Double Sampling Plans Research Articles

A Bayesian approach with double group sampling plan to estimate quality regions for proportion of nonconforming products in industry based on beta prior

To succeed in the global market, firms must prioritize quality over individual goals and preferences. One of the two primary approaches for ensuring quality is acceptance sampling, which is employed in statistical process control to inspect attributes of the product for acceptance. In acceptance sampling, the lot is either accepted or not-accepted based on predetermined acceptance criteria for inspection. This paper presents a proposed Bayesian double group sampling plan (BDGSP) for estimating quality regions. The binomial distribution is used to construct the likelihood function for both nonconforming and conforming products based on acceptance criteria. To calculate the average probability of acceptance, the beta distribution is used as a suitable prior distribution of the binomial distribution. Four distinct quality regions are predicted for various indicated producer’s and consumer’s risk levels. Based on various combinations of values for design parameters, the suggested plan generates variation point values. Risks for producers and consumers are related to acceptable quality level and limiting quality level. To track the effects of changes in the values of the specified parameters, operating characteristic curves are utilized. The applicability of the proposed plan for current industrial strategies is demonstrated using a real dataset.

Developing a stage-independent multiple sampling plan with loss-based capability index for lot disposition

Multiple sampling plan (MSP) is a generalization of single and double sampling plans that enhances the efficiency by reducing the number of sample items needed for inspection. However, the operating characteristic function of MSP is relatively complicated to derive because the inspection at each stage is dependent on others, i.e., the lot judgment on the current lot not only depends on its inspected result but also considers the results of the previous stages. Therefore, in this study, we propose a stage-independent MSP (SIMSP) and integrate it with a loss-based capability index. SIMSP can be regarded as a relaxed form of the traditional MSP, assuming independence in inspections at each stage. SIMSP’s parameters are solved for a cost-efficient purpose under an optimization model that aims to minimize the average sample number (ASN), adhering to constraints aligned with predefined quality and acceptable risk levels. The results indicate that SIMSP can not only perform better discriminatory power but also require fewer ASN for making lot disposition. Besides, SIMSP’s performance is evaluated, analyzed, and contrasted with the traditional sampling plan under various settings. In addition, an example is presented using the developed graphical user interface to illustrate the real-world application of SIMSP.

Optimal double acceptance sampling plans based on truncated life tests for Tsallis q-exponential distributions

Optimal double sampling plans for lot acceptance based on truncated life tests are derived by minimizing the expected sample size when the lifetime variable follows a Tsallis q-exponential distribution. The proposed test plans significantly reduce the inspection effort with respect to the best single sampling schemes. Some tables and figures are presented to analyze the behavior of the suggested test plans. The results show that the proposed lot inspection scheme clearly outperforms the standard single sampling plan. A justification is provided using a comparative study for existing double sampling plans. Finally, several applications are provided for illustrative purposes.

Optimal time truncated double acceptance sampling plan for generalized half normal distribution

Optimal time truncated double acceptance sampling plan for generalized half normal distribution

A double sampling plan for truncated life tests under two-parameter Lindley distribution

A double sampling plan for truncated life tests under two-parameter Lindley distribution

Designing Of Double Sampling Plan Indexed Through Six Sigma Quality Level – 1 Using Truncated Binomial Distribution

Among the various probability distributions utilized to characterize situations where an observational apparatus becomes active only upon the occurrence of at least one event, the Zero Truncated Poisson Distribution (ZTPD) stands out. Shanmugam (1985) demonstrated the applicability of the ZTPD in modeling scenarios such as second quality lots, where there exists the possibility of at least one defective item in the sample. In this paper, a systematic procedure for constructing Double Sampling Plans, indexed through Six Sigma Quality Level – 1 (SSQL - 1), is presented. The methodology employs the Truncated Binomial Distribution (TBD) as the baseline distribution. Furthermore, to facilitate the selection of these plans, tables generated using an Excel packages are provided, ensuring ease of use and accessibility.

Optimal and economic design of modified double sampling plan under new Weibull–Pareto distribution

PurposeThe purpose of this paper is to design a modified version of the double sampling plan to handle the inspection processes requiring a minimum sample size to assure the median life for the products under the new Weibull–Pareto distribution. The economic design of the proposed plan is also considered to assure the product's lifetime with minimum cost.Design/methodology/approachThe authors have developed an optimization model for obtaining the required plan parameters by solving simultaneously two non-linear inequalities and such inequalities have been formed based on the two points on the operating characteristic curve approach.FindingsThe results show that the average sample number, average total inspection and total inspection cost under the proposed plan are smaller than the same of a single sampling plan. This means that the proposed plan will be more efficient than a single sampling plan in reducing inspection effort and cost while providing the desired protection.Originality/valueThe proposed modified double sampling plan designed to assure the median life of the products under the new Weibull–Pareto distribution is not available in the literature. The proposed plan will be very useful in assuring the product median lifetime with minimum sample size as well as minimum cost in all the manufacturing industries.

