Skip-lot Sampling Plan Research Articles

An improved skip-lot sampling scheme with resampling mechanism using an advanced capability index

In today’s competitive market, product quality holds significant importance for consumers, motivating companies to prioritise high-quality product development and enhance their competitiveness. Acceptance sampling plans have proven to be indispensable tools in quality control practices, enabling producers and consumers to protect their interests by establishing evaluation rules for product batches. As defective rates decrease in modern manufacturing, skip-lot sampling plans (SkSP) have emerged as a suitable way for lots exhibiting stable and excellent product quality. Additionally, repetitive group sampling plan (RGSP) offers a cost-effective way to maintain desired protection for both parties, especially in costly or destructive inspection scenarios. Therefore, this study integrates the benefits of process capability indices, SkSP, and RGSP to develop a new variables SkSP with RGSP as its reference plan based on an advanced capability index Cpmk (called Cpmk -based SkSP-RGSP). The proposed plan achieves comparable discriminatory power to traditional sampling plans while significantly reducing the required sample size. Detailed tables of plan parameters are given to facilitate effective implementation for practitioners.

Optimal designing of skip-lot sampling plan with a provision for reducing the normal inspection using the Taguchi process capability index

A product with a strong track record of quality might have less inspection according to the skip-lot sampling plan. As a result, skip-lot sampling plans are created to cut down the inspection cost with desired protection. The skip-lot sampling method is also reliable, practical, and favorable from an economic standpoint. As a result, this work develops the SkSP-V plan, a novel system of skip-lot sampling plan, based on the Taguchi process capability index. The proposed plan stipulates that any lot is rejected during sampling inspection, normal inspection must resume, however, it also allows for a reduced level of normal inspection in the event that higher product quality is demonstrated. The exact sampling distribution of the estimated Taguchi capability index is used to derive the operating characteristic function of the proposed plan. An optimization model is employed to establish the optimal plan parameters, guaranteeing adherence to the specified quality levels and risk criteria. The performance measures such as probability of acceptance and average sample number of the proposed plan are examined and compared with existing plans. This article also includes real-world example to effectively demonstrate the practical implementation of the proposed SkSP-V plan based on the Taguchi process capability index.

A cost-effective skip-lot sampling scheme using loss-based capability index for product acceptance determination

Acceptance sampling plans are essential for quality control and assurance, empowering businesses to make well-informed decisions regarding lot disposition. Among these plans, the skip-lot sampling plan (SkSP) stands out as a cost-effective strategy for suppliers with consistently excellent product quality. In this article, we present an enhanced version of the SkSP, termed Cpm-based SkSP-RGSP, which incorporates a repetitive group sampling plan (RGSP) using the Taguchi capability index Cpm as its reference plan. We develop an optimization model to ensure that the proposed plan meets a two-point condition in its operating characteristic function and effectively minimizes the average sample number (ASN). Through investigations of two critical performance measures, ASN and discriminatory power, we demonstrate the superiority of our plan over conventional sampling approaches. Detailed plan parameters, including required sample size and lot sentencing criteria, are provided to assist examiners in practical implementation. Additionally, we showcase the plan's applicability and practicality through a case study. This research contributes to the field of quality control by offering an efficient and cost-effective sampling scheme for lot disposition.

A switcher skip lot-sampling plan under resubmitted lots using the Taguchi capability index for building a solid vendor-customer relationship

Variable sampling plans incorporating process capability indices (PCIs) have been introduced to adapt to the changing landscape of modern manufacturing, where the occurrence of defective goods has significantly decreased. Skip-lot sampling plans (SkSP) are particularly effective for batches characterized by consistent and high product quality. Additionally, manufacturers with a strong track record of producing high-quality goods or possessing empirical knowledge about their production processes can benefit from resampling. It has been demonstrated that resubmitted sampling plans outperform traditional single sampling plans. In this study, a novel variant of skip-lot sampling, referred to as SkSP-SR, is proposed. SkSP-SR utilizes two reference plans: one for normal inspection (utilizing SSP) and the other for skip inspection (utilizing RSP). The approach also considers the loss of information associated with deviations from the target by incorporating the Taguchi capability index. Compared to traditional sampling plans, the suggested approach not only reduces sample sizes but also enhances discriminating power. Comprehensive tables presenting plan parameters for commonly used quality and risk criteria are provided, enabling practitioners to readily implement the recommended plan.

