Probability Of False Rejection Research Articles

Quality control validation in veterinary laboratories.

Quality control (QC) validation is used to determine: 1) whether statistical QC procedures are appropriate for detecting medically important errors; and 2) the equality of performance required by different laboratory tests. QC validation is well documented in the medical literature, but we are unaware of studies addressing its application, problems or unique differences in veterinary laboratories. We applied QC validation to automated hematology and biochemistry analyses in our laboratories, with goals of >/= 90% probability of error detection and </= 5% probability of false rejection. Analytical quality requirements in the form of total allowable error were defined using regulatory criteria for human proficiency testing; these were later modified based on clinician and pathologist feedback. Initial QC goals were not met for 14 of 49 (28.6%) analyte-control combinations. Subsequent modifications in methodology, analytical quality requirements and technician training achieved QC goals for all but one analyte. For this analyte (platelet count, low control), nonstatistical QC procedures were emphasized. QC validation was beneficial for clarifying statistical QC performance, and for assessing the need and justification for changes in methods and personnel training. The validation exercise allowed simplification of QC rules, enabled machine flagging of abnormal results, and decreased time and expense associated with QC recording, analysis, problem-solving and reruns. QC validation is recommended for all veterinary laboratories as a useful tool in total quality management.

Use of averages of patient data for quality control

Applicability of Hoffman's average of normals (AON) method was evaluated in quality control (QC) for twenty clinical chemistry assays (ALT, Alb, ALP, AMY, AST, T. Bil, inP, Glu, Ca, Cl, T. Chol, Creat, CK, K, LD, T. Prot., Na, TG, BUN, Uric. A.) performed routinely in the Hospital of Medical Faculty of 9 Eylul University. Consecutive Texas Instruments XL-Dacos patient data were accumulated over 10 days. According to the guidelines developed by Cembrowsky et. al. for the implementation of average of patients (AOP) (also known as AON) procedure, the patient population mean, *p, population standard deviation, Sp, the ratio of Sp/Sa (Sa, the analytical standard deviation), and the approximate number of patient results averaged. Np (with Ped=0.50) were determined from the nomogram constructed by Cembrowsky et. al., illustrating the relationship between Np, Sp/Sa, and the probability of detecting a 2Sa shift (Ped) when the probability of false rejection, Pfr, is 0.01. The control limits and the truncation limits were selected as *p±2Sp and *p±2.58×Sp√Np, respectively. The estimated values were assessed for the applicability of AOP procedures in the clinical laboratory. We conclude that the AOP procedure is a valuable tool for instrument monitoring as an adjunct to more costly standard QC procedures and is also an efficient, cost-effective and rapid way of collecting appropriate information on large number of patients.

Genetic algorithms-based design and optimization of statistical quality-control procedures

In general, one cannot use algebraic or enumerative methods to optimize a quality-control (QC) procedure for detecting the total allowable analytical error with a stated probability with the minimum probability for false rejection. Genetic algorithms (GAs) offer an alternative, as they do not require knowledge of the objective function to be optimized and can search through large parameter spaces quickly. To explore the application of GAs in statistical QC, I developed two interactive computer programs based on the deterministic crowding genetic algorithm. Given an analytical process, the program "Optimize" optimizes a user-defined QC procedure, whereas the program "Design" designs a novel optimized QC procedure. The programs search through the parameter space and find the optimal or near-optimal solution. The possible solutions of the optimization problem are evaluated with computer simulation.

Accuracy Requirements for Measurement Systems with Uniform and Normal Errors

ABSTRACTAccuracy requirements are usually determined as a percentage of the specification range of the measured part or process. Setting accuracy requirements in this manner results in a wide and unpredictable range of false rejection and acceptance probabilities. This causes extra costs due to either: 1) over specification of measurement systems accuracy requirements; 2) time, effort, retesting, and resolution of false rejections; or 3) system degradation caused by false acceptance of out‐of‐specification parts. Achieving a consistent and known risk of false acceptance is only possible by considering the measured process Cpk, the process's mean in relation to the center of the specification range, and the measurement system error distribution.This paper presents a method for calculating the probabilities of false rejection and false acceptance for a normal process which is measured with, alternately, uniform and normally distributed error. It is shown that under most conditions uniform error causes 20% to 30% higher false rejection and acceptance probabilities. Thus, knowledge of measurement error distribution could provide lower total production cost.

