Tolerance Intervals Research Articles

Voltammetric determination of pilocarpine hydrochloride in ophthalmic solutions

An express method for the determination of pilocarpine hydrochloride (PHC) in ophthalmic solutions based on titration of the analyte with photogenerated iodine obtained by irradiation of potassium iodide in the presence of a mixture of sensitizers (sodium eosinate:fluorescein:auramine in a molar ratio of 1:1:1) at pH 5.6 has been developed. The titrant content in the cell was controlled by the voltammetric method (amperometric titration with two polarized electrodes): during the PHC titration a decrease in the current strength in the circuit of the amperometric installation was observed. Stabilization of the current in the circuit of the amperometric installation indicated the completeness of the reaction, and, thus provided the possibility of estimation of the PHC content in a dosage form. The measured generation time required to replenish the loss of titrant upon further irradiation of the solution was also used to calculate the PHC content in the preparation. Testing of the developed technique was carried out on an ophthalmic drug «Pilocarpine, eye drops 1%». Introduction of more than 20.0 g of boric acid used as a preservative agent into the cell resulted in a slight underestimation of the PHC content. The determined PHC content in the sample of series 60918 is 0.93 – 0.94% (measured by generation time) is lower than the tolerance interval set by order of the Ministry of Health of the Russian Federation No. 751n, October 26, 2015 (0.95 – 1.05%). The PHC content in other samples falls within the recommended range, which indicates that the drug quality complies with GMP standards. A linear dependence of the analytical signal on the PHC concentration is observed in the range of 15 – 500 μg. The calculated detection and quantitation limits are 5.6 and 18.6 μg, respectively. The developed photochemical method for PHC determination in the drug «Pilocarpine, eye drops 1%» meets the requirements set forth in the manual for the validation of bioanalytical methods. The method is easy to use and does not require expensive equipment.

Content‐adjusted tolerance intervals via bootstrap calibration

Tolerance intervals (TIs) are commonly employed in numerous industries, ranging from engineering to pharmaceuticals. However, closed‐form TIs are unavailable for most distributions. Although some approximate methods can be used to obtain TIs, coverage probabilities (CPs) of these TIs cannot achieve the nominal level, or can be even far different from the nominal level. In this study, we propose two content‐adjusted procedures for TIs based on bootstrap. The first one is based on the bootstrap sample quantile, while the second one is based on the asymptotic normality of empirical distribution. The simulation results show that the two calibration procedures can improve CPs of TIs for some non‐normal distributions according to extensive numerical simulations, and they are both proved to be effective through real data examples.

Image convolution-based experimental technique for flame front detection and dimension estimation: a case study on laminar-to-transition jet diffusion flame height measurement

A computationally-supported experimental technique is presented, to measure height of luminous flames, using convolution and density-based spatial clustering for image processing. The experimental setup employs a high-definition camera array to capture flame imagery from 0°, 45° and 90° visualization planes. The volumetric fuel flow was ranged from 350 to 1800 cc min−1 and images of the resulting flame structure were captured and measured. Results show that output measurements are affected by both the volumetric fuel flow and the visualization plane. Whilst the former is evidently the most significant factor, the latter was found to be relevant, since several flame features, particularly, flame tilt and flickering, are only perceivable through specific visualization planes; attributed to uneven flame structure due non-homogeneous thermal stress. The experimental technique proposed yields an overall statistical tolerance of 1.29 cm and an expanded uncertainty of 0.609 cm (∼11.5%). From these results, the test is considered successful and the proposed experimental technique is deemed to be on par with the already existing ones. The utilization of spatial density clustering of image gridded data has only been tested for this implementation; being severely constrained by the sample size and density variability of the data. Consequently, care should be exercised. Nonetheless, this approach was found to inherently recognize flame front edge, and mitigate variations of pixel value due change in flame intensity, normalizing image processing, hence, it is proposed as a viable alternative for flame feature/structure visualization and estimation, and further research is encouraged.

