Search results

The purpose of this paper is to present the single sampling attribute plan for given acceptance quality level (AQL) and limiting quality level (LQL) involving minimum sum of risks using weighted Poisson distribution.

For the given AQL and LQL, sum of producer's and consumer's risks have been attained. Based on weighted Poisson distribution, the sum of these risks has been arrived at, along with the acceptance number and the rejection number. Also, the operating characteristic function for the single sampling attribute sampling plan, using weighted Poisson distribution, has been derived.

In the final inspection, the producer and the consumer represent the same party. So, the sum these two risks should be minimized. In this paper, the sum of risks has been tabulated using weighted Poisson distribution for different operating ratios. These tabulated values are comparatively less than the sum of risks derived using Poisson distribution.

The sampling plan presented in this paper is particularly useful for testing the quality of finished products in shop floor situations.

Acceptance 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.

GASPs 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.

In 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.

Different 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.

The purpose of this paper is to present the optimal double sampling attribute plan using the weighted Poisson distribution.

For the given AQL and LQL, sum of producer’s and consumer’s risks have been attained. Based on the weighted Poisson distribution, the sum of these risks has been optimized.

In the final inspection, the producer and the consumer represent the same party. So, the sum these two risks should be minimized. In this paper, the sum of risks has been tabulated using the weighted Poisson distribution for different operating ratios. These tabulated values are comparatively less than the sum of risks derived using Poisson distribution.

The sampling plan presented in this paper is particularly useful for testing the quality of finished products in shop floor situations.

This 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.

The 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.

The 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.

There 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).

The 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.

This 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.

A table and a procedure are given for finding the single‐sampling quick switching system for which the sum of producer′s and consumer′s risks is minimum for specified Acceptable Quality Level and Limiting Quality Level.

A procedure for designing chain sampling plans, ChSP‐1, is described for situations where one of the parameters, the sample size, is fixed. The procedure involves minimisation of the sum of the producer′s risk and consumer′s risk with due weights. Expressions have been derived under binomial and Poisson models, for the parameter i , using which one can obtain the plan for desired values of AQL/LQL weights and sample size. Examples are also given.

The purpose of this paper is to design a modified chain sampling plan for assuring the product percentile life where the lifetime follows Weibull or generalized exponential distributions (GEDs). In order to reduce the cost of inspection when implementing the proposed modified chain sampling plan, it is also considered the economic aspect of designing of proposed plan in this paper.

The authors have designed the proposed plan on the basis of two points on the operating characteristic (OC) curve approach. The optimization problem is used to determine the plan parameters of the proposed plan so that the specified values of producer’s risk and consumer’s risk are satisfied simultaneously.

The results we have obtained, confirm that the proposed plan will be very effective in reducing the sample size rather than other existing sampling plans. The OC curves of proposed plan, chain sampling plan and zero acceptance number single sampling plan show that the performance of proposed plan in discriminating the good and poor quality lots is better than other two plans. In this paper, it is proved that the value of number of preceding lots required for current lot disposition plays an important role.

The proposed modified chain sampling plan for assuring the percentile lifetime of the products under Weibull or GEDs is not available in the literature. The proposed plan can be used in all the manufacturing industries to assure the product percentile lifetime with minimum sample size as well as minimum cost.

Acceptance sampling plans are designed to decide about acceptance or rejection of a lot of products on the basis of sample drawn from it. Accelerating the life test helps in obtaining information about the lifetimes of high reliability products quickly. The purpose of this paper is to formulate an optimum time censored acceptance sampling plan based on ramp-stress accelerated life test (ALT) for items having log-logistic life distribution. The log-logistic life distribution has been found appropriate for highly reliable components such as power system components and insulating materials.

The inverse power relationship has been used to model stress-life relationship. It is meant for analyzing data for which the accelerated stress is nonthermal in nature, and frequently used as an accelerating stress for products such as capacitors, transformers, and insulators. The method of maximum likelihood is used for estimating design parameters. The optimal test plan is obtained by minimizing variance of test-statistic that decides on acceptability or rejectibility of lot. The optimal test plan finds optimal sample size, stress rates, sample proportion allocated to each stress and lot acceptability constant such that producer’s risk and consumer’s risk is satisfied.

Asymptotic variance plays a pivotal role in determining the sample size required for a sampling plan for deciding the acceptance/rejection of a lot. The sample size is minimized by optimally designing a ramp-stress ALT so that the asymptotic variance is minimized.

The model suggested is of use to quality control and reliability engineers dealing with highly reliable items.

This paper considers a series system consisting of n different components having unknown and variable failure rates, where the lifetime of components follow exponential distribution having non-constant failure rates. Moreover, the failure rates are bounded by above and are dependent on environmental factors such as temperature, pressure, through linear relationship. The purpose of this paper is to design a component reliability test plan for such a series system with an unknown variable failure rate.

The reliability of the system is estimated with the help of the unbiased estimator of failure rate. The testing procedure is stopped when a fixed number of failures occur for each component.

An optimal reliability test plan is designed and the resultant non-linear integer optimization problem is formulated satisfying the constraints of producer’s and consumer’s risks. The obtained results are compared with the results available in the literature. Some examples are considered to illustrate the approach.

It is observed that use of prior information in the form of an upper bound and incorporation of environmental factors have the advantage of savings in the total testing cost.

The purpose of this paper is to design an optimal reliability acceptance sampling plan (RASP) using the Type-I generalized hybrid censoring scheme (GHCS) for non-repairable products sold under the general rebate warranty. A cost function approach is proposed for products having Weibull distributed lifetimes incorporating relevant costs.

For Weibull distributed product lifetimes, acceptance criterion introduced by Lieberman and Resnikoff (1955) is derived for Type-I GHCS. A cost function is formulated using expected warranty cost and other relevant cost components incorporating the acceptance criterion. The cost function is optimized following a constrained optimization approach to arrive at the optimum RASP. The constraint ensures that the producer's and the consumer's risks are maintained at agreed-upon levels.

Optimal solution using the above approach is obtained for Type-I GHCS. As a special case of Type-I GHCS, the proposed approach is also used to arrive at the optimal design for Type-I hybrid censoring scheme as shown in Chakrabarty et al. (2019). Observations regarding the change in optimal design and computational times between the two censoring schemes are noted. An extensive simulation study is performed to validate the model for finite sample sizes and the results obtained are found to be in strong agreement. In order to analyze the sensitivity of the optimal solution due to misspecification of parameter values and cost components, a well-designed sensitivity analysis is carried out using a real-life failure data set from Lawless (2003). Interesting observations are made regarding the change in optimal cost due to change in parameter values, the impact of warranty cost in optimal design and change in optimal design due to change in lot sizes.

The research presents an approach for designing optimal RASPs using Type-I generalized hybrid censoring. The study formulates optimum life test sampling plans by minimizing the average aggregate costs involved, which makes it valuable in dealing with real-life problems pertaining to product quality management.