Sequential Probability Ratio Test Research Articles

Economic modelling and optimisation of SPRT-based quality control schemes for individual observations

In many industrial processes, it may not be practical to obtain sample sizes larger than one due to various reasons. As a result, practitioners must rely on control charts based on individual observations for statistical process monitoring and control. The sequential probability ratio test (SPRT) chart is an appropriate solution for such situations. Existing literature predominantly delves into the statistical aspects of designing or optimising an SPRT chart, neglecting the economic and associated design aspects. However, past experience suggests that statistical design may not always be optimal from an economic perspective. This paper aims to bridge this research gap by proposing a two-stage Markov chain approach to develop an economic model for the optimal design of the SPRT chart with individual observations. Following the principles of economic-statistical designs, optimal parameters are determined by solving a mixed-integer non-linear programming problem that minimises the long-run cost per item while ensuring compliance with practical constraints. Through an extensive study, we find that the economic performance of the SPRT chart surpasses that of competing individual control charts in many cases. This indicates that the economic-statistical design of the SPRT chart can yield significant economic benefits while maintaining desirable statistical properties. Moreover, enhancements have been introduced to refine the optimal design of the SPRT chart, retaining excellent overall performance across a wide range of shifts. Finally, we provide two industrial examples to illustrate the effectiveness of the proposed SPRT chart.

Expanding Access to Noninvasive Prenatal Diagnosis for Monogenic Conditions to Consanguineous Families.

Cell-free fetal DNA exists within the maternal bloodstream during pregnancy and provides a means for noninvasive prenatal diagnosis (NIPD). Our accredited clinical service offers definitive NIPD for several autosomal recessive (AR) and X-linked conditions using relative haplotype dosage analysis (RHDO). RHDO involves next-generation sequencing (NGS) of thousands of common single nucleotide polymorphism (SNPs) surrounding the gene of interest in the parents and an affected or unaffected offspring to conduct haplotype phasing of the high- and low-risk alleles. NGS is carried out in parallel on the maternal cell-free DNA, and fetal inheritance is predicted using sensitive dosage calculations performed at sites where the parental genotypes differ. RHDO is not currently offered to consanguineous couples owing to the shared haplotype between parents. Here we test the expansion of RHDO for AR monogenic conditions to include consanguineous couples. The existing sequential probability ratio test analysis pipeline was modified to apply to SNPs where both parents are heterozygous for the same genotype. Quality control thresholds were developed using 33 nonconsanguineous cases. The performance of the adapted RHDO pipeline was tested on 8 consanguineous cases. The correct fetal genotype was predicted by our revised RHDO approach in all conclusive cases with known genotypes (n = 5). Haplotype block classification accuracies of 94.5% and 93.9% were obtained for the nonconsanguineous and consanguineous case cohorts, respectively. Our modified RHDO pipeline correctly predicts the genotype in fetuses from consanguineous families, allowing the potential to expand access to NIPD services for these families.

Bayesian sequential probability ratio test for vaccine efficacy trials

Bayesian sequential probability ratio test for vaccine efficacy trials

An integrated optimal-GICP design for the SPRT control chart with estimated process parameters based on the average number of observations to signal

ABSTRACT As a variable-sample-size control scheme, the sequential probability ratio test (SPRT) chart is favoured due to its sensitivity and high sampling efficiency. It is frequently documented that the SPRT chart inspects only a small number of observations at each sampling stage, making the said chart extremely appealing to quality engineers. In the current literature, most developments of the SPRT chart are established based on the average run length and average time to signal metrics. However, these metrics do not consider sampling efficiency. In this paper, we develop two optimal designs of the SPRT chart, based on (i) the average value of the average number of observations to signal (AANOS) and (ii) the expected value of the AANOS, with consideration of Phase-I process parameter estimation. We develop a model that integrates the concept of optimization and the guaranteed in-control performance (GICP) framework to neutralize the adverse effects of parameter estimation. Results show that the proposed optimal-GICP design preserves satisfactory out-of-control performances for moderate and large mean shifts, while keeping the false alarm rates at reasonably low levels. Finally, we illustrate an example of the SPRT chart with estimated process parameters for monitoring loop height measurements from a wire bonding dataset.

