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

In 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 of variables quick switching sampling system by considering process loss functions

This paper proposes a variables quick switching system where the quality characteristic of interest follows a normal distribution and the quality characteristic is evaluated through a process loss function. Most of the variables sampling plans available in the literature focus only on the fraction non-conforming and those plans do not distinguish between the products that fall within the specification limits. The products that fall within specification limits may not be good if their mean is too away from the target value. So developing a sampling plan by considering process loss is inevitable in these situations. Based on this idea, we develop a variables quick switching system based on the process loss function for the application of the processes requiring low process loss. Tables are also constructed for the selection of parameters of variables quick switching system for given acceptable quality level and limiting quality level. The results are explained with examples.     

Zero Acceptance Number Chained Quick Switching System

Zero acceptance number sampling inspection plans are commonly employed for compliance sampling and audit inspection purposes. The discriminatory power of zero acceptance number sampling plans is rather poor. This article remedies this disadvantage by chaining past lot results within a quick switching system.     

Economic design of quick switching sampling system for resubmitted lots

This paper proposes a quick switching sampling system for the inspection of attributes quality characteristics for resubmitted lots. The optimal parameters for both fraction non conforming items and fraction non conformities of the proposed sampling system are determined using an optimization procedure so that producer’s risk and consumer’s risk are simultaneously satisfied. Tables are also constructed for the selection of parameters for specified AQL and LQL. The advantage of the proposed plan over the existing plan is discussed and illustrate. An economic design of the proposed sampling system is also discussed and shown that the proposed sampling system has minimum total cost and average total inspection compared to other existing sampling plans.     

SkSP-R sampling plan based on process capability index

In this paper, we present an optimal designing methodology for the skip-lot sampling plan (SkSP) of type SkSP-R based on the most widely used process capability index (PCI) C_pk. The SkSP-R plan is one of the SkSPs that incorporate the provision of the reinspection concept. In order to design the optimal parameters, we consider both symmetric and asymmetric fraction non conforming cases. Tables are also constructed to determine the optimal parameters by formulating an optimization problem. The advantages of the proposed plan over the existing plan are also discussed. Application of the plan is explained with a real-life example.     

A group acceptance sampling plan for truncated life test having Weibull distribution

In this paper, a group acceptance sampling plan for a truncated life test is proposed when a multiple number of items as a group can be tested simultaneously in a tester, assuming that the lifetime of a product follows the Weibull distribution with a known shape parameter. The design parameters such as the number of groups and the acceptance number will be determined by satisfying the producer's and the consumer's risks at the specified quality levels, while the termination time and the number of testers are specified. The results are explained with tables and examples.     

Economic design of acceptance sampling plans for truncated life test using Frechet distribution

In this article designing of acceptance sampling plans for the truncated life test is proposed using economic approach by assuming that the lifetime of a product follows Frechet distribution based on median. The optimal sampling plans to meet the consumer’s confidence level with minimum total cost are designed. Efficiency of the proposed plan is also analyzed.     

Acceptance Sampling Plans from Truncated Life Tests Based on the Generalized Birnbaum–Saunders Distribution

In this article, we develop acceptance sampling plans when the life test is truncated at a pre-fixed time. The minimum sample size necessary to ensure the specified median life is obtained by assuming that the lifetimes of the test units follow a generalized Birnbaum–Saunders distribution. The operating characteristic values of the sampling plans as well as producer's risk are presented. Two examples are also given to illustrate the procedure developed here, with one of them being based on a real data from software reliability.     

Design of a time-truncated double sampling plan for a general life distribution

A double sampling plan based on truncated life tests is proposed and designed under a general life distribution. The design parameters such as sample sizes and acceptance numbers for the first and the second samples are determined so as to minimize the average sample number subject to satisfying the consumer's and producer's risks at the respectively specified quality levels. The resultant tables can be used regardless of the underlying distribution as long as the reliability requirements are specified at two risks. In addition, Gamma and Weibull distributions are particularly considered to report the design parameters according to the quality levels in terms of the mean ratios.     