Designing of quality interval skip-lot sampling plan with multiple deferred state sampling plan

Designing of quality interval skip-lot sampling plan with multiple deferred state sampling plan

Evaluation and optimal designing of a new system of skip-lot reinspection schemes

A new sampling plan by integrating the resampling concept in a skip-lot sampling plan of type SkSP-3 with a single sampling plan as the reference plan is proposed and designated as SkSP-3-R plan. The performance metrics are derived by using the Markov chain formulation. A designing methodology using two points on the operating characteristic curve approach is proposed to determine the plan parameters of the SkSP-3-R plan involving minimum the average sample number. The execution of the proposed SkSP-3-R plan is discussed with an illustrative example. The comparative study shows that the proposed plan has better performance where the inspection is involved in terms of nonconforming items rather than nonconformities. In addition, it demonstrates that the proposed SkSP-3-R plan is more efficient than SkSP-2 plan, SkSP-3 plan, SkSP-2-R plan, and SSP. Based on average run length, the SkSP-3-R plan's characteristic of response-to-change in quality is also investigated.

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.

Evaluation and optimal designing of a two-level skip-lot sampling plan for resubmitted lots

In the quality management system, skip-lot sampling is a prominent beneficial sampling plan concerning the economic aspect since it requires minimum expenses for inspection. This study attempts to propose an innovative sampling plan by assimilating the concept of a resampling scheme in a two-level skip-lot sampling plan of type 3, that is, SkSP-2L.3, and the resultant plan is designated as SkSP-2L.3-R with a single sampling plan as the reference plan. Using Markov chain formulation, the performance measures are derived. The designing methodology is provided to determine the plan parameters of the SkSP-2L.3-R plan to minimize the average sample number by using two points on the operating characteristic curve approach. Tables are constructed to select the plan parameters under binomial distribution and Poisson distribution by considering various combinations of producer and consumer quality levels along with respective producer and consumer risks. An illustrative example is provided to depict the execution of the proposed SkSP-2L.3-R plan. The comparative study substantiates that the proposed SkSP-2L.3-R plan with a single sampling plan as the reference plan has outstanding performance than some other existing plans under binomial and Poisson distributions.

Optimal design of a two-point variables skip-lot sampling plan with Taguchi capability index

The skip-lot sampling plan, an extension of the lot-by-lot based plan, not only retains the original characteristic of every lot inspection, but also skips lots appropriately when lot acceptance criterion is satisfied. Past studies have revealed that the skip-lot sampling plan saves more inspection samples than the traditional single sampling plan. However, most research related to the skip-lot sampling plan for variables lacks the additional loss assessment, when the quality deviated from the target value. Hence, this study proposes a skip-lot sampling plan based on the Taguchi capability index for variables products. The performance of the designed plan is investigated in terms of the operating characteristic curve and average sample number. Additionally, for the purpose of discussing how to select sampling frequency in this approach, a simulation study for average run length is conducted for validation. Finally, one practical case is presented for illustrating how to apply proposed method to resistor manufacturing to verify its applicability.

Designing and Selection of Bayesian Skip Lot Sampling Plan Type BSkSP-2 with Single Sampling Plan Under Zero-Inflated Poisson Distribution

Sampling plans are effective statistical technique for testing and deciding whether to accept or not a lot based on quality inspection studied under highway construction and materials. This article presents a designing methodology for the selection of Bayesian Skip lot Sampling Plan type 2 (BSkSP-2) based on Gamma-Zero Inflated Poisson (GZIP) distribution. A Gamma distribution is a baseline distribution that is to be considered as a conjugate prior for Zero-Inflated Poisson (ZIP) distribution. Generally, ZIP distribution is used for count data with an excessive number of zeros. In this article, ZIP distribution is mainly focused upon to study the occurrence of defective units in a well-designed manufacturing environment. In such case, one can develop an attribute sampling plan under the SkSP-2 through a G-ZIP model, to protect both the producers and consumers with the minimum inspection efforts rather than the conventional Poisson distribution. Necessary tables are developed for the proposed sampling plan and numerical illustrations are made for the applications on highway construction and materials are given for the execution of the plan.

