn with non-homogeneous Neumann boundary condition from a time-dependent Dirich let boundary measurement. We prove uniqueness and Lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the spatial domain and under weak regularity requirements on the data. The proof is based on aCarleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality. Mathematics Subject Classification. 35R30, 35Q40, 49K20.

This research uses the stability radius approach to investigate the robust stability of an infinite-dimensional linear discrete-time system subjected to stochastic perturbations. First, we characterize the stability radius in terms of a Lyapunov equation. These characterizations improve a computational formula for calculating the stability radius. The second goal is to study how state feedback can maximize the stability radius. We characterize the maximum attainable stability radius using an infinite-dimensional discrete-time Riccati equation. Examples are provided to demonstrate the achieved outcomes.

This research uses the stability radius approach to investigate the robust stability of an infinite-dimensional linear discrete-time system subjected to stochastic perturbations. First, we characterize the stability radius in terms of a Lyapunov equation. These characterizations improve a computational formula for calculating the stability radius. The second goal is to study how state feedback can maximize the stability radius. We characterize the maximum attainable stability radius using an infinite-dimensional discrete-time Riccati equation. Examples are provided to demonstrate the achieved outcomes.

This research uses the stability radius approach to investigate the robust stability of an infinite-dimensional linear discrete-time system subjected to stochastic perturbations. First, we characterize the stability radius in terms of a Lyapunov equation. These characterizations improve a computational formula for calculating the stability radius. The second goal is to study how state feedback can maximize the stability radius. We characterize the maximum attainable stability radius using an infinite-dimensional discrete-time Riccati equation. Examples are provided to demonstrate the achieved outcomes.

Most road crashes at work are caused by Driver Behavioral Drift (DBD). This DBD has become a recurring issue on congested road sections. In this context, this study proposes a method called (MASOCU-DBD) which allows to analyze this DBD problem in two steps: assessment of the dynamics of DBD occurrence using a model called BM-NSA and analysis of DCC using a Cost-Benefit Analysis (CBA) weighted by the Analysis Hierarchical Process (AHP). The application of the MASOCU-DBD on a road section of an Algerian city’s entry highlighted the problem of the DBD in terms of its occurrence and uselessness in the studied section. The merit of the proposed method is that it uses multi-criteria analysis tools (AHP and CBA) as well as a mathematical model (BM-NSA) to analyze professional drivers’ behavioral deviations.

Most road crashes at work are caused by Driver Behavioral Drift (DBD). This DBD has become a recurring issue on congested road sections. In this context, this study proposes a method called (MASOCU-DBD) which allows to analyze this DBD problem in two steps: assessment of the dynamics of DBD occurrence using a model called BM-NSA and analysis of DCC using a Cost-Benefit Analysis (CBA) weighted by the Analysis Hierarchical Process (AHP). The application of the MASOCU-DBD on a road section of an Algerian city’s entry highlighted the problem of the DBD in terms of its occurrence and uselessness in the studied section. The merit of the proposed method is that it uses multi-criteria analysis tools (AHP and CBA) as well as a mathematical model (BM-NSA) to analyze professional drivers’ behavioral deviations.

Most road crashes at work are caused by Driver Behavioral Drift (DBD). This DBD has become a recurring issue on congested road sections. In this context, this study proposes a method called (MASOCU-DBD) which allows to analyze this DBD problem in two steps: assessment of the dynamics of DBD occurrence using a model called BM-NSA and analysis of DCC using a Cost-Benefit Analysis (CBA) weighted by the Analysis Hierarchical Process (AHP). The application of the MASOCU-DBD on a road section of an Algerian city’s entry highlighted the problem of the DBD in terms of its occurrence and uselessness in the studied section. The merit of the proposed method is that it uses multi-criteria analysis tools (AHP and CBA) as well as a mathematical model (BM-NSA) to analyze professional drivers’ behavioral deviations.

