Acceptance sampling plan based on an exponentially weighted moving average statistic with the yield index for autocorrelation between polynomial profiles

Acceptance sampling plans based on process yield indices provide a proven resource for the lot-sentencing problem when the required fraction defective is very low. In this study, a new sampling plan based on the exponentially weighted moving average (EWMA) model with yield index for lot sentencing for autocorrelation between polynomial profiles is proposed. The advantage of the EWMA statistic is the accumulation of quality history from previous lots. In addition, the number of profiles required for lot sentencing is more economical than in the traditional single sampling plan. Considering the acceptable quality level (AQL) at the producer's risk and the lot tolerance percent defective (LTPD) at the consumer's risk, we proposed a new search algorithm to determine the optimal plan parameters. The plan parameters are tabulated for various combinations of the smoothing constant of the EWMA statistic, AQL, LTPD, and two risks. A comparison study and two numerical examples are provided to show the applicability of the proposed sampling plan.     

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.     

Predictive design of single sampling attribute plans

The design of a sampling inspection plan is usually based on the properties of the operating characteristic curve. This approach ensures that the plan has adequate power to discriminate a lot of acceptable quality from a lot rejectable quality. However, the designed plan need not necessarily have adequate predictive power when the sentenced lot is re-inspected using the same sampling plan. The paper introduces a new design approach for the single sampling attributes plan ensuring the decision of acceptance or rejection is consistent for both current and any future inspection of the lot. The proposed design controls the risks of a future sample leading to a contradictory decision of acceptance or rejection of the lot. An increase in sample size is required to achieve the required predictive power if the true lot quality fails to be at very low fraction non-conforming levels. A Bayesian analysis is also provided.     

Comparison between count of cumulative conforming sampling plans and Dodge–Romig single sampling plan

In this research, a new sampling system is introduced based on the concept of count of cumulative conforming control charts (CCC-charts). The proposed method is based on Markov modeling and negative binomial distribution. The proposed sampling system is compared with traditional sampling methods like Dodge–Romig single sampling plan based on lot tolerance percent defective (LTPD) and Dodge–Romig single sampling plan based on average outgoing quality limit (AOQL) and its superiority for larger values of lot sizes and process average is denoted using a comparison study.     

Effects of industrial inspection errors on some plans that utilise the surrounding lot information

The effect of the inspector's accuracy on types I and II errors on Dependent and Deferred double sampling plans by Baker et al. (1978) and Chain-deferred inspection plans by Osanaiye (1983) which utilise the surrounding lot information on sentencing a lot is examined. The proportion of production that is wrongly accepted or rejected by each of the plans are also examined drawing particular attention to the effect of making resorts. A linear trend in process quality is assumed. The Chain-deferred plan in general has more tendency to reject defective items more than any of the other plans irrespective of the magnitude of the inspector's error. Although it has slightly higher tendency to reject good items, this is not very significant compared with the other plan as can be seen in the results.     

Variable repetitive group sampling plans with process loss consideration

Traditionally, most acceptance sampling plans considering the fraction defective do not distinguish among the products that fall within the specification limits. However, products that fall within the specification limits may not be good if their mean is far away from the target. So, developing an acceptance sampling plan with process loss consideration is essential. In this paper, a variable repetitive group sampling plan is proposed to deal with process loss. The design parameters of the proposed plan are tabulated for various combinations of acceptance quality levels. The proposed methodology can be used to determine whether the products meet the desired levels of protection for both producers and consumers.     

A new policy for designing acceptance sampling plan based on Bayesian inference in the presence of inspection errors

The purpose of this article is to present a new policy for designing an acceptance sampling plan based on the minimum proportion of the lot that should be inspected in the presence of inspection errors. It is assumed that inspection is not perfect and every defective item cannot be detected with complete certainty. The Bayesian method is used for obtaining the probability distribution function of the number of defective items in the lot. To design this model, two constraints of producer risk and consumer risk are considered during the inspection process by using two specified points on operating characteristic curve. In order to illustrate the application of the proposed model, an example is presented. In addition, a sensitivity analysis is performed to analyze the model performance under different scenarios of process parameters and the results are elaborated. Finally, the efficiency of the proposed model is compared with the sampling method of Spencer and Kevan de Lopez (2017) at the same conditions.     

