Terms Of Average Sample Number Research Articles

TIME TRUNCATED ACCEPTANCE SAMPLING PLAN FOR ODDS EXPONENTIAL LOG-LOGISTIC DISTRIBUTION

In this paper, the multiple deferred state repetitive acceptance sampling plan (MDSRASP) is proposed and designed for assuring a 50th percentile lifetime of the products under odds exponential log-logistic (OELL) distribution. The optimum parameters of the proposed plan are determined based on satisfying various blends of producer’s risk and consumer’s risk for definite quality levels in light of 50th percentile. The aim is to minimize the average sample number (ASN), though the constraints are connected with the lot acceptance probability at the acceptable and limiting quality levels. The efficiency of the proposed plan is compared with single sampling plan using ASN. Tables are formed to present the outcomes and comparison of the proposed plan with existing sampling plan is done in terms of ASN.

A new approach in the economic design of acceptance sampling plans based on process yield index and Taguchi loss function

Acceptance sampling plan is used for decision making in the field of products quality control. These plans provide the producer and the consumer with decision rules for accepting or rejecting the lot. In this paper, a new approach for the economic design of resubmitted and multiple dependent state (MDS) sampling plans is proposed based on the process yield index considering Taguchi loss function and the average number of sample size n, which minimizes the costs related to the yield index Spk. In the proposed model the loss of a batch is considered rather than a single product. Also, the loss of both producer and consumer based on the yield index is minimized simultaneously through solving an optimization model and the parameters of the proposed sampling plans are obtained. The performance of both proposed sampling plans is analyzed and compared in terms of average sample number and total expected loss. The results indicate that both proposed sampling plans show satisfactory performance. Moreover, the advantages of the proposed model over the existing resubmitted and MDS sampling plans are presented. Finally, the application of the proposed model and sampling plans is illustrated through a real case in batch manufacturing processes.

Implementing new variables RGS plan based on EWMA yield index

This paper develops a new variables repetitive group sampling plan using the exponentially weighted moving average (EWMA) statistic based on the yield index for the submitted lot. The optimal parameters of the proposed plan are determined under three scenarios based on the average sample number. Average sample number (ASN) is minimized to decrease inspection's cost and time by using the optimization problem for the required quality levels and sundry combinations of producer's and consumer's risks. The comparison study is provided to specify the efficiency of the proposed plan. Furthermore, the proposed plan is presented with an example which indicates its applicability in the industry. The proposed plan is compared with the single sampling plan and repetitive group sampling plan based on the yield index. The upshots are tabulated for various quality levels. The obtained outcomes demonstrate that the performance of the proposed sampling plan is more lucrative than the existing sampling plans in terms of ASN.

Designing of tightened-normal-tightened sampling scheme under Weibull and gamma distributions for mean life assurance

A number of sampling plans and sampling systems (or schemes) have been designed in the literature with the intention of improving the discriminating power of operating characteristic curve of zero acceptance number single sampling plans. In this article, we propose one of such sampling schemes namely, tightened-normal-tightened scheme to assure the mean life of the products where the lifetime follows the Weibull or gamma distribution. In order to execute the sampling scheme, we determine the optimal parameters on the basis of two points on the operating characteristic curve approach and for such determination we consider different values of consumer’s risk, shape parameters with predetermined producer’s risk. The implementation of the proposed scheme is explained with real life data. The performance of the proposed scheme is compared with some other existing sampling plans in terms of average sample number. The operating characteristic curve is investigated to show the better performance of the proposed scheme. The average sample number obtained under both distributions is compared with each other. In addition, the economic aspect designing of the proposed scheme is investigated under both distributions and the comparative study is done on the cost of inspection of the proposed scheme with other existing plans.

Multiple dependent state repetitive sampling plans based on one-sided process capability indices

ABSTRACTIn this research, multiple dependent state and repetitive group sampling are used to design a variable sampling plan based on one-sided process capability indices, which consider the quality of the current lot as well as the quality of the preceding lots. The sample size and critical values of the proposed plan are determined by minimizing the average sample number while satisfying the producer's risk and consumer's risk at corresponding quality levels. In addition, comparisons are made with the existing sampling plans [Pearn and Wu (2006a), Yen et al. (2015)] in terms of average sample number and operating characteristic curve. Finally, an example is provided to illustrate the proposed plan.

Optimal designing of quick switching sampling system assuring percentile life under Weibull distribution

ABSTRACTIn this paper, designing methodology of quick switching sampling system under Weibull distribution for assuring product lifetime percentile is proposed. An optimization problem is formulated for determining the optimal parameters of the proposed system using two points on the operating characteristic curve approach. The operating procedure and designing methodology of the proposed system are discussed. A comparative study between the proposed system and other existing plans is accomplished in terms of average sample number and the operating characteristic curve is provided for analyzing the behavior of proposed system. In addition, the effect of mis-specification of shape parameter on the proposed sampling system is discussed.

