Design of single and double acceptance sampling plans based on neutrosophic sets

Although traditional acceptance sampling plans (ASPs) need certain mass quality characteristics, it is not easy to define them as crisp value in some real case problems. The fuzzy set theory (FST) is one of the popular techniques to model uncertainties of the process and therefore fuzzy ASPs have been offered in the literature. Fuzzy set extensions have been proposed recently for better modeling of the uncertainties having different sources and characteristics. One of these extensions named neutrosophic sets (NSs) can be used to increase the sensitiveness and flexibility of ASPs. The ASPs based on NSs can give ability to classify the items as defective, non-defective and indeterminate. Since the operator can become indecisive for slightly defective items, these plans can provide a good representation of human evaluations under uncertainty. In this study, single and double ASPs are designed based on NSs by using binomial and poisson distributions that are also re-analyzed based on NSs. For this aim, some characteristics functions of ASPs such as probability of accepting a lot (Pa), average outgoing quality (AOQ), average total inspection (ATI) and average sample number (ASN) have also been analyzed based on NSs. Numerical examples are presented to analyze the proposed plans.

Design of single and double acceptance sampling plans based on interval type-2 fuzzy sets

Defectiveness of items is generally considered as a certain value in acceptance sampling plans (ASPs). It is clear that, it may not be certainly known in some real-case problems. Uncertainties of the inspection process such as measurement errors, inspectors’ hesitancies or vagueness of the process etc. should be taken into account to obtain more reliable results. The fuzzy set theory (FST) is one of the best methods to overcome these problems. There are some studies in the literature formulating the ASPs with the help of FST. Deciding the right membership functions of the fuzzy sets (FSs) has a vital importance on the quality of the uncertainty modeling. Additionally, the fuzzy set extensions have been offered to model more complicated uncertainties to achieve better modeling. As one of these extensions, type-2 fuzzy sets (T2FSs) gives an ability to model uncertainty in situations where it is not possible to determine exact membership function parameters. In this study, single and double ASPs based on interval T2FSs (IT2FSs) have been designed for binomial and Poisson distributions. Thus, it becomes possible to make more flexible, sensitive and descriptive sensitivity analyzes. The main characteristic functions of ASPs have been derived and the suggested formulations have been illustrated on a comparative application from manufacturing process. Results allowing for more comprehensive analysis as against to the traditional and T1FSs based plans have been obtained.

Group acceptance sampling plans based on time truncated life tests for compound Weibull-exponential distribution

PurposeAcceptance sampling plans are a decision-making process on the basis of a randomly selected sampling from a party, where it is not possible to completely scan the products for reasons such as time and cost being limited or the formation of damaged products during the inspection. For some products, the life span (time from beginning to failure) may be an important quality characteristic. In this case, the quality control adequacy of the products can be checked with an acceptance sampling plan based on the truncated life test with a censored scheme for the lifetime of the products. In this study, group acceptance sampling plans (GASPs) based on life tests are studied under the Type-I censored scheme for the compound Weibull-exponential (CWE) distribution.Design/methodology/approachGASPs based on life tests under the Type-I censored scheme for the CWE distribution are developed by using both the producer's risk and the consumer's risk.FindingsIn this study, optimum sample size, optimum number of groups and acceptance number are obtained under the Type-I censored scheme for the CWE distribution. Real data set illustration is given to show GASPs how to be used for the industry applications.Originality/valueDifferent from acceptance sampling plans with just considering the producer's risk, GASPs are constructed by using two-point approach included both the producer's risk and the consumer's risk for CWE distribution.

Acceptance Sampling Plans from Life Tests Based on Percentiles of New Weibull–Pareto Distribution with Application to Breaking Stress of Carbon Fibers Data

In this paper, acceptance sampling plans (ASPs) are proposed for the new Weibull-Pareto distribution (NWPD) percentiles assuming truncated life tests at a pre-determined time. The minimum sample sizes essential to assert the specified percentile are calculated for a given consumer’s risk. The operating characteristic function values of the developed ASPs and producer’s risk are provided. A real data set related to the breaking stress of carbon fibers data are presented for illustration.

Reliability Test Plan for an Extended Birnbaum-Saunders Distribution

Birnbaum-Saunders distribution has been widely studied in statistical literature because this distribution accommodates several interesting properties. The purpose of this paper is to introduce a new parametric distribution based on the Birnbaum-Saunders model and develop a new acceptance sampling plans for derived extended Birnbaum-Saunders distribution when the mean lifetime test is truncated at a predetermined time. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure a specified mean lifetime worked out. The results are illustrated by a numerical example. The operating characteristic functions of the sampling plans and producer’s risk and the ratio of true mean life to a specified mean life that ensures acceptance with a pre-assigned probability are tabulated. This paper presents relevant characteristics of the new distribution and a new acceptance sampling plans when the lifetime of a product adopts an extended Birnbaum-Saunders distribution. Based on this study, the optimal number of testers demanded is decreases as test termination time increases. Moreover, the operating characteristic values increases as the mean life ratio increases, which indicate that items with increased mean life will be accepted with higher probability compared with items with lower mean life ratio.