Combined continuous lot by lot acceptance sampling plan

For production processes involving low fraction non-conforming, the sample sizes of the usual attribute inspection plans are very large. A continuous sampling plan for such processes would also require either a large clearance interval or a large sampling fraction. This paper simplifies the approach of combining the lot by lot and continuous sampling plans recommended by Pesotchinsky (1987) and provides various performance measures for the combined plan. A discussion of the choice of the parameters is also given.     

Design and Construction of a Variables Repetitive Group Sampling Plan for Unilateral Specification Limit

This paper attempts to develop a repetitive group sampling (RGS) plan by variables inspection for controlling the process fraction defective or the number of nonconformities when the quality characteristic follows a normal distribution and has only the lower or upper specification limit. The proposed sampling plan is derived by the exact sampling distribution rather than the approximation approach. The plan parameters are solved by a nonlinear optimization model which minimizes the average sample number required for inspection and fulfills the classical two-point conditions on the operating characteristic (OC) curve. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. The results indicate that the proposed variables RGS plan could significantly reduce samples required for inspection compared to the traditional variables single sampling plan.     

Assessment of acceptance sampling plans using posterior distribution for a dependent process

In this study, performance of single acceptance sampling plans by attribute is investigated by using the distribution of fraction nonconformance (i.e. lot quality distribution) for a dependent production process. It is the aim of this study to demonstrate that, in order to emphasize consumer risk (i.e. the risk of accepting a bad lot), it is better to evaluate a sampling plan based upon its performance as assessed by the posterior distribution of fractions nonconforming in accepted lots. Similarly, it is the desired posterior distribution that sets the basis for designing a sampling plan. The prior distribution used in this study is derived from a Markovian model of dependence.     

Optimal designing of a new mixed variable lot-size chain sampling plan based on the process capability index

In this paper, a new mixed sampling plan based on the process capability index (PCI) C_pk is proposed and the resultant plan is called mixed variable lot-size chain sampling plan (ChSP). The proposed mixed plan comprises of both attribute and variables inspections. The variable lot-size sampling plan can be used for inspection of attribute quality characteristics and for the inspection of measurable quality characteristics, the variables ChSP based on PCI will be used. We have considered both symmetric and asymmetric fraction non conforming cases for the variables ChSP. Tables are developed for determining the optimal parameters of the proposed mixed plan based on two points on the operating characteristic (OC) approach. In order to construct the tables, the problem is formulated as a non linear programming where the average sample number function is considered as an objective function to be minimized and the lot acceptance probabilities at acceptable quality level and limiting quality level under the OC curve are considered as constraints. The practical implementation of the proposed mixed sampling plan is explained with an illustrative real time example. Advantages of the proposed sampling plan are also discussed in terms of comparison with other existing sampling plans.     

On the performance of a sampling scheme in statistical quality control using incomplete prior information

Assume that a lower bound is known for the probability that the fraction defective of incoming lots does not exceed a certain level. Sampling plans which incorporate this information have been developed by Krumbholz and Schröder. Taking a linear cost model, the range of the gains that may be achieved using these plans instead of the minimax sampling plan is discussed. Some technical results concerning existence and uniqueness of sampling plans based on incomplete prior information are proved.     

A flexible sampling scheme for variables inspection with loss consideration

This article develops a variables sampling scheme for resubmitted lots by incorporating the concept of Taguchi loss function. The probability of lot acceptance is derived based on the exact sampling distribution and two-point condition on operating characteristic curve is used to determine the plan parameters that meet both the producer's and consumer's quality and risk requirements. Moreover, the performance of the proposed variables resubmitted sampling plan is investigated and compared with the classical variables single sampling plan. The results indicate that the developed resubmitted sampling plan can provide the same protection with less inspection when the submitted lot is good enough. Tables of the plan parameters under various conditions are provided and the use of the proposed plan is also illustrated with an example.     