Optimal skip-lot sampling plan based on the yield index for auto-correlated data

Acceptance sampling is one of the most important tools in quality control, and it has been extensively used in the industry for inspecting received lots. As different situations and purposes could be encountered in real life, numerous approaches for sampling plans have been established. When the quality of the process is good and stable, Skip-lot sampling plans (SkSPs) are useful strategies of sampling and could be an advantageous examination scheme. Therefore, this paper aims to incorporate the process yield index for a first-order autoregressive process S p k ; A R ( 1 ) and the SkSP, when the quality characteristic follows a normal distribution with bilateral specification limits, to produce a variables Skip lot sampling plan of type 2 (SkSP-2) with a single sampling plan (SSP) based on S p k ; A R ( 1 ) as the reference plan. A non-linear optimization model is solved to decide the plan parameters, by fulfiling the quality and risk obligations identified by the manufacturer and buyer and minimizing the average sample number (ASN). We investigated the efficiency and performance of the suggested SkSP-2 S p k ; A R ( 1 ) -based, associated with the variables SSP in terms of average sample number curves and the operating characteristic. Furthermore, the plan parameters with particular conditions are delivered for reference as tables, and an industrial application is offered to prove the applicability of the proposed plan.

Design of SkSP-R Plan for Popular Statistical Distributions

The design of a Skip-lot sampling plan of type SkSP-R is presented for time truncated life test for the Weibull, Exponentiated Weibull, and Birnbaum-Saunders lifetime distributions. The plan parameters of the SkSP-R plan under these three distributions are determined through a nonlinear optimization problem. Tables are also constructed for each distribution. The advantages of the proposed plan over the existing sampling schemes are discussed. Application of the proposed plan is explained with the help of an example. The Birnbaum-Saunders distribution is economically superior to other two distributions in terms of minimum average sample number.

Optimal design of a skip-lot sampling reinspection plan with a double sampling plan as a reference plan

Skip-lot sampling plans have the provision of inspecting only a fraction of lots, which reduces time and cost of the inspection. Thus, the skip-lot sampling plan is more cost-effective. The intention of this article is to propose the designing methodology to determine the optimal parameters of skip-lot sampling plan of type 2 with a double sampling plan as a reference plan for resubmitted lots by using two points on the operating characteristic curve. Tables summarize the optimal parameters determined under binomial and Poisson distributions for various combinations of producer quality level and consumer quality level by minimizing the average sample number and subject to satisfying both producer’s risk and consumer’s risk. The execution of the proposed plan is provided with an illustrative example. By comparison, it is proved that the proposed plan is an outstanding plan than the existing skip-lot and conventional sampling plans in terms of probability of acceptance, average sample number, and average total inspection.

Developing a skip-lot sampling scheme by variables inspection using repetitive sampling as a reference plan

ABSTRACT In today’s manufacturing environment, the rate of defective products has been continuously decreasing; thus, variables sampling plans with process capability indices (PCIs) have been recommended to gather more information about a manufacturing process and reduce required sample sizes for inspection. In particular, skip-lot sampling plan (SkSP) is suitable for a series of lots having stable and excellent product quality. Moreover, the concept of repetitive group sampling (RGS), which can allow the use of less samples to maintain desired protection to producers and consumers, is especially appropriate where inspection or testing is costly or destructive. This study, by incorporating the advantages of PCIs, SkSP, and RGS, constructs a variables SkSP with RGS as the reference plan (called SkSP-RGS) based on one-sided PCIs for products with a unilateral specification limit. The proposed plan reduces the sample size while achieving a similar discriminatory power, compared with a conventional variables single sampling plan (SSP), a RGS plan (RGSP), and a SkSP of type 2 (SkSP-2). Tables of plan parameters are provided for frequently applied quality and risk requirements so that practitioners can easily apply the proposed plan.

Variables skip-lot sampling plans on the basis of process capability index for products with a low fraction of defectives

The skip-lot sampling plan (SkSP) is employed in supply chains to decrease the amount of inspection required for submitted lots when they have demonstrated a succession of lots with excellent quality. As only some fractions of lots are examined, the cost of inspection is reduced. With the current abundance of high-yield products, however, the majority of SkSP schemes have been utilized for attributes testing, which does not fully reveal the SkSP’s economic advantages. Thus, on the basis of the process capability index Cpk, the variables SkSP with single sampling as a reference plan (Cpk-SkSP-2) was developed. With management of the lot’s quality and tolerable risks agreeable to both the supplier and the buyer, the Cpk-SkSP-2 were incorporated with acceptance probabilities (rather than asymptotic approximations), which yielded the exact sampling distribution of the Cpk estimator at the specified quality standards. Furthermore, the equilibrium probability for the acceptance of Cpk-SkSP-2 was derived from a Markov chain technique. These treatments enable minimization of the average number of samples required to render more reliable and optimal plan parameters for the inspection of products with a low fraction of defectives. The results are compared with the variables Cpk-based single sampling plans. Finally, a graphical user interface was built on the basis of our proposed Cpk-SkSP-2 procedures and methodologies to facilitate data input, plan selection, criteria computation, and decision-making in practice.