Modified Sequential Probability Ratio Test Based on Truncated Life Tests on the Exponential Distribution Functions

Modified Sequential probability ratio test (MSPRT) technique helps to increase the reliability and speed of stabilization detection on the Non homogenous poison process (NHPP) with the maximum number of software faults to reduce error between the consumer risk and producer risk, with the time cumulative system of hours. Modified sequential probability ratio test can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. The proposed result suggests MSPRT along with maximum number of faults contained in software would be useful in speeding up decision making while dealings error in a software reliability weekly index, we show the graphical performance of the MSPRT and average sample number (ASN).

Tests for skewness parameter of skew log Laplace distribution

Laplace probability density function with additional shape parameter that regulates the degree of skewness is a skew Laplace distribution. The various forms of skew Laplace distribution are found in the literature, the distributions defined by Mc Gill (1962), Holla and Bhattacharya (1968), Lingappaiah (1988), Fernandez and Steel (1998). The skew log Laplace distribution is the probability distribution of a random variable whose logarithm follows a skew Laplace distribution. In this paper, the classical optimum tests for skewness parameter of skew log Laplace distribution (SLLD) derived from Lingappaiah (1988) distribution are discussed. Uniformly most powerful test, uniformly most powerful unbiased test and Wald’s sequential probability ratio test for skewness parameter are compared. The exact likelihood ratio test and Neyman structure test for testing skewness parameter when scale parameter is known are derived. Finally, the underreported income of Road Transport Company is analysed on the basis of the tests derived in this paper.

A two-sided SPRT control chart for process mean

ABSTRACT A two-sided sequential probability ratio test (SPRT) control chart for monitoring the mean of a normal process is proposed in this paper. Its mechanism is based on the SPRT for the mean of a normal distribution that is extended for a two-sided alternative. The exact statistical performance measures of this chart are obtained using a Markov chain approach. An approach to design the chart such that it has a specified in-control performance and the optimal out-of-control performance for detecting a mean shift of a particular size is provided. The statistical performance of this chart is numerically compared with that of various competing charts in the existing literature. It is found that the proposed chart outperforms all these charts for detecting a mean shift of any size. An example to illustrate the mechanism of the chart is provided.

A deep-learning approach for dynamic region merging applied to feature extraction from borehole microresistivity images

The primary purpose of processing borehole resistivity images is to identify and extract high (or low) resistivity anomalous areas, which are associated with resistive fractures and dissolved pores. To improve the accuracy and applicability of these models, a new intelligent method combining dynamic-region merging (DRM) with a deep-learning network (U-net) is proposed. The superpixel method, also referred to as linear spectral clustering (LSC), was applied to segment fractures and dissolved pores that are represented by a resistivity contrast in the original resistivity images. The sequential probability ratio test technique was then used to implement the DRM procedure to group many oversegmented small regions. A convolutional neural network (U-net architecture) model was used to automatically identify geologic features with various scales. The trained neural network was then used to identify the segmented resistivity images that had been processed by the DRM. The results showed that the superpixel algorithm and U-net combination significantly improved the accuracy of the classification and identification of fractures and dissolved pores in different test data sets. Moreover, it solved the problem of few-shot learning, enabling a pretrained model to generalize over new data categories.

A holistic physics-based observer for online flooding and ECSA loss detection in FCEV

This paper addresses the critical need for improving fuel cell electric vehicles (FCEVs) reliability to promote their commercialization. A physics-based observer that combines an Extended Kalman Filter (EKF) with a Sequential Probability Ratio Test (SPRT) has been employed to address two major failure modes in FCEV stacks: flooding and reduction of Electrochemical Active Surface Area (ECSA). Furthermore, the observer estimates the hidden states of a standard automotive airpath system to enable state-feedback control. Therefore, the proposed observer is a novel approach which holistically tackles three coupled problems (i.e., flooding, ECSA loss, and airpath state estimation) which are typically addressed individually. Additionally, the observer is computationally affordable and relies solely on typical vehicle sensors. The observer performance has been validated through simulations, testing various dynamic scenarios in the presence of flooding, ECSA loss failures, and sensors uncertainty. The estimation errors have been confined within a 3% error band for all test cases while the health indicators coherently responded in the presence of faults.

Bayesian safety surveillance with adaptive bias correction.