Acceptance sampling by variables when the remainder of rejected lots is inspected

Acceptance sampling plans for inspection by variables, which minimize the mean inspection cost per lot of process average quality (assuming that the remainder of rejected lots is, inspected), were derived under the condition that the probability of accepting a submitted lot of tolerance quality, shall be 0.1. These plans were tabulated for chosen values of the given parameters, and compared with the Dodge-Romig LTPD attribute sampling plans. From the comparison it follows that under the same protection of consumer the LTPD plans for inspection by variables are in many situations more economical than the corresponding Dodge-Romig plans. This result is valid especially for the large lots and for the small values of the tolerance fraction defective.     

Dodge-Romig AOQL single sampling plans for inspection by variables

Acceptance sampling plans for inspection by variables, which minimize the mean inspection cost per lot of process average quality (assuming that the remainder of rejected lots is inspected), are derived under the condition that the maximum value of the mean fraction defective after sampling inspection, replacing all defective items found by good ones, shall be equal top _L . These plans are tabulated for chosen values of the given parameters, and compared with the Dodge-Romig AOQL attribute sampling plans. From the comparison it follows that under the same protection of consumer the AOQL plans for inspection by variables are in some situations more economical than the corresponding Dodge-Romig plans.     

Lot Sampling Distributions for Bounded Number of Nonconformities

Attributes sampling is an important inspection tool in areas like product quality control, service quality control or auditing. The classical item quality scheme of attributes sampling distinguishes between conforming and nonconforming items, and measures lot quality by the lot fraction nonconforming. A more refined quality scheme rates item quality by the number of nonconformities occurring on the item, e.g., the number of defective components in a composite product or the number of erroneous entries in an accounting record, where lot quality is measured by the average number of nonconformities occurring on items in the lot. Statistical models of sampling for nonconformities rest on the idealizing assumption that the number of nonconformities on an item is unbounded. In most real cases, however, the number of nonconformities on an item has an upper bound, e.g., the number of product components or the number of entries in an accounting record. The present study develops two statistical models of sampling lots for nonconformities in the presence of an upper bound a for the number of nonconformities on each single item. For both models, the statistical properties of the sample statistics and the operating characteristics of single sampling plans are investigated. A broad numerical study compares single sampling plans with prescribed statistical properties under the bounded and unbounded quality schemes. In a large number of cases, the sample sizes for the realistic bounded models are smaller than the sample sizes for the idealizing unbounded model.     

Iql indexed double sampling plans that are compatible with mil-std-105 d in structure

This paper presents a table that can be used to select a double sampling plan indexed by indifference quality level and lot size.     

Repetitive variable acceptance sampling plan for one-sided specification

In this paper, a variable repetitive group sampling plans based on one-sided process capability indices is proposed to deal with lot sentencing for one-sided specifications. The parameters of the proposed plans are tabulated for some combinations of acceptance quality levels with commonly used producer's risk and consumer's risk. The efficiency of the proposed plan is compared with the Pearn and Wu [Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives. Omega – Int J Manag Sci. 2006;34(1):90–101] plan in terms of sample size and the power curve. One example is given to illustrate the proposed methodology.     

Attribute-variable Inspection Policy for Lots Using Resampling Based on EWMA

A new mixed sampling plan which is a combination of the attribute single sampling plan and variables resampling scheme based on EWMA statistic is proposed in this paper. The operating characteristic function of the proposed plan is derived and the plan parameters are determined such that the probability of acceptance of good lot is larger than the specified producer's confidence level and the bad lot acceptance probability is smaller than the consumer's confidence level. The efficiency and the advantages of the proposed plan are discussed over the existing attribute sampling plan. The extensive tables are provided for industrial applications. The use of tables is discussed with the help of a real-time industrial example.     

An improved sampling plan by variables inspection with consideration of process yield and quality loss

Repetitive group sampling (RGS) plan, a modified version of single sampling (SS) plan, has been shown to be more efficient than the SS plan for lot sentencing. However, because it does not consider the valuable sample information from preceding lots, that could reduce its sampling efficiency and discriminatory power. Therefore, this study proposes a modified-RGS plan by considering the quality history of preceding lots based on the C_pmk index. Additionally, the mathematical model for the plan parameters is formulated such that the objective function is to minimize the average sample number (ASN), and the required quality levels and risks as specified by producer and consumer are satisfied. The performance of the proposed plan is examined and compared with traditional sampling plans. Finally, an example is presented to illustrate its applicability.