Speaker verification using randomized phrase prompting

Speaker verification is a viable method of controlling access to computer and communications networks and physical places. The system described here is capable of accurately verifying an individual’s claimed identity from a short sample of his or her speech. Design requirements for the system included the following: (1) an enrollment session should take no longer than 3 min; (2) an acceptance or rejection decision should be reached within 20 s; (3) the probabilities of false rejection and false acceptance should be as low as possible; and (4) prompts should be chosen at random from a large number of possibilities. A number of systems have been designed to satisfy the first three requirements [l-3], but do not adequately address requirement (4). Several systems use a single fixed word or phrase as a “voice password” [4,5]. To address requirement (4), the system described here uses a prompting strategy in which phrases are composed at random using a small vocabulary of words. The spoken phrases are compared with word templates derived from enrollment sessions. This strategy introduces the following difficulty. Words occur in the test material in contexts that did not occur in the enrollment material. The context in which a word is spoken influences its pronunciation through coarticulation, caused by limitations in the movement of the speech articulators. These unmodeled coarticulations contribute to the measured dissimilarity between the input speech and the claimant’s word templates, increasing the likelihood of rejecting valid users. A scoring method called likelihood ratio scoring partially overcomes this difficulty. Likelihood ratio scoring is based on an approximation to the likelihood ratio, the ratio of the probability of the observed input assuming it was spoken by the claimant to the probability of the observed input assuming it was spoken by someone else. To compute this approximation, input speech is compared with the claimant’s templates and with the templates of a set of other speakers (who may be other enrolled users) called the ratio set. All templates are derived from enrollment sessions in which the same scripts were read; therefore, the same contexts are represented in the templates. When a new context is encountered in test material, all raw match scores to templates are affected similarly. The likelihood ratio score, however, by virtue of its definition as a ratio, is relatively unaffected. The template matching algorithm, which is otherwise conventional [6], is modified for computation of the likelihood ratio score. In particular, a specialized syntax is used, and additional data from the template match, other than the “recognized” word sequence, are saved. The syntax is constructed to make certain that the algorithm is quite robust with respect to false starts and nonspeech sounds. A reliable enrollment method, in which speaker-specific word templates are computed automatically using several incremental steps, starting with speaker-pooled templates for male and female speakers, was developed. Two real-time prototype systems were developed using Sun-3 workstations with additional processor boards. One such system was tested, simultaneously collecting a large speaker verification database. A rationale was developed for determining the size of the test required to allow hypotheses regarding the system’s true error rates to be tested with stated confidence levels. The remainder of the paper is organized as follows. The speech material used for verification is described in Section 2. The algorithm is then presented in Sec-

Performance Characteristics of Quality Control Systems

The purpose of a quality control program is to monitor analytical systems, detecting errors when they become significant. Quality control rules and procedures can be characterized by their performance characteristics. These characteristics quantitate thepowerofa particular procedure in terms of its probability of error detection (Ped) and probability of false rejection (Pfr. Quality control systems should be designed so as to maximize Pfr and minimize Ped The performance characteristics of many of the more common quality control rules have been determined and are available in the literature. Computer simulation experiments are valuable tools for delineating the characteristics of different quality control rules and procedures, and provide a basis for predicting how effective a given system will be in detecting error.

Implementation of Multirule Quality Control Procedures

Multirule quality control procedures employ combinations of individual quality control rules to increase the probability of error detection without increasing the probability of false rejections to unacceptable levels. Performance characteristics of several example multirule procedures are described, and general recommendations are made for their selection and use. Multistage quality control procedures tailor the control rules employed to the frequency of errors expected during a given phase of analyzer operation. During analyzer startup, sensitive rules are employed; after acceptable analyzer performance is demonstrated, less sensitive rules are used for routine monitoring. As they tend to deteriorate quality control rule performance, between-run variations should be minimized.

Ultrasonic flaw detection in refractory products

Ultrasonic flaw detection can be used to identify in green brick and fired products craters and cracks exposed in dimensions exceeding 0.01 mm. The greatest sensitivity and validity using automatic ultrasonic flaw detection of refractories is ensured by detecting defects with respect to the change in the time of dissemination of ultrasonic oscillations during straight-through sound transmission (time shadow method). With a probability of false rejection of 2.3% in refractories using the time shadow method we can identify surface defects (thermal and other cracks) with a depth of more than 7.5–15 mm, and exposed defects (excess pressing cracks, etc.) whose minimum size exceeds 0.3–0.5 of the thickness of the article.

Assessment of "Average of Normals" quality control procedures and guidelines for implementation.

The capabilities of "Average of Normals" control procedures have been assessed by determining power functions, graphs of the probability of error detection versus the size of analytic error. The power functions indicate that the most important determinants of statistical power are the ratio of the standard deviation of the patient population (Sp) to the analytic standard deviation (Sa), Sp/Sa; the number of data points averaged (N); the control limits (probability for false rejection); truncation limits for selecting the population; and the magnitude of the population lying outside the truncation limits. General guidelines for the implementation of "Average of Normals" are provided, along with a nomogram for the selection of N as a function of Sp/Sa and the probability of error detection. Optimal performance of these procedures may require simulation studies on a per analyte basis.