Application and validation of machine vision inspection for efficient in-process monitoring of complex biomechanical device manufacturing

A technique is presented for shifting the manufacturing quality control of complex biomechanical catheters away from destructive testing of finished parts. This technique uses a more efficient real-time in-process monitoring through the application of machine vision inspection of patient critical quality parameters. The approach acknowledges the challenge of this industry operating in a strict regulated environment. The higher standards of built-in quality are achieved by developing automated inspection solutions that are more accurate and repeatable. Machine vision system and associated inspection job tools are developed and used to detect defects at crucial stages of manufacturing. The vision system is then tested for its robustness using a statistical approach to ensure its measurement capability is within the allowable process range and tolerances. The integrated solution developed is proven to be robust and highly precise in maintaining the manufacturing process stable. It enabled the manufacturing process to move away from a destructive double sampling plan with a standard LTPD of 5% to an otherwise real-time 100% non-destructive verification of units. This technique provides an alternative to otherwise cost-inefficient quality control inspections utilized in regulated manufacturing environment. It gives confidence to these conservative industries to move towards adopting digital manufacturing and Industry 4.0 practices.

Quality Control Testing with Experimental Practical Illustrations under the Modified Lindley Distribution Using Single, Double, and Multiple Acceptance Sampling Plans

Quality control testing under acceptance sampling plans involves inspecting a representative sample of products or materials from a larger lot or batch to determine whether the lot meets predetermined quality standards. In this research, the modified Lindley distribution is used as a model for lifetime study. When a life test is amputated at a pre-appropriated time to decide on the admission or refusal of the submitted batches, the problems of the single, double, and multiple (three and four stages) acceptance sampling strategies are introduced. The optimal sample sizes are computed for single, double, and multiple acceptance sampling plans to ensure that the veritable mean life is greater than the prescribed mean life at the stipulated consumer’s risk. The operating characteristic functions are investigated at diverse quality levels. For single, double, and multiple acceptance sampling plans, the minimal ratios of the veritable mean life to the prescribed mean life at the established percent of the producer’s risk are obtained. To demonstrate the uses of single, double, and multiple, some numerical experiments are presented.

Design of double acceptance sampling plan for Weibull distribution under indeterminacy

<abstract> <p>This paper addresses neutrosophic statistics that will be used to design a double- acceptance sampling plan. We will design the sampling plans when the lifetime of the product follows the neutrosophic Weibull distribution. The plan parameters of the proposed double sampling plan will be determined using nonlinear optimization at various indeterminacy values and parameters. The productivity of the double sampling plan using neutrosophic statistics over the sampling plan under classical statistics will be given. The presentation of the proposed double sampling plan will be given with the help of industrial data.</p> </abstract>

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan (AMDSSP) was designed to inspect products from a continuous manufacturing process under the accelerated life test (ALT) using both double sampling plan (DSP) and multiple dependent state sampling plan (MDSSP) concepts. Under accelerated conditions, the lifetime of a product follows the Weibull distribution with a known shape parameter, while the scale parameter can be determined using the acceleration factor (AF). The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive. An economic design of the proposed sampling plan was also considered for the ALT. A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number (ASN) and total cost of inspection (TC) under both producer’s and consumer’s risks. Numerical results are presented to support the AMDSSP for the ALT, while performance comparisons between the AMDSSP, the MDSSP and a single sampling plan (SSP) for the ALT are discussed. Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions. The AMDSSP also had a higher operating characteristic (OC) curve than both the existing sampling plans. Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

Construction and selection of conditional double sampling plan indexed through AOQcc

Construction and selection of conditional double sampling plan indexed through AOQcc

Determination of modified double sampling plan based on the process capability index

Sampling plans developed based on the process capability indices have great impact in assuring the quality of procured goods since such indices are widely applied in industries to monitor the process quality. In this manuscript, a modified double sampling plan is proposed for variables inspection based on the process capability index Cpk. The proposed sampling plan, an alternative to the existing double sampling plan, can be used with less complexity for the inspection of normally distributed quality characteristics when both mean and variance are unknown. To determine the optimal parameters of the proposed plan for symmetric and asymmetric cases of fraction nonconforming with double specification limits, we use the methodology of two points on the operating characteristic curve. It is shown that the proposed plan is more advantageous than other existing sampling plans under variables inspection. Finally, an economic aspect of design of the proposed sampling plan is also presented.

