Fixed Failure Rate Research Articles

Questions of the overall dependability of the scada system in the corporate infrastructure

The paper considers the peculiarities of the SCADA (energy infrastructure management system in the railway infrastructure), as well as issues of the overall dependability in the corporate infrastructure, which is the aim of the study. The study, based on the accepted structure and values of the parameters, examines what depends on and how the readiness factor of a SCADA system changes when the recovery intensity changes and at a fixed failure rate. The results show that with increasing recovery intensity, the readiness factors of the telecommunications network and SCADA system thus defined increase, while reducing the downtime. For a more in-depth study of the overall reliability of the SCADA system, it is necessary to set specific normatively accepted dependability parameters of all connected elements, as well as a real set structure. Based on the fact that with backup resources provided, a defined dependability of the system can be ensured at preset values of the reliability parameters of its components and the backup structure; the opposite problem can also be solved. The proposed approach for studying the reliable behavior of the SCADA system within the corporate infrastructure can be noted as a contribution of the present work and conclusions are made for the practical use of the results.

Extremal risk management: expected shortfall value verification using the bootstrap method

In this paper, the authors refer to the axiomatic theory of risk and investigate the problem of formal verification of the expected shortfall (ES) model based on a sample ES. Recognizing the infeasibility of parametric methods, they explore the bootstrap technique, which, unlike the current value-at-risk model-based (VaR model-based) Basel III testing framework, permits the creation of more powerful sample ES-based procedures. Their contribution to the debate on the possibilities of sample ES-based testing is twofold. First, the authors introduce a bootstrap test based on the idea of ES prediction corrected variables. In this way, they obtain a procedure that makes no distributional assumptions about the underlying returns process, and whose p-value computation does not assume any asymptotic convergence. Second, they provide a unifying framework for ES value verification, in which they compare alternative sample ES-based approaches: the residual-based procedures versus the ES prediction corrected tests as well as the VaR model-dependent approach versus the fixed failure rate tests. By examining its statistical properties and practical applicability, they find evidence that the proposed bootstrap procedure, based on ES prediction corrected variables, is superior to other methods. This provides important guidance for developing international standards of market risk management.

A Controllable Success Fix Rate Threshold Determination Method for GNSS Ambiguity Acceptance Tests

Global navigation satellite system (GNSS) integer ambiguity acceptance test is one of the open problems in GNSS data processing. A number of ambiguity acceptance tests have been proposed from different perspectives and then unified into the integer aperture estimation framework. The existing comparative studies indicate that the impact of test statistics form on the test performance is less critical, while how to construct an efficient, practical test threshold is still challenging. Based on the likelihood ratio test theory, a new computationally efficient ambiguity acceptance test with controllable success fix rate, namely the fixed likelihood ratio (FL-) approach is proposed, which does not require Monte Carlo simulation. The study indicates that the fixed failure rate (FF-) approach can only control the overall failure rate of the acceptance region, but the local failure rate is not controllable. The proposed FL-approach only accepts the fixed solution meeting the likelihood ratio requirement. With properly chosen likelihood ratio threshold, the FL-approach achieves comparable success rate as the FF-approach and even lower failure rate than the FF-approach for the strong underlying model cases. The fixed success fix rate of the FL-approach is verified with both simulation data and real GNSS data. The numerical results indicate that the success fix rate of the FL-approach achieves >98% while the failure rate is <1.5%. The real-time kinematic (RTK) positioning with ambiguities tested by the FL-approach achieved 1–2cm horizontal precision and 2–4 cm vertical precision for all tested baselines, which confirms that the FL-approach can serve as a reliable and efficient threshold determination method for the GNSS ambiguity acceptance test problem.

Improving GNSS Ambiguity Acceptance Test Performance with the Generalized Difference Test Approach.

In Global navigation satellite system (GNSS) data processing, integer ambiguity acceptance test is considered as a challenging problem. A number of ambiguity acceptance tests have been proposed from different perspective and then unified into the integer aperture estimation (IA) framework. Among all the IA estimators, the optimal integer aperture (OIA) achieves the highest success rate with the fixed failure rate tolerance. However, the OIA is of less practical appealing due to its high computation complexity. On the other hand, the popular discrimination tests employ only two integer candidates, which are the essential reason for their sub-optimality. In this study, a generalized difference test (GDT) is proposed to exploit the benefit of including three or more integer candidates to improve their performance from theoretical perspective. The simulation results indicate that the third best integer candidates contribute to more than 70% success rate improvement for integer bootstrapping success rate higher than 0.8 case. Therefore, the GDT with three integer candidates (GDT3) achieves a good trade-off between the performance and computation burden. The threshold function is also applied for rapid determination of the fixed failure rate (FF)-threshold for GDT3. The performance improvement of GDT3 is validated with real GNSS data set. The numerical results indicate that GDT3 achieves higher empirical success rate while the empirical failure rate remains comparable. In a 20 km baseline test, the success rate GDT3 increase 7% with almost the same empirical failure rate.