Postmarket safety surveillance is an integral part of mass vaccination programs. Typically relying on sequential analysis of real-world health data as they accrue, safety surveillance is challenged by sequential multiple testing and by biases induced by residual confounding in observational data. The current standard approach based on the maximized sequential probability ratio test (MaxSPRT) fails to satisfactorily address these practical challenges and it remains a rigid framework that requires prespecification of the surveillance schedule. We develop an alternative Bayesian surveillance procedure that addresses both aforementioned challenges using a more flexible framework. To mitigate bias, we jointly analyze a large set of negative control outcomes that are adverse events with no known association with the vaccines in order to inform an empirical bias distribution, which we then incorporate into estimating the effect of vaccine exposure on the adverse event of interest through a Bayesian hierarchical model. To address multiple testing and improve on flexibility, at each analysis timepoint, we update a posterior probability in favor of the alternative hypothesis that vaccination induces higher risks of adverse events, and then use it for sequential detection of safety signals. Through an empirical evaluation using six US observational healthcare databases covering more than 360 million patients, we benchmark the proposed procedure against MaxSPRT on testing errors and estimation accuracy, under two epidemiological designs, the historical comparator and the self-controlled case series. We demonstrate that our procedure substantially reduces Type 1 error rates, maintains high statistical power and fast signal detection, and provides considerably more accurate estimation than MaxSPRT. Given the extensiveness of the empirical study which yields more than 7 million sets of results, we present all results in a public R ShinyApp. As an effort to promote open science, we provide full implementation of our method in the open-source R package EvidenceSynthesis.

Assessment of the learning curve of peribulbar blocks using the Learning-Curve Cumulative Sum Method (LC-CUSUM): an observational study

IntroductionThis study aimed to assess the learning curves of peribulbar anesthesia and estimate the number of blocks needed to attain proficiency. MethodsAnonymized records of sequential peribulbar blocks performed by first-year anesthesia residents were analyzed. The block sequential number and the outcomes were extracted from each record. Success was defined as a complete sensory and motor block of the eye, and failure was defined as an incomplete block requiring supplemental local anesthetic injections or general anesthesia. Learning curves using the LC-CUSUM method were constructed, aiming for acceptable and unacceptable failure rates of 10% and 20%, and 10% probability of type I and II errors. Simulations were used to determine the proficiency limit h0. Residents whose curves reached h0 were considered proficient. The Sequential Probability Ratio Test Cumulative Sum Method (SPRT-CUSUM) was used for follow-up. ResultsThirty-nine residents performed 2076 blocks (median = 52 blocks per resident; Interquartile Range (IQR) [range] = 27–78 [4–132]). Thirty residents (77%) achieved proficiency after a median of 13 blocks (13–24 [13–24]). ConclusionsThe LC-CUSUM is a robust method for detecting resident proficiency at peribulbar anesthesia, defined as success rates exceeding 90%. Accordingly, 13 to 24 supervised double-injection peribulbar blocks are needed to attain competence at peribulbar anesthesia.

A truncated test scheme design method for success-failure in-orbit tests

Based on the success-failure test feature of in-orbit tests (IOTs) for typical space equipment, this paper presents a method for designing a truncated test scheme for success-failure in-orbit tests. With this method, a small upper boundary of the sample size for the IOT verification test can be obtained before the test starts. The method introduces the truncated Bayes-sequential mesh test (SMT) method into the design of the IOT verification test scheme and greatly compresses the continuous test area by incorporating optimization theory, resulting in a smaller upper limit of the IOT sample size. First, this paper derives a specific calculation formula for the Bayes-SMT critical line. Second, the Markov chain model is adopted to calculate the occurrence probabilities of each acceptance and rejection point through state transition. Finally, an optimal truncated test optimization algorithm based on the augmented lagrangian genetic algorithm is proposed. Simulation tests show that, compared with the classical single sampling method, the truncated sequential probability ratio test method, the truncated SMT method, and the truncated Bayes-SMT method based on step-by-step calculation, the method presented in this paper can be used to obtain a sequential test scheme with smaller truncated sample size.

Location Privacy-Aware and Energy-Efficient Offloading for Distributed Edge Computing