Designing of Variables Double Sampling Plan Under Rectifying Inspection for Consumer Protection

Designing of acceptance sampling plans based on operating characteristics fail to prescribe the corrective action for rejected lots although they guarantee the producer’s and the consumer’s protection at their corresponding quality levels. But, rectification sampling inspection plan suggests 100% inspection for rejected lots and hence, the producer’s risk is reduced and also there is a guarantee to the consumer by restricting upper limit of the maximum expected proportion of non-conforming of the shipping lot. Although the variables single sampling plan for rectifying inspection is available, variables double sampling inspection plan under rectifying inspection has not yet been designed. Hence, in this paper, we design a variables double sampling plan for rectifying inspection indexed by acceptable quality level and average outgoing quality limit to meet the needs of the producer as well as the consumer. A non-linear optimization problem is developed to determine the optimal parameters with minimum average sample number at acceptable quality level for both cases of standard deviation are known and unknown. We investigate the validation and limitation of the proposed plan through the simulation study and industrial application of the proposed plan is also given. It can be confirmed from the investigations on the results that in many situations, variables double sampling plan designed under rectifying inspection is more economical than variables single sampling plan designed with the same conditions in providing the same protection to consumer.

A DESIGN OF SPECIAL PURPOSE DOUBLE SAMPLING PLAN OF TYPE DSP(0, 1) USING FUZZY PARAMETER

In traditional sampling plan, the proportion defective is generally assumed to be crisp value. But, in real life parameters are vague and assumptions are too rigid. So traditional methods are inaccurate. In this paper Fuzzy set theory is applied to acceptance sampling. A procedure for designing Special Purpose Double Sampling Plan of Type DSP(0, 1) using trapezoidal fuzzy number is developed and it is based on fuzzy binomial distribution. The OC curve values are determined using fuzzy parameter while fixing the sample size. Fuzzy probability of acceptance values are calculated for different AQL ] and LQL ] values and are presented in Tables for the selection of DSP(0, 1) Plan. Optimum value of the sample size is obtained such that it satisfies both the condition of producer’s risk and consumer’s risk for given AQL ] and LQL ] values. The sample size is obtained such that it minimizes the sum of risks. Numerical examples are provided for the illustrations.

An economic model based on SkSP-2 with double sampling plan as the reference plan

Skip-lot sampling plans have been widely used in industries to reduce inspection efforts when products have excellent quality records. This paper provides an economic model based on SkSP-2 with the double sampling plan as a reference plan. The various combinations of producer quality level and consumer quality level by minimizing both the producer’s and the consumer’s risk have been discussed. Numerical examples are provided to confirm the application of the proposed concept.

Construction and Selection of Double Inspection Single Sampling Plan for an Independent Process Using Bivariate Poisson Distribution

There are more sampling concepts active in production Industries, for inspecting the samples and analysing performance of the population. Also the sampling plans reduce errors in the production and produce the error free products. In this study, construction and selection of Double Inspection with reference to Single Sampling Plan i.e., DISSP, by attribute are investigated by using the Bivariate Poisson distribution. The Methodology, DISSP, was proposed based on two quality characteristics of the same sample size, and the planning parameters (n, C₁, C₂) are based on the operating characteristics, the conventional two-point condition by the planning table parameters (AQL and LQL). It is based on selected quality requirements and risks designed to allow manufacturers to easily determine the required sample size and corresponding acceptance criteria. A Comparison was done based on the efficiency of the plan with an existing single sampling plan and gave a numerical example to expose the operating tables. Also, the study shows the advantages of the proposed plan, and performance of the curves like, Operating characteristics, Average Outgoing Quality, and Average Total Inspection to expose the proposed double inspection sampling plan.

Design of double sampling inspection plans for life tests under time censoring based on Pareto type IV distribution

Sampling inspection plans for life tests, called reliability sampling plans, are generally employed to determine the acceptance or non-acceptance of the lot(s) of finished products by performing tests on the sampled items, measuring the lifetime of the items and observing the number of failures of items. Lifetime of individual items is a prime quality characteristic that can be treated as a continuous random variable and can be modeled by an appropriate probability distribution. In this article, double sampling plans for life tests under time censoring with a provision to draw two random samples and to admit a maximum of one failure in the combined samples are formulated assuming that the lifetime random variable follows a Pareto type IV distribution. A methodical procedure for the selection of the plan parameters using reliable life criterion with the desired discrimination protecting the interests of the producer and the consumer in terms of the acceptable reliable life and unacceptable reliable life is evolved. The operating ratio is used as a measure of discrimination in designing the proposed reliability sampling plans.

A design for special type double sampling plan under fuzzy environment

Acceptance sampling is effective tool in quality assurance. This paper introduces a new design for special type double sampling plan when their main parameters are fuzzy. Fuzzy special type double sampling plan (FSTDSP) is given by providing fuzzy acceptance probability of special type double sampling plan using fuzzy Poisson distributions. Definitions and calculation of fuzzy special purpose double sample plan (FSTDSP) is provided with an example. OC curve for fuzzy special purpose double sampling plan is provided.

Comparative study on double inspection single sampling plan with existing single sampling plan

Sampling inspection plans are playing a vital role in the production Industries. The professionals insist on the product very strict quality control measures should be adopted in order to avoid rejection and satisfying the need of the customer. In this article describes comparative study of Double Inspection Sampling Plan with Single Sampling Plan through operating characteristics curve and sample size. Also this article discussed the brief review of operating procedures, flow charts and operating characteristics functions of above plans.