Most road crashes at work are caused by Driver Behavioral Drift (DBD). This DBD has become a recurring issue on congested road sections. In this context, this study proposes a method called (MASOCU-DBD) which allows to analyze this DBD problem in two steps: assessment of the dynamics of DBD occurrence using a model called BM-NSA and analysis of DCC using a Cost-Benefit Analysis (CBA) weighted by the Analysis Hierarchical Process (AHP). The application of the MASOCU-DBD on a road section of an Algerian city’s entry highlighted the problem of the DBD in terms of its occurrence and uselessness in the studied section. The merit of the proposed method is that it uses multi-criteria analysis tools (AHP and CBA) as well as a mathematical model (BM-NSA) to analyze professional drivers’ behavioral deviations.

Liquefied petroleum gas (LPG) storage fires and explosions occur due to uncontrolled gas leaks and the gradual breakdown of associated safety barriers. By installing an effective safety barrier, these accidents can be greatly reduced. However, this study assesses the probability of failure of emergency safety barriers (ESBs) to help decision makers understand how they can support decisions to reduce the risks associated with LPG storage. In this context, an extension of the event tree analysis is proposed named emergency event tree analysis (EETA). The aim of this paper is to develop an integrated approach that uses interval type-2 fuzzy sets and Analytic Hierarchy Process (AHP) method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers (ESBs). In addition, a case study on the failure probability assessment of the emergency safety barriers of the LPG plant in Algeria based on the proposed methodology is provided and carried out to illustrate its effectiveness and feasibility. The results demonstrated the ability of interval type-2 fuzzy sets and the AHP method to provide highly reliable results and to evaluate the failure probability of emergency safety barriers in emergencies situations. However, the classical event tree analysis (CETA) does not take into account the possibility of assessing the emergency consequences of different accident scenarios. Consequently, it only allows you to estimate the occurrence probability of accident scenarios. The results of this study show that the value of the probability of failure of the emergency safety barriers can be used to estimate the probability of occurrence of emergency consequences under different accident scenarios, improved the reliability and help prioritize emergency improvement measures. The study provides scientific and operational references for analyzing emergency consequences of the various accident scenarios in all fields such as petrochemical, maritime industry, and health occupational.

Liquefied petroleum gas (LPG) storage fires and explosions occur due to uncontrolled gas leaks and the gradual breakdown of associated safety barriers. By installing an effective safety barrier, these accidents can be greatly reduced. However, this study assesses the probability of failure of emergency safety barriers (ESBs) to help decision makers understand how they can support decisions to reduce the risks associated with LPG storage. In this context, an extension of the event tree analysis is proposed named emergency event tree analysis (EETA). The aim of this paper is to develop an integrated approach that uses interval type-2 fuzzy sets and Analytic Hierarchy Process (AHP) method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers (ESBs). In addition, a case study on the failure probability assessment of the emergency safety barriers of the LPG plant in Algeria based on the proposed methodology is provided and carried out to illustrate its effectiveness and feasibility. The results demonstrated the ability of interval type-2 fuzzy sets and the AHP method to provide highly reliable results and to evaluate the failure probability of emergency safety barriers in emergencies situations. However, the classical event tree analysis (CETA) does not take into account the possibility of assessing the emergency consequences of different accident scenarios. Consequently, it only allows you to estimate the occurrence probability of accident scenarios. The results of this study show that the value of the probability of failure of the emergency safety barriers can be used to estimate the probability of occurrence of emergency consequences under different accident scenarios, improved the reliability and help prioritize emergency improvement measures. The study provides scientific and operational references for analyzing emergency consequences of the various accident scenarios in all fields such as petrochemical, maritime industry, and health occupational.