Confidence Interval, Prediction Interval and Tolerance Interval for the Skew Normal Distribution: A Pivotal Approach

The class of skew normal distributions, introduced by Azzalini (1985), which is an asymmetric distribution and allows the presence of skewness. In this paper, we propose the pivotal quantity approach to construct the confidence interval for the mean, prediction interval for the mean of the future sample, and tolerance interval for the quantile. The fiducial distribution is also studied. Moreover, the performances of all the proposed confidence intervals are investigated through the Monte Carlo simulation. The pivotal quantity is a common method for calculating confidence intervals, which is used to construct confidence intervals in this paper. And the convergence of the obtained confidence interval is illustrated by the figures. Finally, a real data is used to explain proposed intervals in real life.

Statistical tolerance–cost–service life optimization of blade bearing of controllable pitch propeller considering the marine environment conditions through meta-heuristic algorithm

Abstract Blade bearing is the key mechanism of the controllable pitch propellers (CPPs) to adjust the pitch to change the thrust. In the marine environment, wear and deformation of the contact surface of the blade bearing are quite large, which may result in leakage to reduce the service life of CPP. However, most studies on tolerance optimization of blade bearing disregard deformations and wear, and it could result in unreasonable tolerances and impair the CPP’s service life. In this paper, to establish the statistical tolerance–cost–service life optimization model of the blade bearing of the CPP considering the marine environment effects in propellers, a prediction model about the relationship between the thrust and rotation speed of the CPP considering environment conditions of wind, wave, and ocean currents is constructed. Based on this, the wear and deformation are simulated according to the predicted rotation speed in the marine environment. Considering the deformation and wear in the marine environment, a tolerance analysis model of the assembly deviations of the blade bearing is introduced, and the assembly characteristics and functional requirements are established and converted into probability constraints to establish the service-life model based on statistical tolerance analysis and Monte Carlo simulation methods. Afterward, a statistical tolerance–cost–service life optimization model is established and transformed into a single-objective optimization problem through the normalization method and the weighted sum method, and solved by a meta-heuristic algorithm named cuckoo search. Finally, the application of the proposed model is demonstrated through a case involving the blade bearing of a CPP, and the optimized results show that the manufacturing cost of the blade bearing is reduced and its service life is extended.

Security engineering problems: determination of tolerance intervals for azimuthal positional errors

Security engineering problems: determination of tolerance intervals for azimuthal positional errors

Adaptive benchmarking design for additive manufacturing processes

Standards enabling the objective tolerancing and evaluation of dimensional and geometrical performances of additive manufacturing (AM) printers are still missing. The design, printing and measurements of geometrical benchmark test artefacts (GBTA) is the current solution proposed in literature. However, the current GBTA with fixed dimensions cannot cover most of the available printing area of printers with large building platform dimensions. This article proposes to solve this problem by developing an adaptive GBTA design whose main dimensions can be adapted to any common 3D printer. Moreover, an innovative design is implemented to decrease the risk of warping. The adaptive GBTA will then be used to characterise the performances of two different architecture material extrusion printers (Ultimaker 2+ and Pollen AM Series MC). Dimensional and geometrical accuracy, as well as top surface topography, were evaluated. The Ultimaker printer could reproduce features with maximum deviations below the tolerance interval (IT) 13 of the ISO 286-1, while the Pollen machine achieved a higher IT of 15 or 16. The highest geometrical deviations were observed for the coaxiality of cylinders oriented along the build direction (Ultimaker: 0.250 mm and Pollen: 0.497 mm). Top surface topography exhibited higher Ra values for Pollen (13.7 µm) than for Ultimaker 2+ (4.9 µm). The performances of the Pollen printer were lower than the Ultimaker machine in terms of surface topography, dimensional and geometrical accuracy. The proposed adaptive GBTA design covers most of the printing areas exhibited by Pollen and Ultimaker printers and offers flexibility to test other printers even with larger or smaller dimensions.

