Operating Characteristic Function Research Articles

Optimizing Group Size using Percentile Based Group Acceptance Sampling Plans with Application

The present paper focuses on optimizing the sample size and the acceptance number which are commonly known as design parameters for the group acceptance sampling plan (GASP). Design parameters are analyzed under the assumption that the characteristic of interest for the product follows Another Generalized Transmuted-Exponential (AGTransmuted-Exponential) distribution. Using different values of the quality levels (median lifetime), the values of the Operating Characteristic function is determined. The proposed plan satisfies two types of risks based on producer's point of view and consumer’s point of view at varied stipulated quality levels. Optimization of the sample size, group size and acceptance numbers is obtained through Monte Carlo simulation, for which relevant R codes were developed. Specific R codes are appended for future usage by academia and practitioners from various fields of life. The simulated results of the study are exhibited in the form of tables and explained with relevant examples. Results of the proposed GASP are compared with plan parameters obtained using MLE estimates of AGTransmuted-Exponential distribution and also by design parameters obtained using mean as quality level. Results of the study exhibited that Median as a quality parameter resulted in the decrease of group size and acceptance number simultaneously at all quality levels. Easy to follow the methodology of the current paper will open new vistas for applying the proposed GASP to a family of transmuted probability distributions. For illustration purposes, a real data set for fatigue fracture stress is analyzed using MLE estimates of AGTransmuted-Exponential distribution to demonstrate the implementation of the proposed sampling plan.

Constructing Optimal Quick Switching System with Hurdle Poisson Distribution

Objectives: Optimizing the sum of risks involved in the selection of acceptance sampling plans playing a vital role. This paper uses the Hurdle Poisson distribution to design an optimal quick switching system attribute plan for a given acceptable quality level (AQL) and limiting quality level (LQL) involving a minimum sum of risks. Methods: The sum of producer's and consumer's risks has been met for the specified AQL and LQL. The sum of these risks, as well as the acceptance and rejection numbers have been calculated using the Hurdle Poisson distribution. The operating characteristic function for the quick switching system attribute plan has also been derived using the Hurdle Poisson distribution. Findings: The producer and the consumer both represent the same party in the final inspection. As a result, the sum of these two risks should be minimized. In this paper, the sum of risks for various operating ratios are tabulated using the Hurdle Poisson distribution. These tabulated values are less than the sum of risks calculated using the Weighted Poisson distribution. Novelty: Reducing the sum of risks is the ultimate aim of the work. In this proposed paper, to attain the minimum sum of risks, the authors make an attempt to approach the Quick Switching System Sampling Plan, when the number of defectives in the submitted lots are very less. In other words, the probability of getting defective is very less. This indicates the quality of the lot selected for the inspection to ensure the protection for the consumer. And the plan is also designed in the way that the producer is also not get affected by rejecting a good lot by the consumer. This is the requirement of minimizing the risks. Keywords: Acceptable Quality Level (AQL), Limiting Quality Level (LQL), Minimum Risk Plan, Quick Switching System Sampling Attribute Plan, Operating Characteristic (OC) Function, Hurdle Poisson Distribution

Acceptance Sampling Plans based on Percentiles of Exponentiated Inverse Kumaraswamy Distribution

Objectives: To prepare the percentile-based acceptance sampling plans for the Exponentiated Inverse Kumaraswamy Distribution (EIKD) at a specific truncation time to inspect the defective lots corresponding to the desired acceptance level. Methods: The failure probability value is estimated using the cumulative probability function F(.) at time ‘t’ which is converted in terms of the scale parameter σ as 100th percentile using quantile function. The minimum size of the sample, Operating Characteristic (OC) and the minimum ratios are calculated for a required levels of consumer’s as well as producer’s risk. Findings: The percentile-based sampling plans are obtained through the minimal size of the sample ‘n’ under a truncated life test with a target acceptance number c in a manner that the proportion of accepting a lot which is not good (consumer’s risk) would not be more than . These values are calculated at The function of probability of acceptance for variations in the quality of a lot (OC function) L(p) of the sample plan are evaluated for the acceptance values of c=1 and c=5. The minimum ratio values are calculated for the acceptability of the lot with producers’ risk of using the sampling plan. Novelty: The modernity of this study is the designing of the acceptance sampling plans to a non-normal data using an asymmetrical distribution that has all three shape parameters. Also, the monitor of the implementation and suitability of statistical quality control and process control aspects using Exponentiated Inverse Kumaraswamy Distribution when compared to other asymmetrical distributions which has at least one scale parameter. Keywords: Sampling plans, Consumer's risk, Operating characteristics function, Truncated life tests, Producer's risk