Feature extraction and decision procedure for automated inspection of textured materials

This paper proposes a general system approach applicable to the automatic inspection of textured material. First, the input image is preprocessed in order to be independent of non-uniformities. A tone-to-texture transform is then performed by mapping the original grey level picture on a multivariate local feature sequence, which turns out to be normally distributed. More specifically, features derived with the help of the Karhunen-Loève decomposition of a small neighbourhood of each pixel are used. A decision as to conformity with a reference texture is arrived at by thresholding the Mahalanobis distance for every realization of the feature vector. It is shown that this approach is optimum under the Gaussian assumption in the sense that it has a minimum acceptance region for a fixed probability of false rejection.

A predictive value model for quality control: effects of the prevalence of errors on the performance of control procedures.

A predictive value model has been developed to describe the usefulness of results from quality control tests or procedures. The model shows that the critical parameters are the probability for false rejection, probability for error detection, and prevalence or frequency of occurrence of analytical errors. When prevalence is low, control procedures should have a low probability for false rejection. When prevalence is high, control procedures should have a high probability for error detection. The predictive value model for a quality control (QC) test is analogous to the predictive value model for a diagnostic test, thus suggesting new strategies for optimizing the performance of QC tests.

A Method for Discriminating Between Failure Density Functions Used In Reliability Predictions

Unless sufficient evidence to the contrary exists, the exponential distribution is often assumed as a model for the failure density function in reliability predictions. The generalized gamma distribution, with known location parameter, is a three parameter distribution which encompasses the exponential, Weibull, gamma and many others. In this paper, (i) maximum likelihood estimation for the three parameters is indicated, (ii) it is noted that these estimators are asymptotically multivariate normally distributed, and (iii) using the distribution of the estimators, probability regions for the estimators of the parameters of the generalized gamma distribution are established for large sample situations. In situations where the generalized gamma can be assumed as the correct density function, the exponential and the Weibull are special cases. A method is presented using experimental or life data for rejecting (with a known probability of false rejection) the Weibull and (or) the exponential functions when the...

A Method for Discriminating between Failure Density Functions Used in Reliability Predictions

Unless sufficient evidence to the contrary exists, the exponential distribution is often assumed as a model for the failure density function in reliability predictions. The generalized gamma distribution, with known location parameter, is a three parameter distribution which encompasses the exponential, Weibull, gamma and many others. In this paper, (i) maximum likelihood estimation for the three parameters is indicated, (ii) it is noted that these estimators are asymptotically multivariate normally distributed, and (iii) using the distribution of the estimators, probability regions for the estimators of the parameters of the generalized gamma distribution are established for large sample situations. In situations where the generalized gamma can be assumed as the correct density function, the exponential and the Weibull are special cases. A method is presented using experimental or life data for rejecting (with a known probability of false rejection) the Weibull and (or) the exponential functions when they do not appear to describe the failure density function of a unit.

Significance Level and Power

Significance testing, as described in most textbooks, consists in fixing a standard significance level $\alpha$ such as .01 or .05 and rejecting the hypothesis $\theta = \theta_0$ if a suitable statistic $Y$ exceeds $C$ where $P_{\theta_0}\{Y > C\} = \alpha$. Such a procedure controls the probability of false rejection (error of the first kind) at the desired level $\alpha$ but leaves the power of the test and hence the probability of an error of the second kind to the mercy of the experiment. It seems more natural when deciding on a significance level (and this suggestion is certainly not new) to take into account also what power can be achieved with the given experiment. In Section 3 a specific suggestion will be made as to how to balance $\alpha$ against the power $\beta$ obtainable against the alternatives of interest. The adoption of this or some similar rule for choosing a significance level has important consequences for the theory of testing composite hypotheses, where nuisance parameters are present. Since the quantity $\alpha$ is then potentially a function of the nuisance parameter $\vartheta$, the classical rule of a fixed significance level leads to the condition that the tests be exact or similar, that is, that $\alpha(\vartheta)$ equal the preassigned value $\alpha$ for all $\vartheta$. On the other hand, the power $\beta$ that can be attained against any alternative $\theta = \theta_1$ frequently depends on $\vartheta$. The requirement that $\alpha(\vartheta)$ and $\beta(\vartheta)$ be in a certain balance thus leads to tests which are not similar and hence do not agree with the standard solutions. To obtain a suitable setting for this discussion, we consider first a minimal complete class of tests for testing the hypothesis $H:\theta \leqq \theta_0$ in a multiparameter exponential family (Section 2). The proposed $\alpha, \beta$-relation is discussed in Section 3, and in Section 4 is applied to the exponential family. Section 5 gives some illustrations of the theory.