A data driven partial ambiguity resolution: Two step success rate criterion, and its simulation demonstration

Ambiguity Resolution (AR) is a key technique in GNSS precise positioning. In case of weak models (i.e., low precision of data), however, the success rate of AR may be low, which may consequently introduce large errors to the baseline solution in cases of wrong fixing. Partial Ambiguity Resolution (PAR) is therefore proposed such that the baseline precision can be improved by fixing only a subset of ambiguities with high success rate.This contribution proposes a new PAR strategy, allowing to select the subset such that the expected precision gain is maximized among a set of pre-selected subsets, while at the same time the failure rate is controlled. These pre-selected subsets are supposed to obtain the highest success rate among those with the same subset size. The strategy is called Two-step Success Rate Criterion (TSRC) as it will first try to fix a relatively large subset with the fixed failure rate ratio test (FFRT) to decide on acceptance or rejection. In case of rejection, a smaller subset will be fixed and validated by the ratio test so as to fulfill the overall failure rate criterion. It is shown how the method can be practically used, without introducing a large additional computation effort. And more importantly, how it can improve (or at least not deteriorate) the availability in terms of baseline precision comparing to classical Success Rate Criterion (SRC) PAR strategy, based on a simulation validation. In the simulation validation, significant improvements are obtained for single-GNSS on short baselines with dual-frequency observations. For dual-constellation GNSS, the improvement for single-frequency observations on short baselines is very significant, on average 68%. For the medium- to long baselines, with dual-constellation GNSS the average improvement is around 20–30%.

Reliability control of single-epoch RTK ambiguity resolution

Reliability is an important indicator of GNSS performance, especially for the safety-critical applications. Carrier phase-based GNSS positioning can achieve high precision, but its reliability depends on the ambiguity resolution reliability. The ambiguity acceptance test is a popular way to improve the reliability of ambiguity resolution, although the popular ratio test with empirical threshold is not capable of controlling the reliability. A fixed failure rate (FF) approach has been proposed to solve this problem from a theoretical prospective, but its performance has not been verified with real GNSS data. In this study, the threshold function method is used to calculate the FF-difference test threshold; its performance in single-epoch RTK situation is evaluated with two GPS data sets. The numerical results indicate that the threshold function can control the failure rate of ambiguity resolution according to the user requirements. The ratio test also performs well, but it obtains different failure rates for different baselines using a particular empirical threshold. The FF-difference test outperforms the ratio test in the short-baseline case since the inaccurate variance factor degrades its performance. The performance of the FF-difference test can be improved if a better stochastic model is applied.

Instantaneous and controllable integer ambiguity resolution: review and an alternative approach

In the high-precision application of Global Navigation Satellite System (GNSS), integer ambiguity resolution is the key step to realize precise positioning and attitude determination. As the necessary part of quality control, integer aperture (IA) ambiguity resolution provides the theoretical and practical foundation for ambiguity validation. It is mainly realized by acceptance testing. Due to the constraint of correlation between ambiguities, it is impossible to realize the controlling of failure rate according to analytical formula. Hence, the fixed failure rate approach is implemented by Monte Carlo sampling. However, due to the characteristics of Monte Carlo sampling and look-up table, we have to face the problem of a large amount of time consumption if sufficient GNSS scenarios are included in the creation of look-up table. This restricts the fixed failure rate approach to be a post process approach if a look-up table is not available. Furthermore, if not enough GNSS scenarios are considered, the table may only be valid for a specific scenario or application. Besides this, the method of creating look-up table or look-up function still needs to be designed for each specific acceptance test. To overcome these problems in determination of critical values, this contribution will propose an instantaneous and CONtrollable (iCON) IA ambiguity resolution approach for the first time. The iCON approach has the following advantages: (a) critical value of acceptance test is independently determined based on the required failure rate and GNSS model without resorting to external information such as look-up table; (b) it can be realized instantaneously for most of IA estimators which have analytical probability formulas. The stronger GNSS model, the less time consumption; (c) it provides a new viewpoint to improve the research about IA estimation. To verify these conclusions, multi-frequency and multi-GNSS simulation experiments are implemented. Those results show that IA estimators based on iCON approach can realize controllable ambiguity resolution. Besides this, compared with ratio test IA based on look-up table, difference test IA and IA least square based on the iCON approach most of times have higher success rates and better controllability to failure rates.