Designing an economically optimal repetitive group-sampling plan based on loss functions

ABSTRACTAcceptance sampling is a quality assurance tool, which provides a rule for the producer and the consumer to make acceptance or rejection decision about a lot. This paper attempts to develop a more efficient sampling plan, variables repetitive group sampling plan, based on the total loss to the producer and consumer. To design this model, two constraints are considered to satisfy the opposing priorities and requirements of the producer and the consumer by using Acceptable quality level (AQL) and Limiting quality level (LQL) points on operating characteristic (OC) curve. The objective function of this model is constructed based on the total expected loss. In order to illustrate the application of the proposed model, an example is presented. In addition, the effects of process parameters on the optimal solution and the total expected loss are studied by performing a sensitivity analysis. Finally, the efficiency of the proposed model is compared with the variables single sampling plan, the variables double sampling plan and the repetitive group sampling plan of Balamurali and Jun (2006) in terms of average sample number, total expected loss and its difference with ideal OC curve.

Developing a variable repetitive group sampling plan based on the coefficient of variation

The coefficient of variation (CV) is an important quality parameter to measure the product quality. A variable repetitive group sampling (VRGS) plan based on the CV is developed in this paper when the quality characteristic follows normal distribution. The optimal plan parameters of the proposed VRGS plan are determined by satisfying the commonly used producer’s risk and consumer’s risk at the same time by minimizing the average sample number (ASN) and then tabulated for various combinations of acceptance quality level and limiting quality level. Moreover, the efficiency of the proposed VRGS plan is compared with the single sampling plan and the two-stage sampling plan. The results show that proposed plan has better performance than existing sampling plans in terms of ASN. Finally, the proposed VRGS plan is illustrated with an industrial example.

Sampling Schemes by Variables Inspection for the First-Order Autoregressive Model between Linear Profiles

We present four new sampling schemes by variables inspection to deal with the first-order autoregressive model between linear profiles. The first plan is based on exponentially weighted moving average (EWMA) and the rest of three plans are using the resubmitted sampling, repetitive group sampling (RGS), and multiple dependent state (MDS) sampling schemes. The nonlinear optimization problem is developed to find the number of profiles and the corresponding acceptance criteria, such that the producer’s and consumer’s risk are satisfied simultaneously. The efficiency of the proposed plans is compared with the conventional single sampling plan in terms of average sample number and the probability of acceptance. The result implies that all of the proposed sampling plans are superior to the single acceptance sampling plan by variables. In addition, the EWMA method appeared to be better than the others. The applications of proposed plans are shown with the help of industrial examples taken from calibration of an optical imaging system, and tire cornering stiffness test.

Design and Construction of Plan for Exponential Distribution Using Repetitive Sampling

In this paper, sampling plan using exact and approximated approaches is presented when the quality of interest follows the exponential distribution. The designing both presented using the repetitive group sampling plan. The design parameters of the proposed sampling plans are determined through non-linear optimization. The efficiency of proposed sampling plans is compared with the existing sampling plans in terms of average sample number. The application of the proposed plans is discussed by industrial data.

Two New Independent Mixed Sampling Plans for Inspecting a Product with Linear Profiles

Acceptance‐sampling plans have been widely used to decide whether an inspection lot should be accepted or rejected. From an economical point of view, a mixed sampling plan is better than the attribute sampling plan. In this paper, we present two new independent mixed sampling plans based on the yield index for linear profiles. The first plan is based on the traditional mixed sampling scheme, and the second plan is based on the modified mixed sampling scheme with marginal quality. A nonlinear optimization model determines the plan parameters that the criterion is to meet the specification of two points on the operating characteristic curve. We found that the number of profiles required in the first stage is smaller than in the second stage. The results confirm that the independent plan with marginal quality is superior to the independent plan and the single and double sampling plans by attributes in terms of average sample number. Two real examples are used to illustrate the proposed plans. Copyright © 2016 John Wiley & Sons, Ltd.

Designing a Repetitive Group Sampling Plan for Weibull Distributed Processes

Acceptance sampling plans are useful tools to determine whether the submitted lots should be accepted or rejected. An efficient and economic sampling plan is very desirable for the high quality levels required by the production processes. The process capability indexCLis an important quality parameter to measure the product quality. Utilizing the relationship between theCLindex and the nonconforming rate, a repetitive group sampling (RGS) plan based onCLindex is developed in this paper when the quality characteristic follows the Weibull distribution. The optimal plan parameters of the proposed RGS plan are determined by satisfying the commonly used producer’s risk and consumer’s risk at the same time by minimizing the average sample number (ASN) and then tabulated for different combinations of acceptance quality level (AQL) and limiting quality level (LQL). The results show that the proposed plan has better performance than the single sampling plan in terms of ASN. Finally, the proposed RGS plan is illustrated with an industrial example.

