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.     

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.     

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.     

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.     

Acceptance sampling based on truncated life tests for generalized Rayleigh distribution

This paper considers the problem of an acceptance sampling plan for a truncated life test when the lifetime follows the generalized Rayleigh distribution. For different acceptance numbers, confidence levels, and values of the ratio of the fixed experiment time to the specified mean life, the minimum sample sizes necessary to ensure the specified mean life are found. The operating characteristic values of the sampling plans and producer's risk are discussed. Some tables are presented and the use of the tables is illustrated by a numerical example.     

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 an SkSP-R double sampling plan

In this article, we propose a method of planning and determining the optimum parameters of a SkSP-R skip-lot sampling plan by using the attribute double sampling plan as the reference plan. The SkSP-R plan is a new type of skip-lot sampling plan which has a provision for re-inspecting the submitted lots. The optimal plan parameters of the suggested sampling plan are estimated with the target that the average sample number be minimized and satisfying both the specified producer's as well as the consumer's risks simultaneously. In order to obtain the optimum parameters, tables are also built for different combinations of the acceptable quality level and the limiting quality level in conjunctions with different producer's and consumer's risks. An illustrative example is provided for the implementation of the suggested plan. The advantages of the suggested plan over the existing conventional sampling plans and other existing skip-lot sampling plans are also described.     

A new sampling plan under the exponential distribution

This article considers a sampling plan when the quality characteristic follows the exponential distribution. We provide the exact approach and propose an approximated approach. In the proposed approximation, a new statistic combined with a Weibull transformation is used for the normal approximation. The plan parameters are obtained through the two-point approach at the acceptable quality level (AQL) and the limiting quality level (LQL). The tables for plan parameters are reported according to various values of the AQL and the LQL when the producer's and the consumer's risks are given. A real example is given to illustrate the proposed approximation approach.     

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 mixed double sampling plan based on Cpk

Abstract

Acceptance sampling plans are quality tools for the manufacturer and the customer. The ultimate result of reduction of nonconforming items will increase the profit of the manufacturer and enhance the satisfaction of the consumer. In this article, a mixed double sampling plan is proposed in which the attribute double sampling inspection is used in the first stage and a variables sampling plan based on the process capability index C_pk is used in the second stage. The optimal parameters are determined so that the producer’s and the consumer’s risks are to be satisfied with minimum average sample number. The optimal parameters of the proposed plan are estimated using different plan settings using two points on the operating characteristic curve approach. In designing the proposed mixed double sampling plan, we consider the symmetric and asymmetric nonconforming cases under variables inspection. The efficiency of the proposed plan is discussed and compared with the existing sampling plans. Tables are constructed for easy selection of the optimal plan parameters and an industrial example is also included for implementation of the proposed plan.     

Design of an attribute np control chart for process monitoring based on repetitive group sampling under truncated life tests

In this paper, an attribute control chart under repetitive group sampling is designed for monitoring the production process where the lifetime of the product is considered as quality of the product. We assume that the lifetime follows the Pareto distribution of second kind with known shape parameter. The performance of the proposed chart is evaluated by average run length. The control limits coefficients as well as the repetitive group sampling parameter such as sample size are determined such that the in-control average run length is as close as to the specified average run length. Out-of-control average run length is also reported for different shift constants with corresponding optimal parameters. In addition, performance of proposed control chart is compared with the performance of existing chart. An economical designing of proposed control chart is also discussed.     

A variables repetitive group sampling plan under failure-censored reliability tests for Weibull distribution

We propose a variables repetitive group sampling plan under type-II or failure-censored life testing when the lifetime of a part follows a Weibull distribution with a known shape parameter. The acceptance criteria do not involve unknown scale parameter differently from the existing plans. To determine the design parameters of the proposed plan, the usual approach of using two points on the operating characteristic curve is adopted and an optimization problem is formulated so as to minimize the average number of failures observed. Tables for design parameters are constructed when the quality of parts is represented by the unreliability or the ratio of the mean lifetime to the specified life. It is found that the proposed sampling plan can reduce the sample size significantly than do the single sampling plan.     

An economic reliability test plan: Log-logistic distribution

Sampling plans in which items that are put to test, to collect the life of the items in order to decide upon accepting or rejecting a submitted lot, are called reliability test plans. The basic probability model of the life of the product is specified as the well-known log-logistic distribution with a known shape parameter. For a given producer's risk, sample size, termination number, and waiting time to terminate the test plan are computed. The preferability of the test plan over similar plans existing in the literature is established with respect to cost and time of the experiment.     

Time truncated acceptance sampling plans for generalized exponential distribution

Acceptance sampling plans for generalized exponential distribution when the lifetime experiment is truncated at a pre-determined time are provided in this article. The tables are provided for the minimum sample size required to ensure a certain median life of the experimental unit when the shape parameter is two. The operating characteristic function values of the sampling plans and the associated producer's risks are also presented. It is shown that the tables presented here can be used if instead of median life, other percentile life is chosen as the criterion or if the shape parameter is not two. Examples are provided for illustrative purposes.     

Determination of a new mixed variable lot-size multiple dependent state sampling plan based on the process capability index

This article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on C_pk and the mixed variable lot size plan based on C_pk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.     

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.     

Exact calculations for sequential tests based on Bernoulli trials

We consider methods of computing exactly the probability of “acceptance” and the “average sample size needed” for the sequential probability ratio test (SPRT) and likewise the newer “2-SPRT,” concerning the value of a Bernoulli parameter. The methods permit one to approximate, iteratively, the desired operating characteristics for the test.     

Repetitive group sampling plan based on the process capability index for the lot acceptance problem

An acceptance sampling plan is a method used to make a decision about acceptance or rejection of a product, based on adherence to a standard. Meanwhile, process capability indices (PCIs) have been applied in different manufacturing industries as capability measures based on specified criteria which include process departure from a target, process consistency, process yield and process loss. In this paper, a repetitive group sampling (RGS) plan based on PCI is introduced for variables’ inspection. First, the optimal parameters of the developed RGS plan are obtained considering constraints related to the risk of consumers and producers and also a double sampling plan, a multiple dependent state sampling plan and a sampling plan for resubmitted lots have been designed. Finally, after the development of variable sampling plans based on the Bayesian and exact approach, a comparison study has been performed between the developed RGS plan and other types of sampling plans and the results are elaborated.     

Multiple dependent state repetitive sampling plans with or without auxiliary variable

In this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.