Industrial systems are becoming more sophisticated, and their failure can result in significant losses for the company in terms of production loss, maintenance costs, fines, image loss, etc. Conventional approaches to modeling and evaluating the failure mechanisms of these systems do not consider certain important aspects, such as the interdependencies between failure modes (FMs) with information and data containing uncertainties as they are generally collected from experts’ judgments. These restrictions may lead to improper decision-making. The use of more advanced techniques to model and assess the interdependencies among components’ failures under uncertainties seems to be more than necessary to overcome these deficiencies. It is in this context that the proposed approach fits. It consists of proposing a hybrid multicriteria decision-aking (MCDM) approach that combines several techniques for a better selection of maintenance strategies. Using the failure mode and effects analysis (FMEA) technique, the potential FMs of components, along with their causes and effects, are identified. The relative importance (or weight) of these FMs is determined using the fuzzy simple additive weighing (FSAW) method based on how they affect the system’s goals. The causal relationships between FMs and their final weights are determined by the fuzzy cognitive maps (FCM) method and the nonlinear Hebbian learning and differential evolution (NHL-DE) algorithm. Finally, based on the final FM weights provided by the FCM, the simple additive weighing (SAW) method is used to select the optimal maintenance strategies. The results of applying the proposed approach to an operating compressor lubrication and sealing oil system demonstrate its importance and usefulness in assisting system operators to efficiently allocate the optimal maintenance strategies, considering the strong correlation between FMs and their effects on system performance while accounting for the uncertainties associated with experts’ judgments. These correlation effects have led to changes in the assigned weights of the selected FMs. Specifically, the FM related to the low output of the lube/seal oil pump, which was initially assigned a lower priority, and with the correlation effects has become the first critical FM. This shift in prioritization emphasizes the need to address this particular FM promptly. By focusing on addressing these high-priority FMs, maintenance efforts can be optimized to prevent or mitigate more severe consequences. Among the various maintenance strategies evaluated, it was determined that the combination of condition-based maintenance (CBM) and precision maintenance (PrM) yields the most favorable outcome in terms of mitigating the impact of accidental failures and undesired events on the selected system.

Industrial systems are becoming more sophisticated, and their failure can result in significant losses for the company in terms of production loss, maintenance costs, fines, image loss, etc. Conventional approaches to modeling and evaluating the failure mechanisms of these systems do not consider certain important aspects, such as the interdependencies between failure modes (FMs) with information and data containing uncertainties as they are generally collected from experts’ judgments. These restrictions may lead to improper decision-making. The use of more advanced techniques to model and assess the interdependencies among components’ failures under uncertainties seems to be more than necessary to overcome these deficiencies. It is in this context that the proposed approach fits. It consists of proposing a hybrid multicriteria decision-aking (MCDM) approach that combines several techniques for a better selection of maintenance strategies. Using the failure mode and effects analysis (FMEA) technique, the potential FMs of components, along with their causes and effects, are identified. The relative importance (or weight) of these FMs is determined using the fuzzy simple additive weighing (FSAW) method based on how they affect the system’s goals. The causal relationships between FMs and their final weights are determined by the fuzzy cognitive maps (FCM) method and the nonlinear Hebbian learning and differential evolution (NHL-DE) algorithm. Finally, based on the final FM weights provided by the FCM, the simple additive weighing (SAW) method is used to select the optimal maintenance strategies. The results of applying the proposed approach to an operating compressor lubrication and sealing oil system demonstrate its importance and usefulness in assisting system operators to efficiently allocate the optimal maintenance strategies, considering the strong correlation between FMs and their effects on system performance while accounting for the uncertainties associated with experts’ judgments. These correlation effects have led to changes in the assigned weights of the selected FMs. Specifically, the FM related to the low output of the lube/seal oil pump, which was initially assigned a lower priority, and with the correlation effects has become the first critical FM. This shift in prioritization emphasizes the need to address this particular FM promptly. By focusing on addressing these high-priority FMs, maintenance efforts can be optimized to prevent or mitigate more severe consequences. Among the various maintenance strategies evaluated, it was determined that the combination of condition-based maintenance (CBM) and precision maintenance (PrM) yields the most favorable outcome in terms of mitigating the impact of accidental failures and undesired events on the selected system.