A Sequential Test of Traffic Intensity for the M/M/1 Queueing System

This paper deals with testing traffic intensity, which is the most important parameter of the queue system. The Wald-type sequential probability ratio test (SPRT) is performed to determine traffic intensity by taking advantage of the fact that the total number of customers arriving up to the kth service period, including the kth service period, has a negative binomial distribution. Acceptance and rejection limits obtained from the SPRT are arranged as a multiple sampling plan. This plan is applied with a finite Markov chain. Then, the Operating Characteristic (OC) function and the Average Sample Number (ASN) are obtained precisely. Obtaining the standard errors of the sample number compared to the studies on SPRT applications is the novelty brought by this paper. The sequential analysis method based on the finite Markov chain is also applied to a numerical sample.

Cost-effective optimization strategies and sampling plan for Weibull quantiles under type-II censoring

This article introduces a conditional reliability sampling plan for the Weibull distribution. The plan is applicable when the interested quality characteristic is a lower quantile and the life data are observed according to a progressive type-II censoring scheme. It is called “conditional”, since its operating characteristic function is derived by conditioning on a vector of ancillary statistics. We approximate the conditional operating characteristic function by a fixed vector that does not change by the sample. The plan is optimally designed by concentrating on economic considerations while the producer’s and consumer’s confidences are satisfied. In this regard, three cost models are proposed. The first cost function is constructed based on the inspection cost, while the second model accounts for the inaccurate estimation cost. The third cost function is a weighted-relative combination of the other two costs. Based on some combinations of requirements, the optimal plan parameters are prepared in some tables. We further conduct a series of simulations to show that the approximated conditional operating characteristic function can ensure the inspection’s risks well. Finally, an example based on the well-known data set on the strength of carbon fibers is discussed to demonstrate the applicability of the proposed plan.

A SkSP-R Plan under the Assumption of Gompertz Distribution

In this study, we designed a time-truncated SkSP-R sampling plan when the lifetime of units follows a Gompertz distribution (GmzD). The GmzD is briefly discussed. All of the plan parameters were obtained using a two-point approach, which is based on limiting quality level (LQL) and acceptable quality level (AQL). Moreover, operating characteristic (OC) values were calculated for the determined value of the plan parameters by using the OC function of the SkSP-R. Applications of two real life situations in engineering were presented to illustrate the applicability of the offered sampling inspection plan. It was found that the new SkSP-R sampling inspection plan can be used efficiently in the field.

Small-layered Feed-Forward and Convolutional neural networks for efficient P wave earthquake detection

The number and efficiency of seismic networks have steadily increase over time delivering large datasets to be analyzed for earthquake occurrence. Automatic tools for accurate earthquake detection are under emerging and intense development. This paper first proposes a new windowing procedure of seismic traces that highly facilitates earthquake detection. This procedure applies regular trace filtering and normalization, but also performs a strict window alignment to P wave onset. These event-aligned windows represent the input data to our P wave detection networks, with relatively small or moderate number of layers. We then develop Feed-Forward (FFNN) and Convolutional (CNN) neural networks and explore multiple architecture configurations to find relevant hyperparameter patterns for better detection. To assess network performance, we adopt the widely used metrics of accuracy (ACC) and the area under the curve (AUC) of the Receiver Operating Characteristic function. In terms of ACC, the best FFNN and CNN reach performances of 91% and 98%, respectively. On the other hand, the best FFNN and CNN in terms of AUC achieve performances of 96% and 99%, respectively. Thus, our novel trace windowing procedure allows developing networks with few hyperparameters, for correct earthquake detection under low computational costs. Finally, we use the CNN with best AUC performance as an effective trace filtering with the purpose of P wave arrival time estimation.

A Research Algorithm to Sentence the Lots for Costly or Destructive Products in Mixed Quality Characteristics

This paper deals with the new operating procedure of Acceptance Sampling Plans for costly or destructive products when the incoming lots have mixed quality characteristics. The Operating Characteristic function and other associated measures of the plan are derived and provided. The procedure is given and designing of sampling plan are indexed through standard quality levels. Tables are constructed for easy selection of the plan.Illustrations are also provided.