Driven by the ever-increasing scale and intensity of the computing tasks arising from various mobile applications, distributed edge computing has fostered wide research interests. It can effectively reduce the task processing delay by partitioning the original large-scale task into several small subtasks and offloading them to multiple edge nodes (ENs) for parallel computing. In edge computing, as the mobile user usually tends to offload computing tasks to closer ENs to save transmit power, the attacker may stealthily infer user location by exploiting this feature. Although there have been some pioneering works on offloading related location privacy, they mainly focused on the scenario where each task can only be offloaded to a single EN, and may not be directly applicable to distributed edge computing. Besides, the privacy issues considered in existing works are mainly based on good heuristics, and there is still a lack of concrete examples of location privacy attacks in edge computing. To the best of our knowledge, the location privacy issue in distributed edge computing still remains largely unexplored in existing literature. With this consideration, a location inference attack based on matrix sequential probability ratio test (MSPRT) is identified in this work. Besides, a countermeasure based on dynamic multi-EN selection is proposed, together with a location privacy-aware and energy-efficient distributed offloading scheme based on the generic Lyapunov optimization framework. Both theoretic analysis and simulations based on real-world channel measurements are employed to validate the feasibility of the identified MPSRT attack and the effectiveness of the proposed defense scheme.

Statistical rules for safety monitoring in clinical trials.

Protecting patient safety is an essential component of the conduct of clinical trials. Rigorous safety monitoring schemes are implemented for these studies to guard against excess toxicity risk from study therapies. They often include protocol-specified stopping rules dictating that an excessive number of safety events will trigger a halt of the study. Statistical methods are useful for constructing rules that protect patients from exposure to excessive toxicity while also maintaining the chance of a false safety signal at a low level. Several statistical techniques have been proposed for this purpose, but the current literature lacks a rigorous comparison to determine which method may be best suitable for a given trial design. The aims of this article are (1) to describe a general framework for repeated monitoring of safety events in clinical trials; (2) to survey common statistical techniques for creating safety stopping criteria; and (3) to provide investigators with a software tool for constructing and assessing these stopping rules. The properties and operating characteristics of stopping rules produced by Pocock and O'Brien-Fleming tests, Bayesian Beta-Binomial models, and sequential probability ratio tests (SPRTs) are studied and compared for common scenarios that may arise in phase II and III trials. We developed the R package "stoppingrule" for constructing and evaluating stopping rules from these methods. Its usage is demonstrated through a redesign of a stopping rule for BMT CTN 0601 (registered at Clinicaltrials.gov as NCT00745420), a phase II, single-arm clinical trial that evaluated outcomes in pediatric sickle cell disease patients treated by bone marrow transplant. Methods with aggressive stopping criteria early in the trial, such as the Pocock test and Bayesian Beta-Binomial models with weak priors, have permissive stopping criteria at late stages. This results in a trade-off where rules with aggressive early monitoring generally will have a smaller number of expected toxicities but also lower power than rules with more conservative early stopping, such as the O-Brien-Fleming test and Beta-Binomial models with strong priors. The modified SPRT method is sensitive to the choice of alternative toxicity rate. The maximized SPRT generally has a higher number of expected toxicities and/or worse power than other methods. Because the goal is to minimize the number of patients exposed to and experiencing toxicities from an unsafe therapy, we recommend using the Pocock or Beta-Binomial, weak prior methods for constructing safety stopping rules. At the design stage, the operating characteristics of candidate rules should be evaluated under various possible toxicity rates in order to guide the choice of rule(s) for a given trial; our R package facilitates this evaluation.

Fault-Tolerant SINS/Doppler Radar/Odometer Integrated Navigation Method Based on Two-Stage Fault Detection Structure.

To improve the reliability of strapdown inertial navigation system (SINS)/Doppler radar/odometer integrated navigation system, the federated Kalman filter with two-stage fault detection structure is designed, and a fault-tolerant SINS/Doppler radar/odometer integrated navigation method is proposed. Firstly, the pre-fault detection module sets before the local filter, and the residual chi-square test in the carrier coordinate system is selected to detect the abrupt faults of Doppler radar and odometer. Then, the secondary-fault detection module emplaces between the local filter and the main filter, and the sequential probability ratio test (SPRT) is selected to further detect the ramp faults that are difficult to detect by the residual chi-square test. To address the limitation of the SPRT in accurately determining the end time of faults, an improved SPRT is proposed. The improved SPRT reduces the influence of historical fault on the fault statistics by introducing forgetting factors to improve its sensitivity to the fault end. The simulation experiment indicates that the proposed method can quickly detect and isolate abrupt and ramp faults, and promptly restore normal operation of the integrated navigation system after the fault ends, effectively improving the fault tolerance and reliability of the integrated navigation system.