GNSS integer ambiguity validation based on posterior probability

GNSS integer ambiguity validation is considered to be a challenge task for decades. Several kinds of validation tests are developed and widely used in these years, but theoretical basis is their weakness. Ambiguity validation theoretically is an issue of hypothesis test. In the frame of Bayesian hypothesis testing, posterior probability is the canonical standard that statistical decision should be based on. In this contribution, (i) we derive the posterior probability of the fixed ambiguity based on the Bayesian principle and modify it for practice ambiguity validation. (ii) The optimal property of the posterior probability test is proved based on an extended Neyman–Pearson lemma. Since validation failure rate is the issue users most concerned about, (iii) we derive the failure rate upper bound of the posterior probability test, so the user can use the posterior probability test either in the fixed posterior probability or in the fixed failure rate way. Simulated as well as real observed data are used for experimental validations. The results show that (i) the posterior probability test is the most effective within the R-ratio test, difference test, ellipsoidal integer aperture test and posterior probability test, (ii) the posterior probability test is computational efficient and (iii) the failure rate estimation for posterior probability test is useful.

Integer aperture estimation comparison between ratio test and difference test: from theory to application

Acceptance testing or ambiguity validation is a key step in global navigation satellite system (GNSS) ambiguity resolution, which combined with integer estimator is the so-called integer aperture (IA) estimator. The difference test and ratio test are the two most popular tests. In order to compare the performances of both IA estimators, their differences in different GNSS models are analyzed from algebraic and geometrical perspectives. Furthermore, both tests are connected by comparing with the optimal acceptance test, and then, they can be transformed each other based on certain numerical conditions. As to the instantaneous applications, both tests are first compared with their corresponding instantaneous approaches, including the fixed failure rate approach for ratio test IA (RTIA) and the instantaneous and controllable approach for difference test IA (DTIA). Advantages and drawbacks of both IA estimators in theory and application are analyzed based on these comparisons. In order to verify these conclusions, typical multi-frequency, multi-GNSS situations are constructed to evaluate the performances of DTIA and RTIA ambiguity resolution. Then, both IA estimators are compared based on their instantaneous approaches in the field test. All the simulation experiments and field test results indicate that DTIA has more advantages and is better than RTIA not only in theory, but also in the practical applications.

A new ambiguity acceptance test threshold determination method with controllable failure rate

The ambiguity acceptance test is an important quality control procedure in high precision GNSS data processing. Although the ambiguity acceptance test methods have been extensively investigated, its threshold determine method is still not well understood. Currently, the threshold is determined with the empirical approach or the fixed failure rate (FF-) approach. The empirical approach is simple but lacking in theoretical basis, while the FF-approach is theoretical rigorous but computationally demanding. Hence, the key of the threshold determination problem is how to efficiently determine the threshold in a reasonable way. In this study, a new threshold determination method named threshold function method is proposed to reduce the complexity of the FF-approach. The threshold function method simplifies the FF-approach by a modeling procedure and an approximation procedure. The modeling procedure uses a rational function model to describe the relationship between the FF-difference test threshold and the integer least-squares (ILS) success rate. The approximation procedure replaces the ILS success rate with the easy-to-calculate integer bootstrapping (IB) success rate. Corresponding modeling error and approximation error are analysed with simulation data to avoid nuisance biases and unrealistic stochastic model impact. The results indicate the proposed method can greatly simplify the FF-approach without introducing significant modeling error. The threshold function method makes the fixed failure rate threshold determination method feasible for real-time applications.

Optimal single-shot strategies for discrimination of quantum measurements

We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably m <= n. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones.

The inertial attitude augmentation for ambiguity resolution in SF/SE-GNSS attitude determination.

The Unaided Single Frequency/Single Epoch Global Navigation Satellite System (SF/SE GNSS) model is the most challenging scenario for ambiguity resolution in the GNSS attitude determination application. To improve the performance of SF/SE-GNSS ambiguity resolution without excessive cost, the Micro-Electro-Mechanical System Inertial Measurement Unit (MEMS-IMU) is a proper choice for the auxiliary sensor that carries out the inertial attitude augmentation. Firstly, based on the SF/SE-GNSS compass model, the Inertial Derived Baseline Vector (IDBV) is defined to connect the MEMS-IMU attitude measurement with the SF/SE-GNSS ambiguity search space, and the mechanism of inertial attitude augmentation is revealed from the perspective of geometry. Then, through the quantitative description of model strength by Ambiguity Dilution of Precision (ADOP), two ADOPs are specified for the unaided SF/SE-GNSS compass model and its inertial attitude augmentation counterparts, respectively, and a sufficient condition is proposed for augmenting the SF/SE-GNSS model strength with inertial attitude measurement. Finally, in the framework of an integer aperture estimator with fixed failure rate, the performance of SF/SE-GNSS ambiguity resolution with inertial attitude augmentation is analyzed when the model strength is varying from strong to weak. The simulation results show that, in the SF/SE-GNSS attitude determination application, MEMS-IMU can satisfy the requirements of ambiguity resolution with inertial attitude augmentation.