Improved binomial and Poisson approximations to the Type-A operating characteristic function

PurposeIn acceptance sampling, the hypergeometric operating characteristic (OC) function (so called type-A OC) is used to be approximated by the binomial or Poisson OC function, which actually reduce computational effort, but do not provide suffcient approximation results. The purpose of this paper is to examine binomial- and Poisson-type approximations to the hypergeometric distribution, in order to find a simple but accurate approximation that can be successfully applied in acceptance sampling.Design/methodology/approachThe authors present a new binomial-type approximation for the type-A OC function, and derive its properties. Further, the authors compare this approximation via an extensive numerical study with other common approximations in terms of variation distance and relative efficiency under various conditions on the parameters including limiting cases.FindingsThe introduced approximation generates best numerical results over a wide range of parameter values, and ensures arithmetic simplicity of the binomial distribution and high accuracy to meet requirements regarding acceptance sampling problems. Additionally, it can considerably reduce the computational effort in relation to the type-A OC function and therefore is strongly recommended for calculating sampling plans.Originality/valueThe newly presented approximation provides a remarkably close fit to the type-A OC function, is discrete and needs no correction for continuity, and is skewed in the same direction by roughly the same amount as the exact OC. Due to less factorials, this OC in general involves lower powers than the type-A OC function. Moreover, the binomial-type approximation is easy to fit to the conventional statistical computing packages.

DEVELOPING SINGLE-ACCEPTANCE SAMPLING PLANS BASED ON A TRUNCATED LIFETIME TEST FOR AN ISHITA DISTRIBUTION

Abstract Acceptance sampling plans are statistical procedures that are used for quality control and improvement in cases where it is not possible to test every item in a lot of materials. The outcome of this test determines whether the entire lot is accepted or rejected based on a random sample. In this procedure, an important characteristic of the materials is their lifetime sampling distribution, and this can vary from sample to sample. In this article, a new lifetime distribution, known as an Ishita distribution, is considered for developing a new single-acceptance sampling plan. The new acceptance sampling plan is developed under a condition wherein the mean lifetime test is truncated within a pre-specified time period. Based on this condition, the parameters of the acceptance sampling plan including the operating characteristics function and the minimum sample size are obtained. The producer’s risk in relation to the entire lot of materials is derived and illustrated by numerical examples.

Mixed Sampling Product Control for Costly or Destructive Items

This paper presents the derivation of operating characteristics function and associated measures of performance of mixed sampling Plans for costly or destructive items. The first stage is concerned with single sample variable inspection and in the second stage modified Chain Sampling inspection is recommended. If the first stage inspection of mixed plans does not lead to acceptance of the batch or lot then the second stage becomes more important. In the second stage of mixed plans, it is advisable to have small sample size for costly or destructive items. Therefore, in the second stage, the modified chain sampling plan which always utilizes the past lot inspection results in order to achieve very small sample size is taken into consideration. The economic or cost-effective of the sampling plans is measured through Average Sample Number which is smaller compared to any other mixed sampling plans. Designing procedure is given and tables are constructed to facilitate easy application in the production industries.

Construction and selection of continuous sampling plan of type (CSP-T) indexed through maximum allowable average outgoing quality

In this paper, we have introduced a novel designing and selection procedure of continuous sampling plan (CSP-T) indexed through Maximum Allowable Average Outgoing Quality (MAAOQ). Expressions for performance measures such as Operating Characteristic function and MAAOQ function are derived in this paper. The association of Average Outgoing Quality Level (AOQL), Maximum Allowable Percent Defective (MAPD) and MAAOQ in CSP-T are discussed. Comparisons between various CSPs plans are given. Tables and figures are constructed for easy selection of plan parameters.

Control charts for mean for non-normally correlated data

Traditionally, quality control methodology is based on the assumption that serially-generated data are independent and normally distributed. On the basis of these assumptions the operating characteristic (OC) function of the control chart is derived after setting the control limits. But in practice, many of the basic industrial variables do not satisfy both the assumptions and hence one may doubt the validity of the inferences drawn from the control charts. In this paper the power of the control chart for the mean is examined when both the assumptions of independence and normality are not tenable. The OC function is calculated and compared with the normal population.

Achieving Cost-Efficient Indoor Fingerprint Localization on WLAN Platform: A Hypothetical Test Approach

Received signal strength (RSS) is a typical type of measurements used for indoor fingerprint localization on wireless local area network platform. To make good use of RSS information, we rely on the hypothetical test approach to perform localization with the optimized access points (APs). Specifically, in offline phase, the operating characteristics function is used to minimize the sample capacity of fingerprints at each reference point, and meanwhile the APs are optimally selected based on the concept of information gain criterion. Then, in online phase, the F-test and T-test approaches are used to conduct the RSS variance and mean test, respectively, with the purpose of achieving RPs matching, namely coarse localization. After that, the density-based spatial clustering of applications with noise is developed to realize fine localization with the improved accuracy performance. The extensive experimental results demonstrate that the proposed system is able to avoid the blindness of fingerprints collection as well as improve the effectiveness of fingerprints matching especially under the small sample capacity of fingerprints.