Designing a yield-based skip-lot sampling plan for lot acceptance determination

Acceptance sampling has been widely used in practical applications for incoming or receiving inspections, and various sampling plans have been developed for different circumstances and purposes. Skip-lot sampling plans (SkSPs) are an effective sampling procedure and may be useful as a reduced inspection system when a submitted lot’s quality is good and stable. Thus, this study attempts to integrate the concept of the SkSP and the process yield index Spk to develop a variables SkSP of type 2 (SkSP-2) with an Spk -based single sampling plan (SSP) as the reference plan. This plan is suitable for today’s high-yield process environments and products, with a normally distributed quality characteristic under bilateral specification limits. The plan parameters are solved by an optimisation model with nonlinear constraints, which minimises the average sample number (ASN) and satisfies the quality and risk requirements specified by the producer and consumer. The performance and efficiency of the proposed SkSP-2 are examined and compared with the variables SSP in terms of the operating characteristic and ASN curves. Additionally, tables of the plan parameters under selected conditions are provided for reference, and an example from the printed circuit board industry is presented to demonstrate the practicality of the proposed plan.

Optimal designing of two-level skip-lot sampling reinspection plan

Skip-lot sampling plan is often applied in industries for reducing the cost and effort of the inspection of the product having excellent quality history. Consequence of skip-lot sampling plans is to reduce the cost of inspection so which are more attractive in economical aspect. In this paper, we develop a sampling plan by incorporating the idea of resampling in two-level skip lot sampling plan and the new plan is designated as SkSP-2L.1-R. This paper presents the Markov chain formulation of the proposed plan along with the derivation of performance measures of the plan. We also provide the designing methodology to determine the optimal parameters of the SkSP-2L.1-R plan so as to minimize the average sample number by using two points on the operating characteristic curve approach. By contemplating various combinations of producer and consumer quality levels along with respective risks, a table is constructed to determine the optimal parameters. An industrial application of the proposed SkSP-2L.1-R plan is discussed. The SkSP-2L.1-R with single sampling plan as a reference plan is compared with the conventional single sampling plan, SkSP-2 plan and SkSP-2-R plan and proved that the proposed SkSP-2L.1-R plan outperforms these plans.

A variable-type skip-lot sampling plan for products with a unilateral specification limit

Acceptance sampling plans are practical quality management tools for lot sentencing. The rapid advancement of manufacturing technologies has reduced the defective rate substantially, and as a result, variables sampling plans with process capability indices (PCIs) have been adopted widely so that the required sample size can be decreased. Skip-lot sampling plan (SkSP), which evolved from the continuous sampling plan type-1, is applicable to bulk materials or products manufactured in successive batches or lots. It requires a smaller fraction of lots being examined, and the cost of inspection thus can be reduced. Hence, this paper consolidates the advantages of PCIs and SkSP, and proposes a skip-lot sampling plan of type-2, called SkSP-2, based on the one-sided PCIs for products with a unilateral specification limit. The proposed plan uses the exact sampling distribution of the estimators to develop a mathematical model for determining plan parameters, and the research prepares tables of plan parameters under different combinations of quality requirements and risk levels for quick reference in real applications. In addition, the results are compared with a conventional sampling plan to examine the contribution of the approach, and extensions to two types of SkSP are also presented. Finally, a graphical user interface is constructed to facilitate data input, criteria calculation and decision-making in practice.

Skip-lot sampling plan of type SkSP-T for life testes based on percentiles of exponentiated Rayleigh distribution

This paper developed a scheming procedure of skip-lot sampling plan of type SkSP-T with single sampling plan for life tests based on the median percentiles of exponentiated Rayleigh distribution and applied it to determine the lifetime of any product. This procedure finds minimum sample size at required producer and consumer quality levels. In this study, life testing plans based on 50th percentile (median) is measured. Tables are simulated for various parametric values of SkSP-T and exponentiated Rayleigh distribution.

Designing of Skip-lot Sampling Plan -V with Minimum Angle Criteria

Designing of Skip-lot Sampling Plan -V with Minimum Angle Criteria