Industrial systems are becoming more sophisticated, and their failure can result in significant losses for the company in terms of production loss, maintenance costs, fines, image loss, etc. Conventional approaches to modeling and evaluating the failure mechanisms of these systems do not consider certain important aspects, such as the interdependencies between failure modes (FMs) with information and data containing uncertainties as they are generally collected from experts’ judgments. These restrictions may lead to improper decision-making. The use of more advanced techniques to model and assess the interdependencies among components’ failures under uncertainties seems to be more than necessary to overcome these deficiencies. It is in this context that the proposed approach fits. It consists of proposing a hybrid multicriteria decision-aking (MCDM) approach that combines several techniques for a better selection of maintenance strategies. Using the failure mode and effects analysis (FMEA) technique, the potential FMs of components, along with their causes and effects, are identified. The relative importance (or weight) of these FMs is determined using the fuzzy simple additive weighing (FSAW) method based on how they affect the system’s goals. The causal relationships between FMs and their final weights are determined by the fuzzy cognitive maps (FCM) method and the nonlinear Hebbian learning and differential evolution (NHL-DE) algorithm. Finally, based on the final FM weights provided by the FCM, the simple additive weighing (SAW) method is used to select the optimal maintenance strategies. The results of applying the proposed approach to an operating compressor lubrication and sealing oil system demonstrate its importance and usefulness in assisting system operators to efficiently allocate the optimal maintenance strategies, considering the strong correlation between FMs and their effects on system performance while accounting for the uncertainties associated with experts’ judgments. These correlation effects have led to changes in the assigned weights of the selected FMs. Specifically, the FM related to the low output of the lube/seal oil pump, which was initially assigned a lower priority, and with the correlation effects has become the first critical FM. This shift in prioritization emphasizes the need to address this particular FM promptly. By focusing on addressing these high-priority FMs, maintenance efforts can be optimized to prevent or mitigate more severe consequences. Among the various maintenance strategies evaluated, it was determined that the combination of condition-based maintenance (CBM) and precision maintenance (PrM) yields the most favorable outcome in terms of mitigating the impact of accidental failures and undesired events on the selected system.

Industrial systems are becoming more sophisticated, and their failure can result in significant losses for the company in terms of production loss, maintenance costs, fines, image loss, etc. Conventional approaches to modeling and evaluating the failure mechanisms of these systems do not consider certain important aspects, such as the interdependencies between failure modes (FMs) with information and data containing uncertainties as they are generally collected from experts’ judgments. These restrictions may lead to improper decision-making. The use of more advanced techniques to model and assess the interdependencies among components’ failures under uncertainties seems to be more than necessary to overcome these deficiencies. It is in this context that the proposed approach fits. It consists of proposing a hybrid multicriteria decision-aking (MCDM) approach that combines several techniques for a better selection of maintenance strategies. Using the failure mode and effects analysis (FMEA) technique, the potential FMs of components, along with their causes and effects, are identified. The relative importance (or weight) of these FMs is determined using the fuzzy simple additive weighing (FSAW) method based on how they affect the system’s goals. The causal relationships between FMs and their final weights are determined by the fuzzy cognitive maps (FCM) method and the nonlinear Hebbian learning and differential evolution (NHL-DE) algorithm. Finally, based on the final FM weights provided by the FCM, the simple additive weighing (SAW) method is used to select the optimal maintenance strategies. The results of applying the proposed approach to an operating compressor lubrication and sealing oil system demonstrate its importance and usefulness in assisting system operators to efficiently allocate the optimal maintenance strategies, considering the strong correlation between FMs and their effects on system performance while accounting for the uncertainties associated with experts’ judgments. These correlation effects have led to changes in the assigned weights of the selected FMs. Specifically, the FM related to the low output of the lube/seal oil pump, which was initially assigned a lower priority, and with the correlation effects has become the first critical FM. This shift in prioritization emphasizes the need to address this particular FM promptly. By focusing on addressing these high-priority FMs, maintenance efforts can be optimized to prevent or mitigate more severe consequences. Among the various maintenance strategies evaluated, it was determined that the combination of condition-based maintenance (CBM) and precision maintenance (PrM) yields the most favorable outcome in terms of mitigating the impact of accidental failures and undesired events on the selected system.