The two‐sided SPRT sign charts

AbstractA two‐sided nonparametric sequential probability ratio test (SPRT) control chart for process location is proposed. The mechanism of this chart is based on the SPRT for location based on the signs of the sequential observations that is extended for a two‐sided alternative hypothesis. Approximate expressions that relate the statistical performance measures of this chart with that of its corresponding one‐sided charts are obtained through a simulation study and are shown to be quite accurate. Furthermore, an approach to design the proposed chart is provided. The statistical performance of the proposed chart is numerically compared to that of the two‐sided Shewhart, cumulative sum, and exponentially weighted moving average sign charts for location and it is observed that in general the proposed chart significantly outperforms these charts for detecting a location shift of any size. An example is provided to illustrate the mechanism of the proposed chart. Also, the chart is extended for monitoring process dispersion.

Optimal designs of the omnibus SPRT control chart for joint monitoring of process mean and dispersion

The vast majority of control schemes related to the sequential probability ratio test (SPRT) are designed for the purpose of monitoring only the process mean. Nonetheless, most manufacturing processes are vulnerable to external factors that cause the process mean and variability to change simultaneously. It is, therefore, crucial to consider a joint scheme for monitoring both the location and scale parameters of a production process. In this article, we develop a scheme that combines both mean and variance information in a single SPRT, known as the omnibus SPRT (OSPRT) chart. Expressions for the run-length properties of the OSPRT chart are derived by means of the Markov chain approach. We also propose optimal designs for the OSPRT chart based on two different metrics, i.e. by minimising the average time to signal and the average extra quadratic loss. Through a comprehensive analysis, this article reveals that the optimal OSPRT chart outperforms the classical -S, weighted-loss cumulative sum, absolute-value SPRT, and two maximum weighted-moving-average-type charts. The optimal OSPRT chart also has the advantage of collecting a small number of samples on average before producing a decision. Finally, the implementation of the OSPRT chart is presented with a wire bonding industrial dataset.

Discriminating among Generalized Exponential, Weighted Exponential and Weibull Distributions

In this paper, we consider the problem of discriminating among three different positively skewed lifetime distributions, namely the generalized exponential distribution, the weighted exponential distribution, and the Weibull distribution. All of these distributions have been used quite effectively to analyze positively skewed lifetime data. We use the methods of the ratio of maximized likelihood, the minimum Kolmogorov distance, and the sequential probability ratio test to discriminate among these three distributions. The probability of correct selection is considered for each hypothesis based on several scenarios with Monte Carlo simulation. Real data applications are studied to illustrate the effectiveness of these proposed methods.

Study of a New Software Reliability Growth Model under Uncertain Operating Environments and Dependent Failures

The coronavirus disease (COVID-19) outbreak has prompted various industries to embark on digital transformation efforts, with software playing a critical role. Ensuring the reliability of software is of the utmost importance given its widespread use across multiple industries. For example, software has extensive applications in areas such as transportation, aviation, and military systems, where reliability problems can result in personal injuries and significant financial losses. Numerous studies have focused on software reliability. In particular, the software reliability growth model has served as a prominent tool for measuring software reliability. Previous studies have often assumed that the testing environment is representative of the operating environment and that software failures occur independently. However, the testing and operating environments can differ, and software failures can sometimes occur dependently. In this study, we propose a new model that assumes uncertain operating environments and dependent failures. In other words, the model proposed in this study takes into account a wider range of environments. The numerical examples in this study demonstrate that the goodness of fit of the new model is significantly better than that of the existing SRGM. Additionally, we show the utilization of the sequential probability ratio test (SPRT) based on the new model to assess the reliability of the dataset.

Unsupervised Anomaly Detection in Marine Diesel Engines using Transformer Neural Networks and Residual Analysis

This paper presents a novel unsupervised approach for detecting anomalies in marine diesel engines using a Transformer Neural Network based autoencoder (TAE) and residual analysis with Sequential Probability Ratio Test (SPRT) and Sum of Squares of Normalized Residuals (SSNR). The proposed method can capture temporal dependencies in normal timeseries data without the need for labeled failure data. To assess the effectiveness of the proposed approach, a dataset of faulty data is generated under the same operational profile as the normal training data. The model is trained using normal data, and the faulty data is reconstructed using the trained model. SPRT and SSNR are then used to analyze the residuals from the observed and reconstructed faulty data, with significant deviations exceeding a predefined threshold being identified as anomalous behavior. The experimental results demonstrate that the proposed approach can accurately and efficiently detect anomalies in marine diesel engines. Therefore, this approach can be considered as a promising solution for early anomaly detection, leading to timely maintenance and repair, and preventing costly downtime.