Analytical quality-by-design optimization of UHPLC method for the analysis of octreotide release from a peptide-based hydrogel in-vitro

In this article, a UHPLC-PDA method has been developed using the quality-by-design (QbD) principles for the determination of the therapeutic peptide – octreotide – in its in vitro released samples. Due to the complexity of the peptide-based hydrogel matrix a reliable separation of the analyte from the matrix has to be performed. Risk assessment and multivariate analysis were employed for the method evaluation. Following method scouting towards the selection of appropriate and rapid UHPLC operative mode, quality risk assessment tools were applied to set the critical method parameters (CMPs) to be considered in screening phase. The effects of CMPs on critical method attributes (CMAs) were assessed further by means of a screening design. A response surface methodology was utilized to model CMAs as a function of the selected CMPs and the optimum separation conditions were additionally evaluated using desirability function. The method operable design region was complimented by establishment of a robust zone using Monte Carlo simulation and capability analysis. The method was validated in the range of 1 – 20 μg /mL using the accuracy profiles as a graphical decision-making tool. The β-expectation tolerance intervals was within the pre-set acceptance criteria of ± 10% meaning that 95% of future results will be included in the defined bias limits. The relative bias was varied between ─ 0.8% and 1.4% and the RSD values for repeatability and intermediate precision were below to 2.8% in all cases. The achieved limit of detection (LOD) and the lower limit of quantification (LLOQ) were adequate for the specific purpose and found to be 0.3 and 1 μg /mL, respectively. The developed method was successfully applied to the analysis of octreotide in in-vitro drug release samples obtained from peptide-based hydrogels.

Wavelet Transformation and Spectral Subtraction Method in Performing Automated Rindik Song Transcription

Rindik is Balinese traditional music consisting of bamboo rods arranged horizontally and played by hitting the rods with a mallet-like tool called "panggul". In this study, the transcription of Rindik's music songs was carried out automatically using the Wavelet transformation method and spectral subtraction. Spectral subtraction method is used with iterative estimation and separation approaches. While the Wavelet transformation method is used by matching the segment Wavelet results with the Wavelet result references in the dataset. The results of the transcription were also synthesized again using the concatenative synthesis method. The data used is the hit of 1 Rindik rod and a combination of 2 Rindik rods that are hit simultaneously, and for testing the system, 4 Rindik songs are used. Each data was recorded 3 times. Several parameters are used for the Wavelet transformation method and spectral subtraction, which are the length of the frame for the Wavelet transformation method and the tolerance interval for frequency difference in spectral subtraction method. The test is done by measuring the accuracy of the transcription from the system within all Rindik song data. As a result, the Wavelet transformation method produces an average accuracy of 83.42% and the spectral subtraction method produces an average accuracy of 78.51% in transcription of Rindik songs.

Machine Learning-Based COVID-19 Patients Triage Algorithm Using Patient-Generated Health Data from Nationwide Multicenter Database.

IntroductionA prompt severity assessment model of patients with confirmed infectious diseases could enable efficient diagnosis while alleviating burden on the medical system. This study aims to develop a SARS-CoV-2 severity assessment model and establish a medical system that allows patients to check the severity of their cases and informs them to visit the appropriate clinic center on the basis of past treatment data of other patients with similar severity levels.MethodsThis paper provides the development processes of a severity assessment model using machine learning techniques and its application on SARS-CoV-2-infected patients. The proposed model is trained on a nationwide data set provided by a Korean government agency and only requires patients’ basic personal data, allowing them to judge the severity of their own cases. After modeling, the boosting-based decision tree model was selected as the classifier while mortality rate was interpreted as the probability score. The data set was collected from all Korean citizens with confirmed COVID-19 between February 2020 and July 2021 (N = 149,471).ResultsThe experiments achieved high model performance with an approximate precision of 0.923 and area under the curve of receiver operating characteristic (AUROC) score of 0.950 [95% tolerance interval (TI) 0.940–0.958, 95% confidence interval (CI) 0.949–0.950]. Moreover, our experiments identified the most important variables affecting the severity in the model via sensitivity analysis.ConclusionA prompt severity assessment model for managing infectious people has been attained through using a nationwide data set. It has demonstrated its superior performance by surpassing that of conventional risk assessments. With the model’s high performance and easily accessible features, the triage algorithm is expected to be particularly useful when patients monitor their health status by themselves through smartphone applications.

