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.

Bayesian Two-sided Complete Group Chain Sampling Plan for Binomial Distribution using Beta Prior through Quality Regions

Acceptance sampling is a technique for statistical quality assurance based on the inspection of a random sample to decide the lot disposition: accept or reject. Producer’s risk and consumer’s risk are inevitable in acceptance sampling. Most conventional plans only focus on minimizing the consumer’s risk. This study focused on minimizing both producer’s and consumer’s risks through the quality region. Experts from available historical knowledge concurred that Bayesian is the best approach to make the correct decision. In this study, a Bayesian two-sided complete group chain sampling plan (BTSCGChSP) was proposed for the average probability of acceptance. The binomial distribution was used to derive the probability of lot acceptance, and the beta distribution was used as the prior distribution. For selected design parameters in BTSCGChSP, the acceptable quality level and limiting quality level were considered to estimate quality regions that were directly associated with producer’s and consumer’s risks, respectively. Four quality regions: (i) quality decision region , (ii) probabilistic quality region (PQR), (iii) limiting quality region, and (iv) indifference quality region, were evaluated. To compare with the existing Bayesian group chain sampling plan (BGChSP), operating characteristic curves were used for the same parameter values and probability of lot acceptance. The findings explained that BTSCGChSP provided a smaller proportion of defectives than BGChSP for the same probability of acceptance. If quality regions were found for the same values of consumer and producer risks, then the BTSCGChSP region would contain fewer defectives than in the BGChSP region. Therefore, for industrial practitioners, the proposed plan is a better substitute for existing BGChSP and other conventional plans.

Bayesian two-sided group chain sampling plan for beta binomial distribution under quality regions

PurposeThis paper introduces a Bayesian two-sided group chain sampling plan (BT-SGChSP) by using binomial distribution to estimate the average proportion of defectives. In this Bayesian approach, beta distribution is used as a suitable prior of binomial distribution. The proposed plan considers both consumer's and producer's risks. Currently, group chain sampling plans only consider the consumer's risk and do not account for the producer's risk. All existing plans are used to estimate only a single point, but this plan gives a quality region for the pre-specified values of different design parameters. In other words, instead of point wise description for the designing of sampling plan based on a range of quality by involving a novel approach called quality region.Design/methodology/approachThe methodology is based on five phases, which are (1) operating procedure, (2) derivation of the probability of lot acceptance, (3) constructing plans for given acceptable quality level (AQL) and limiting quality level (LQL), (4) construction of quality intervals for BT-SGChSP and (5) selection of the sampling plans.FindingsThe findings show that the operating characteristic (OC) curve of BT-SGChSP is more ideal than the existing Bayesian group chain sampling plan because the quality regions for BT-SGChSP give less proportion of defectives for same consumer's and producer's risks.Research limitations/implicationsThere are four limitations in this study: first is the use of binomial distribution when deriving the probability of lot acceptance. Alternatively, it can be derived by using distributions such as Poisson, weighted Poisson and weighted binomial. The second is that beta distribution is used as prior distribution. Otherwise, different prior distributions can be used like: Rayleigh, exponential and generalized exponential. The third is that we adopt mean as a quality parameter, whereas median and other quintiles can be used. Forth, this paper considers probabilistic quality region (PQR) and indifference quality region (IQR).Practical implicationsThe proposed plan is an alternative of traditional group chain sampling plans that are based on only current lot information. This plan considers current lot information with preceding and succeeding lot and also considers prior information of the product.Originality/valueThis paper first time uses a tight (three acceptance criteria) and introduces a BT-SGChSP to find quality regions for both producer's and consumer's risk.

The influence of measurement error on the risks of the consumer and the manufacturer when completing connections

The influence of the measuring device error on the consumer’s and manufacturer’s risks was studied for three cases of the organization of completing: complete interchangeability, selective completing and completing with ranking. The presence of measurement error does not allow to avoid risks; however, their values must be estimated so that they do not have a significant impact on manufactured products. The study was carried out for a “shaft-hole” connection by statistical modeling, the laws of dimension distribution were accepted as normal, as well as the laws of distribution of measurement errors. For the case of completing with complete interchangeability, the accuracy of two-stage control was studied; it is recommended to establish the accuracy of the initial measurements at 20–25 % of the tolerance field, repeated measurements at 10–12 % of the tolerance field, while the manufacturer’s risk does not exceed 0.2 %, the consumer’s risk is practically zero. In the case of selective completing, the requirements for the accuracy of the measuring device are significantly higher than in the case of completing with complete interchangeability, since errors are possible not only at the limits of the tolerance field but also at the limits of the selection groups. Therefore, the measurement error should not exceed 5 % of the tolerance field width; it is also advisable to limit the number of selection groups. When completing with ranking, the accuracy of the measuring device has the least impact on risks, especially if the number of parts in the batch is large enough and the measurement error complies with the standards in mechanical engineering. It was established that for the number of sets greater than 10, almost complete assemblability is achieved and the risks associated with the measurement error become insignificant. Thus, if it is necessary to increase the accuracy of products at the assembly stage, it is recommended to use completing with ranking instead of selective completing.

Odd generalized exponential log logistic distribution: A new acceptance sampling plans based on percentiles

<span>In this paper, acceptance sampling plans are developed for the odd generalized exponential log logistic distribution based on percentiles when the life test is truncated at a pre-specified (pre-determined) time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given consumer’s risk. The operating characteristic values of the sampling plans as well as the producer’s risk are presented. One example with real data set is also given as an illustration.</span>