Analytical Modeling of Inertial and Droop Responses From a Wind Farm for Short-Term Frequency Regulation in Power Systems

Available inertia and variable droop responses from a wind farm to support the short-term frequency control in power systems are analytically evaluated. The novelty lies in the approach to formulating the inertia constant and primary power reserve for a variable speed wind turbine (VSWT) that operates at derated conditions. The formulations are extended to evaluate the capability of providing inertia and primary frequency support from a wind farm using an aggregated wind speed. As a consequence, the capability as a function of VSWT operating characteristics and conditions is quantified to rationally adjust the frequency controller gains, thereby ensuring stable performance of the wind farms during frequency transients. A modified system frequency response (SFR) model considering available inertial and droop responses from wind farms is developed to well simulate the SFR following wind power fluctuations. The effectiveness of the analytical method is verified through comparisons of the results with those obtained from the empirical method.

A note on efficient performance evaluation of the Cumulative Sum chart and the Sequential Probability Ratio Test

We establish a simple connection between certain in‐control characteristics of the Cumulative Sum (CUSUM) Run Length and their out‐of‐control counterparts. The connection is in the form of paired integral (renewal) equations. The derivation exploits Wald's likelihood ratio identity and the well‐known fact that the CUSUM chart is equivalent to repetitive application of Wald's Sequential Probability Ratio Test (SPRT). The characteristics considered include the entire Run Length distribution and all of the corresponding moments, starting from the zero‐state average run length. A particular practical benefit of our result is that it enables the in‐control and out‐of‐control characteristics of the CUSUM Run Length to be computed concurrently. Moreover, owing to the equivalence of the CUSUM chart to a sequence of SPRTs, the Average Sample Number and Operating Characteristic functions of an SPRT under the null and under the alternative can all be computed simultaneously as well. This would double up the efficiency of any numerical method that one may choose to devise to carry out the actual computations. Copyright © 2016 John Wiley & Sons, Ltd.

Performance of Multiple Alternatives to Reduce Carbon Emissions for Transit Fleets: A Real-world Perspective

Transit agencies are always seeking opportunities to reduce fuel consumption, which typically provides simultaneous emissions reductions. However, the effectiveness and efficiency of fuel conservation and emission reduction alternatives differ as a function of local transit operating characteristics. The fact that emissions reductions from multiple alternatives are not necessarily additive further complicates these analyses. In selecting a set of alternatives, transit agencies need to evaluate multiple options simultaneously, and under agency-specific operating parameters. This paper presents the analysis of emissions reduction alternatives of eco-driving and purchasing new fleet with compressed natural gas, utilizing real-world operating data collected from the Metropolitan Atlanta Rapid Transit Authority (local transit) and the Georgia Regional Transportation Authority (express bus) fleets. Each individual emissions reduction alternative was first investigated for effectiveness individually and then in combination to assess cumulative impacts. The results show that the comparative performance of emissions reductions alternatives is highly dependent on vehicle operating characteristics, and thus the preferred alternatives, differ between different fleets. The analysis conducted for the Atlanta, Georgia region in the United States provides insight to how such modeling techniques can assist planning for future fleets given each agency's unique local conditions.

Time truncated acceptance sampling plans for Generalized Inverse Weibull Distribution

Acceptance sampling plans for a Generalized Inverse Weibull Distribution (GIWD) when the lifetime is truncated at a pre-determined time are suggested in this paper. The minimum sample sizes necessary to ensure the specified mean life time for a given consumer's risk are obtained. The operating characteristic function (OC) values of the developed sampling plans as well as the associated producer's risk are obtained. The ratio of the actual average life to a specified average life that asserts acceptance with a pre-determined probability is presented.

Financial and real sector Leading indicators of Recessions in Brazil using Probabilistic Models

We examine the usefulness of various financial and real sector variables to forecast recessions in Brazil between one and eight quarters ahead. We estimate probabilistic models of recession and select models based on their outof-sample forecasts, using the Receiver Operating Characteristic (ROC) function. We find that the predictive out-of-sample ability of several models vary depending on the numbers of quarters ahead to forecast and on the number of regressors used in the model specification. The models selected seem to be relevant to give early warnings of recessions in Brazil.

Time truncated acceptance sampling plans for generalized inverted exponential distribution

In this paper, acceptancesampling plans are developed based on truncated lifetimes when the life of anitem follows a generalized inverted exponential distribution. The minimum samplesizes required to assure a specified mean life time is done. The operatingcharacteristic function values of the sampling plans are obtained andproducer's risk is discussed. Tables of the ratio of the true mean life tospecified mean life that asserts acceptance with a pre-assigned probability arepresented.