Setting Multivariate and Correlated Acceptance Limits for Assessing the Conformity of Items

Many industrial products, foodstuffs and environmental samples are checked for values of different chemical parameters against tolerance limits or intervals defined in a specification or legislation. In some cases, the measured values of the different parameters are correlated due to how materials are obtained, chemical constraints and/or due to the simple fact that determinations are performed by multi-analyte procedures that share analytical operations and effects. In these cases, instead of defining an acceptance criterion for each measured value on the tested item separately based on the respective measurement uncertainty, the multivariate problem should be addressed by defining multivariate criteria. These multivariate criteria are set for a maximum total risk of wrong conformity decisions that is a complex function of all particular risks of the item being rejected or accepted by comparing each measured value with its respective limit. Computational tools have been developed to estimate the total specific risk of an item being wrongly considered to conform or not to conform with tolerance limits for various components when the measured values are independent or correlated. However, these tools must be applied for each test to check if the total specific risk is acceptable. This work presents a tool for setting multivariate acceptance limits applicable to correlated measurements and referenced to a defined total specific risk. The acceptance limits allow the decision about conformity of an item based on the simple comparison of the measured values with the acceptance limits. The acceptance limits are estimated by a user-friendly and iterative tool implemented in a MS-Excel spreadsheet and available in the Supplementary Material. This tool is successfully applied to various conformity problems. Acceptance limits based on informative and non-informative prior information are compared for a critical review of the merits and problems associated with Bayesian or frequentist conformity assessments.

Impact of resource-based conditional interaction on cooperation in spatial social dilemmas

Due to the contradiction between the finiteness of resources and people’s infinite demand for them, we cannot deny the impact of the limited resources on human behavior. To this end, we construct a novel resource-based conditional interaction model from a tiny perspective, in which not only can limited resources be redistributed among the population, but resources owned by players also affect whether they can interact with each other or not. To be specific, a player who successfully imitates his neighbor’s strategy will have to pay ɛ proportion of his resources to the opponent as the learning cost. In addition, if and only if the resource difference between the focal player x and one of his neighbors y is within an acceptable tolerance interval τ, they will indisputably interact with each other. We mainly resort to the prisoner’s dilemma game and asynchronous strategy update to verify the effectiveness of the model. By resorting to extensive Monte Carlo simulations, we find that there exists an optimal acceptable tolerance interval τ, varying with the value of cost-to-benefit ratio u, to make the promotion of cooperation the most obvious. We also confirm that players’ irrational behavior can be influenced by this resource-based partner selection. However, if we introduce one kind of minimal resource protection mechanism into our proposed model, the level of cooperation cannot be further elevated, or even be hindered when compared with the case without the minimal resource protection mechanism. In the end, we further verify the robustness and effectiveness of the proposed model through other social dilemmas, network topologies, and synchronous strategy update pattern. To a certain extent, we wish that our efforts can wipe out some barriers for researching the evolution of cooperation within the selfish population.

Left/Right Judgment Task for the Chest Region, Part 1: Performance Outcomes in Healthy Women Compared to Women Post Breast Cancer Treatment

Background: Movement planning and execution involve using our internal representations within motor and sensory areas of our brain. Left/right judgment tasks (LRJTs) are behavioral tests that involve determining the side of the body when shown an image, without performing the movement. Individuals theoretically need to use their working body schemas to complete LRJTs. Objectives: To develop a chest LRJT testing protocol and document performance in healthy women and women post breast cancer (BrCA) treatment. Design: Observational, cohort study. Method: We recruited women with and without a history of unilateral BrCA. Participants provided demographic and health history information online, followed by hand, shoulder, and chest LRJTs. Images were digitally mirrored to create equal numbers of left and right images. Images were presented in random order within each body region. We measured accuracy and response time for LRJTs. Results: A total of 316 healthy women and 160 women post-BrCA treatment competed all testing. The BrCA group was consistently slower and less accurate at performing LRJTs for all 3 regions. The side of the image presented was not associated with performance. Conclusions: We successfully developed a chest LRJT testing method. Performance on LRJT of the upper quarter is diminished after BrCA treatment. We established tolerance intervals for anticipated performance in healthy women for future clinical and research comparisons.