GNSS carrier phase ambiguity resolution based on integrity restriction in ambiguity domain

Carrier phase ambiguity resolution of Global Navigation Satellite System (GNSS) is a key technology for high-precision navigation and positioning, and it is a challenge for applications which require both high accuracy and high integrity. This paper proposes efficient ambiguity resolution methods based on integrity restriction using Fixed Failure rate Ratio Test (FF-RT) and Doubly Non-central F-distribution Ratio Test (DNF-RT), and derives the related processing models and numerical algorithms compared with the traditional Ratio Test (RT) method. Firstly, the integer ambiguity resolution and validation procedures, especially the Least squares AMBiguity Decorrelation Adjustment (LAMBDA) estimation and RT validation are analyzed. Then the quality evaluation using success rate, the FF-RT method using Integer Aperture (IA) estimation and the NDF-RT method are proposed. Lastly, the simulation and analysis for LAMBDA using RT, FF-RT and DNF-RT methods are performed. Simulation results show that in case of unbiased scenario FF-RT and DNF-RT have similar performances, which are significantly better than RT. In case of biased scenario it is difficult for FF-RT to predict the biased success rate thus it should not be used for bias detection, while DNF-RT can detect biases in most cases except for the biases are approximate or equal to integer, which has the important benefit for early detection of potential threat to the position solution.

The ratio test for future GNSS ambiguity resolution

The performance of the popular ambiguity ratio test is analyzed. Based on experimental and simulated data, it is demonstrated that the current usage of the ratio test with fixed critical value is not sustainable in light of the enhanced variability that future global navigation satellite system (GNSS) ambiguity resolution will bring. As its replacement, the model-driven ratio test with fixed failure rate is proposed. The characteristics of this fixed-failure rate ratio test are described, and a performance analysis is given. The relation between its critical value and various GNSS model parameters is also studied. Finally, a procedure is presented for the creation of fixed failure rate look-up tables for the critical values of the ratio test.

Variable duration fixed failure rate ambiguity resolution

In global navigation satellite system ambiguity resolution, it is common to use a configurable acceptance test, like the popular ratio test, to control the failure rate. Work in the literature proposes acceptance tests which let users directly choose an acceptable failure rate, but it focuses on instantaneous and fixed duration ambiguity resolution (where results may be success, failure, or undecided). We present a fixed failure rate acceptance test which avoids undecided results by varying the duration of the ambiguity resolution window. The proposed method uses Monte Carlo simulation with a time-correlated noise model to select acceptance test parameters that will minimize mean ambiguity resolution time while maintaining the target failure rate. Results of real-world experiments with single-frequency data from receivers with patch antennas show with 24 h of stationary data the method produces a mean ambiguity resolution time reduction of 52 % (from 525 to 250 s) compared with a ratio test. In a test with 90 min of kinematic data, the reduction was 33 % (from 620 to 410 s).

The GNSS ambiguity ratio-test revisited: a better way of using it

Integer carrier phase ambiguity resolution is the key to fast and high-precision global navigation satellite system (GNSS) positioning and application. Apart from integer estimation, also acceptance tests are part of the ambiguity resolution process. A popular acceptance test is the so-called ratio-test. In this contribution we study the properties and the underlying concepts of the ratio-test. We discuss some misconceptions of the ratio-test and in particular show that the ratio-test is not a test for testing the correctness of the integer least-squares solution. We also show that the common usage of the ratio-test with a fixed critical value has shortcomings. Instead, the fixed failure rate approach is recommended. This approach is part of the more general theory of integer aperture estimation, and enables that the failure rate does not exceed a user-defined value. Results of the fixed failure-rate ratio-test and its improved performance are illustrated with a number of examples.

Operating Window: An Engineering Measure for Robustness

This article presents a metric for measuring and improving the robustness of engineering systems. Robustness is the ability of the system to avoid failure modes, even in the presence of realistic noises. The metric is the operating window (OW). The OW is the range in some input noise that produces a fixed failure rate in the failure modes. It can be thought of as an inverse method of measuring the ratio of output variance to input variance. The OW is determined while keeping the magnitude of some aggravating noise—the stressing noise—large and controlled. This allows the OW to be measured quickly. This OW approach has proved in practice to be very superior to the traditional ways of trying to develop reliability.

Optimal maintenance—replacement policy under imperfect maintenance

Abstract During a given planning period, in order to have the system working at or below a fixed failure rate, it may be necessary to replace the system to minimize the expected total cost. Preventive maintenance (PM) or replacement should be performed whenever the system reaches the maximum failure rate. This paper formulates a cost model and a branching algorithm to determine the number of PM interventions to be performed between each replacement and the number of such replacements during the planning period to minimize the expected total cost. Adjustment of the failure rate for the system degradation after each PM intervention and inflationary trends in cost factors are also incorporated. Numerical illustration and computational times have been presented.