Purpose This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers. Design/methodology/approach The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert’s imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis. Findings A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures. Research limitations/implications This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account. Originality/value Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

Purpose This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers. Design/methodology/approach The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert’s imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis. Findings A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures. Research limitations/implications This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account. Originality/value Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

Purpose The reliability prediction is among the most important objectives for achieving overall system performance, and this prediction carried out by anticipating system performance degradation. In this context, the purpose of this research paper is to development of methodology for the photovoltaic (PV) modules’ reliability prediction taking into account their future operating context. Design/methodology/approach The proposed methodology is framed by dependability methods, in this regard, two methods of dysfunctional analysis were used, the Failure Mode and Effects Criticality Analysis (FMECA) method is carried out for identification of the degradation modes, and the Fault Tree Analysis (FTA) method is used for identification the causes of PV modules degradation and the parameters influencing its degradation. Then, based on these parameters, accelerated tests have been used to predict the reliability of PV modules. Findings The application of the proposed methodology on PWX 500 PV modules’ in different regions of Algeria makes it possible to predict its reliability, taking into account the future constraints on its operation. In this case, the temperature and relative humidity vary from one region to another was chosen as constraints. The results obtained from the different regions confirms the reliability provided by the designer of the Saharan cities Biskra, In Salah, Tamanraset, and affirms this value for the two Mediterranean cities of Oran and Algiers. Originality/value The proposed methodology is developed for the reliability prediction of the PV modules taking into account their future operating context and, the choice of different regions confirms or disproves the reliability provided by the designer of the PV modules studied. This application confirms their performance within the framework of the reliability prediction.

Purpose The reliability prediction is among the most important objectives for achieving overall system performance, and this prediction carried out by anticipating system performance degradation. In this context, the purpose of this research paper is to development of methodology for the photovoltaic (PV) modules’ reliability prediction taking into account their future operating context. Design/methodology/approach The proposed methodology is framed by dependability methods, in this regard, two methods of dysfunctional analysis were used, the Failure Mode and Effects Criticality Analysis (FMECA) method is carried out for identification of the degradation modes, and the Fault Tree Analysis (FTA) method is used for identification the causes of PV modules degradation and the parameters influencing its degradation. Then, based on these parameters, accelerated tests have been used to predict the reliability of PV modules. Findings The application of the proposed methodology on PWX 500 PV modules’ in different regions of Algeria makes it possible to predict its reliability, taking into account the future constraints on its operation. In this case, the temperature and relative humidity vary from one region to another was chosen as constraints. The results obtained from the different regions confirms the reliability provided by the designer of the Saharan cities Biskra, In Salah, Tamanraset, and affirms this value for the two Mediterranean cities of Oran and Algiers. Originality/value The proposed methodology is developed for the reliability prediction of the PV modules taking into account their future operating context and, the choice of different regions confirms or disproves the reliability provided by the designer of the PV modules studied. This application confirms their performance within the framework of the reliability prediction.

Purpose The reliability prediction is among the most important objectives for achieving overall system performance, and this prediction carried out by anticipating system performance degradation. In this context, the purpose of this research paper is to development of methodology for the photovoltaic (PV) modules’ reliability prediction taking into account their future operating context. Design/methodology/approach The proposed methodology is framed by dependability methods, in this regard, two methods of dysfunctional analysis were used, the Failure Mode and Effects Criticality Analysis (FMECA) method is carried out for identification of the degradation modes, and the Fault Tree Analysis (FTA) method is used for identification the causes of PV modules degradation and the parameters influencing its degradation. Then, based on these parameters, accelerated tests have been used to predict the reliability of PV modules. Findings The application of the proposed methodology on PWX 500 PV modules’ in different regions of Algeria makes it possible to predict its reliability, taking into account the future constraints on its operation. In this case, the temperature and relative humidity vary from one region to another was chosen as constraints. The results obtained from the different regions confirms the reliability provided by the designer of the Saharan cities Biskra, In Salah, Tamanraset, and affirms this value for the two Mediterranean cities of Oran and Algiers. Originality/value The proposed methodology is developed for the reliability prediction of the PV modules taking into account their future operating context and, the choice of different regions confirms or disproves the reliability provided by the designer of the PV modules studied. This application confirms their performance within the framework of the reliability prediction.