Including material conditions effects in statistical geometrical tolerance analysis of mechanical assemblies

Including material conditions effects in statistical geometrical tolerance analysis of mechanical assemblies

Salting-out homogeneous liquid-liquid microextraction for the determination of azole drugs in human urine: Validation using total error concept.

A salting-out homogeneous liquid-liquid microextraction was proposed for the quantification of four azole drugs in human urine prior to high-performance liquid chromatography analysis. The procedure involved the mixing of the sample with acetonitrile in appropriate volumes followed by the addition of sodium sulfate solution in order to facilitate phase separation. The parameters influencing the extraction performance were studied and optimized using a two-step experimental design. The analytical procedure was thoroughly validated using the accuracy profiles as a graphical decision-making tool. The β-expectation tolerance intervals did not exceed the acceptance criteria of ±15% meaning that 95% of future results will be included in the defined bias limits. The limits of detection of the procedure were satisfactory, ranging between 0.01 and 0.03 μg/mL. The mean analytical bias in the spiking levels was satisfactory and ranged between -10.3 and 4.2% while the relative standard deviation was lower than 5.6%. Monte-Carlo simulations followed by capability analysis were employed to investigate the ruggedness of the sample preparation protocol. The developed method offers advantages compared to previously reported approaches for the same type of analysis including extraction efficiency and scaling down of the sample volume and extraction time.

Rapid Patient-Side Evaluation of Endothelial Glycocalyx Thickness in Healthy Sedated Cats Using GlycoCheck® Software.

The endothelial glycocalyx (EG) determines transvascular fluid fluxes, and influences inflammation, coagulation, and capillary blood flow. The GlycoCheck® software calculates EG thickness using sidestream dark field videomicroscopy recordings. This method has not been evaluated for use in cats. The aim of the present study was to evaluate the use of GlycoCheck® for estimating EG thickness in healthy cats, and to investigate the variability of EG thickness in this population. One hundred and one healthy research-purposed cats were included in the study. The cats were sedated, and a handheld videomicroscope, connected to GlycoCheck® software, was used to evaluate the sublingual microvasculature. The parameters measured included perfused boundary region (PBR, an indirect measurement of EG thickness) in vessels between 5 and 25 μm in diameter, valid vessel density, percentage red blood cell filling, and median red blood cell column width. Heart rate, respiratory rate, pulse oximetry and oscillometric blood pressure readings were also recorded. There were 35 neutered male cats, 11 intact males, 38 neutered females, and 17 intact females. The average age was 63 months (range, 11–160 months). Tolerance intervals for PBR (vessel diameter 5–25 μm) were 1.89–3.00 μm (95% CI, lower limit 1.76–2.04, upper limit 2.83–3.13 μm); for valid vessel density were 73.33–333.33 μm/mm2 (95% CI, lower limit 77.00–99.33, upper limit 312.67–350.33 μm/mm2); for percentage red blood cell filling were 59.85–85.07% (95% CI, lower limit 58.97–63.33, upper limit 83.07–88.20 %); and for median red blood cell column width were 5.63–8.59 μm (95% CI, lower limit 5.28–6.07, upper limit 8.14–9.51 μm). There was a negative association between median red blood cell column width and body weight (p = 0.007). The median red blood cell column was significantly wider in intact females when compared to spayed females (p = 0.033). The GlycoCheck® analysis was easily performed in healthy sedated cats. Clinical variables did not have an effect on the EG thickness. These results suggest that this technique could be valuable for evaluation of the EG and microvascular parameters in cats.