Bayesian Design of Special Type of Double Sampling Plans for Compliance Testing

Bayesian acceptance sampling plans, which utilize prior information on the process variation, can be employed as an alternative to conventional types of plans for taking decisions on the disposition of submitted lots. A special type of double sampling inspection plans by attributes with small acceptance numbers using Bayesian methodology is presented in this paper emphasizing its significance over small acceptance number single sampling plans. The procedures for designing such sampling plans for specified degree of discrimination which would ensure protection to the producer and consumer are discussed with illustrations under the conditions for the application of gamma-Poisson distribution.     

Time truncated attribute control chart for the Weibull distribution using multiple dependent state sampling

In this article, an attribute control chart is proposed for time truncated tests using the Weibull distribution. The design of proposed control chart is presented using the multiple dependent state (MDS) sampling. The control chart coefficients are determined for various specified average run length. The efficiency of the proposed control chart is elaborated with the help of a simulation data and a real data. The proposed control chart perform better than the existing control chart in terms of average run length.     

Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.     

An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.     

On the mean residual life of a generalized k-out-of-n system

A generalized k-out-of-n system consists of N modules in which the i th module is composed of n_i components in parallel. The system failswhen at least f components in the whole system or at least k consecutive modules have failed. In this article, we obtain the mean residual life function of such a generalized k-out-of-n system under different conditions, namely, when the number of components in each module is equal or unequal and when the components of the system are independent or exchangeable.     

Acceptance sampling plans based on truncated life tests for weighted exponential distribution

Gupta and Kundu proposed a new class of weighted exponential distributions using the idea of Azzalini. In this article, we develop an acceptance sampling plan for the weighted exponential distribution under a truncated life test. For various acceptance numbers, consumer’s confidence levels and values of the ratio of the experimental time to the specified mean lifetime, the minimum sample size necessary to ensure a certain mean lifetime are obtained. The operating characteristic function values and the associated producer’s risks are also presented. A numerical example is provided to illustrate the acceptance sampling plan.     

Optimal designing of skip-lot sampling plan of type SkSP-2 with group acceptance sampling plan as reference plan under Burr-type XII distribution

In this paper, skip-lot sampling plan of type SkSP-2 with group acceptance sampling plans is proposed when the lifetime of the product follows the Burr-type XII distributions. The optimal parameters of the proposed plan are determined when two points on operating characteristics curve namely acceptable quality level and limiting quality level and the number of testers are specified. We also considered the Burr-type XII distribution to find the plan parameters. Several tables are given for practical use. We compare the results of proposed plan with the existing plans. Results are explained using real-world examples.     

A family of shrinkage estimators for Weibull shape parameter in censored sampling

In this paper a new class of shrinkage estimators has been introduced for the shape parameter in an independently identically distributed two-parameterWeibull model under censored sampling. The main idea is to incorporate the prior guessed value by correcting the standard estimator, which is essentially an unbiased estimator, with optimally weighted ratios of the guessed value and the standard estimator, instead of considering a convex combination of the standard estimator and the difference of the guessed value and the standard estimator. The resulting estimator dominates the standard estimator in a surprisingly large neighborhood of the guessed value. The suggested estimator has also been compared with the minimum mean squared error estimator and a class of estimators suggested by Singh and Shukla in IAPQR Trans 25(2), 107–118, 2000. It is found that the suggested class of estimators has lesser bias as well as lesser mean squared error than its competitors subject to certain conditions.      

Double acceptance sampling plan based on truncated life tests for half exponential power distribution

In this paper, we develop a double acceptance sampling plan for half exponential power distribution when the lifetime experiment is truncated at a prefixed time. The zero and one failure schemes are considered. We obtain the minimum sample sizes of the first and second samples necessary to ensure the specified mean life at the given consumer’s confidence level. The operating characteristic values and the minimum ratios of the mean life to the specified life are also analyzed. Numerical example is provided to illustrate the double acceptance sampling plan.     

Performances of some goodness-of-fit tests for sampling designs in ranked set sampling

In this study, we consider different sampling designs of ranked set sampling (RSS) and give empirical distribution function (EDF) estimators for each sampling designs. We provide comparative graphs for the EDFs. Using these EDFs, power of five goodness-of-fit tests are obtained by Monte Carlo simulations for Tukey's g–h distributions under RSS and simple random sampling (SRS). Performances of these tests are compared with the tests based on the SRS. Also, critical values belong to these tests are obtained for different set and cycle sizes.