Resubmitted lots with single sampling plans by attributes under the conditions of zero-inflated poisson distribution

ABSTRACTFor a well-monitored process, occurrence of nondefect is a frequent event sampling inspection. A suitable model for this situation is a zero-inflated Poisson (ZIP) distribution. In this manuscript, we will focus on the designing of a more flexible sampling plan called the resubmitted lots plan. The parameters of the proposed sampling plan are determined through the nonlinear optimization solution. The advantage of the proposed plan over the existing sampling in terms of average sample number is discussed. An example is given for the illustration purpose.

Two stage group acceptance sampling plan for half normal percentiles

In this paper, a time truncated life test based on two stage group acceptance sampling plan for the percentile lifetime following half-normal distribution is proposed. The optimal parameters for the proposed plan are determined such that both producer’s and consumer’s risks are satisfied simultaneously for the given experimentation time and sample size. The efficiency of the proposed sampling plan is discussed in terms of average sample number with the existing sampling plan. The proposed sampling plan is explained with the help of industrial examples.

A Sequential Energy Detection Based Spectrum Sensing Scheme in Cognitive Radio

Reliable and swift spectrum sensing is a crucial technical challenge of cognitive radio. This study proposes a Sequential Energy Detection (SED) scheme to reduce the average required sample number and sensing time for spectrum sensing in low signal-to-noise ratio regime. In the scheme, the data samples are first grouped into data blocks and the Sequential Probability Ratio Test (SPRT) use the energies of the data blocks as the statistic variables. The resulting detection rule exhibits simplicity in implementation and in analysis and retains the high sample-efficiency of sequential probability ratio test. The detection performance in terms of Average Sample Number (ASN) is evaluated theoretically. Simulation results are provided to verify the theoretical analysis.

Sequential testing of sorted and transformed data as an efficient way to implement long GLRTs

It is often required to detect a long weak signal in Gaussian noise, and frequently, the exact form of that signal is parameterized but not known. A bank of matched filters provides an appropriate detector. However, in some practical applications, there are very many matched filters, and most are quite long. The consequent computational needs may render the classical bank-of-filters approach infeasibly expensive. One example, and our original motivation, is the detection of chirp gravitational waves by an Earth-based interferometer. In this paper, we provide a computational approach to this problem via sequential testing. Since the sequential tests to be used are not for constant signals, we develop the theory in terms of average sample number (ASN) for this case. Specifically, we propose two easily calculable expressions for the ASN: one a bound and the other an approximation. The sequential approach does yield moderate computational savings, but we find that by preprocessing the data using short/medium fast Fourier transforms (FFTs) and an appropriate sorting of these FFT outputs such that the most informative samples are entered to a sequential test first, quite high numerical efficiency can be realized. The idea is simple but appears to be quite successful: Examples are presented in which the computational load is reduced by several orders of magnitude. The FFT is an example of an energy-agglomerating transform, but of course, there are many others. The point here is that the transform need not match the sought signal exactly in the sense that all energy becomes confined to a single sample; it is enough that the energy becomes concentrated, and the more concentrated the better.

Evaluation of sequential sampling plans for the larger grain borer (Coleoptera: Bostrichidae) and the maize weevil (Coleoptera: Curculionidae) and of visual grain assessment in West Africa.

Repeated sampling of rural maize stores in Benin was conducted to evaluate published parameters of a sequential sampling plan for a negative binomial distribution to determine pest status for Prostephanus truncatus (Horn) and Sitophilus zeamais Motschulsky. A computer program was used to rerandomize the data and evaluate the effects, in terms of average sample number and error rates, of different sampling plan parameter values. With respect to P. truncatus, lower and upper thresholds of 0.2 and 1.0 insects per ear and parameter values of k = 0.2 and alpha = beta = 0.1 were found to be adequate. With respect to S. zeamais, lower and upper thresholds of 10 and 20 insects per ear and parameter values of k = 1.0 and i alpha = beta = 0.1 were found to be adequate. Simplified sampling rules were proposed in which 11 ears should be sampled and if no P. truncatus are found, the population is low; otherwise the Wald plan should be followed. Owing to the lower per capita rate of damage, effective simplified sampling rules for S. zeamais were difficult to construct. An evaluation of the visual assessment scale rising whole ears showed that a visual scale estimating percentage damage rather than percentage loss, might be easy to construct and preferable for traders. Further work is needed to improve the usefulness of the visual scale in pest management decision support.

Group sequential designs for one-sided and two-sided hypothesis testing with provision for early stopping in favor of the null hypothesis

In this paper we consider a class of boundaries for group sequential clinical trials that allow for early stopping also when small treatment differences are observed. They are based on the one-parameter family of boundaries introduced by Wang and Tsiatis (Biometrics) 43 (1987) 193–199), can be derived exactly for any choice of type I and type II error probabilities, and can be easily applied to both one- and two-sided hypothesis testing. Plans corresponding to different choices of the design parameters are compared in terms of average sample number. Tables of relevant parameters are provided to help in the design of group sequential tests.