Assessing Uncertainty in Plutonium Production Estimates Based on the Isotope Ratio Method

Independent estimates of lifetime plutonium production can be made using forensic measurements of characteristic indicator isotope ratios in core structural elements in shut-down nuclear reactors. Incomplete knowledge of a reactor’s operational history, including fuel burnup, as well as uncertainties in nuclear cross-section data, can significantly affect such plutonium estimates, making it potentially difficult to match estimates with a state’s declaration. Monte Carlo methods and sensitivity analysis techniques are used to assess the propagation of different uncertainties and their impact on plutonium estimates in infinite lattice models of a heavy-water moderated reactor (CANDU 6) and a graphite-moderated reactor (the 5 MWe reactor in North Korea), with titanium-48/titanium-49 and boron-10/boron-11 as the respective indicator isotope ratios. A tolerance interval model, with specified confidence levels, rather than one based on mean values and standard deviations, is proposed for assessing plutonium estimates based on isotope ratios measurements.

On the identification of the probability density function of a dimension from data with measurement errors

Metrology tools are applicable to check whether dimensions lay within their tolerance intervals. However, measurement errors cannot be avoided. This paper develops a method to partially correct the effect of such errors in case their probability density function is known. We assume that the probability density function associated with the measured dimension is available, for instance identified after multiple parts are manufactured and their dimension is measured. In this context, the probability density function of the measured value is the convolution product between the probability density functions of the measurement error and of the true value, respectively. Therefore, characterizing the true value is a challenging task, as this involves a deconvolution. We propose a procedure based on: (i) the transformation of the integral involved in the convolution product into a sum using numerical integration; (ii) the definition of a set of non-linear equalities solved using Newton-Raphson's procedure. An application example is used to discuss the relevance of the proposed method and the influence of various parameters on the results.

Verifying Valve Lash in Engine Assembly Using Tolerance Interval Method for Monitoring Process Performance

The process capability refers to the ability of a process to produce parts or provide services that are able to meet the given specification requirement. The process capability is commonly measured by process capability indices (PCIs) such as Cp and Cpk to evaluate process yield, process consistency, and statistical variation compared to the specification. Most of the component or hardware manufacturing industries require exhibiting a process capability index (Cpk) of 1.33 or above. This paper presents an alternate approach for monitoring a process to verify valve lash in engine assembly. Valve lash is the gap between the rocker arm and the valve spring in an engine and this gap must be tightly controlled due to the critical role valves play in engine performance. Achieving and maintaining process capability of valve lash of 1.33 is difficult and unrealistic due to the nature of the assembly process and multiple factors being involved. Using historical data collected from 1200 valves in 100 engines assembly, this paper illustrates the tolerance interval method for monitoring the process performance of valve lash in engine assembly is more practical and economical as compared to the conventional process capability.

Statistical Analysis of the Thermal Performance and Reliability in the Heat Sink With Heat Pipes for the Power Electronics Module

Cooling devices are often used with power electronics systems to allow them to operate stably over long periods of time, they help guarantee not only thermal performance but also reliability. To understand the performance of these cooling devices it is important they are verified by various types of testing, also the test results themselves should be quantified and analyzed using recognized statistical methods. For this paper, we investigated an air-cooled heat sink with heat pipes by conducting heat load, high/low temperature storage limits, accelerated life, and transport vibration tests. The collected experimental data were analyzed by statistical methods such as the independent samples t-test, the paired samples t-test, correlation analysis, process capability analysis, and the tolerance interval analysis. A newly manufactured power conditioning system had one heat sink on which the two power electronics modules were attached while providing a heat load of up to 3.2 kW. It was found that there was no deterioration in the thermal performance of the heat sink due to vibrations while being transported from the Republic of Korea to the United States. If such a heat sink is used over 20 years, it is anticipated that there will be a performance degradation of 6.2% over those years with a 95% confidence level for a B10 life. Based on our accelerated life testing, the heat sink is capable of dealing with a heat load of up to 3.1 kW over the design lifetime of 20 years. Thermal engineers should eventually introduce design margins in consideration of the reduction in quality and reliability that can occur over the lifetime of a cooling device.