Optimal acceptance sampling policy considering Bayesian risks

In this paper, we propose a sampling policy considering Bayesian risks. Various definitions of producer's risk and consumer's risk have been made. Bayesian risks for both producer and consumer are proven to give better information to decision-makers than classical definitions of the risks. So considering the Bayesian risk constraints, we seek to find optimal acceptance sampling policy by minimizing total cost, including the cost of rejecting the batch, the cost of inspection, and the cost of defective items detected during the operation. Proper distributions to construct the objective function of the model are specified. In order to demonstrate the application of the proposed model, we illustrate a numerical example. Furthermore, the results of the sensitivity analysis show that lot size, the cost of inspection, and the cost of one defective item are key factors in sampling policies. The acceptable quality level, the lot tolerance proportion defective, and Bayesian risks also affect the sampling policy, but variations of acceptable quality level and producer Bayesian risks, for values more than a specified value, cause no changes in sampling policy.     

Designing an economically optimal repetitive group-sampling plan based on loss functions

Acceptance sampling is a quality assurance tool, which provides a rule for the producer and the consumer to make acceptance or rejection decision about a lot. This paper attempts to develop a more efficient sampling plan, variables repetitive group sampling plan, based on the total loss to the producer and consumer. To design this model, two constraints are considered to satisfy the opposing priorities and requirements of the producer and the consumer by using Acceptable quality level (AQL) and Limiting quality level (LQL) points on operating characteristic (OC) curve. The objective function of this model is constructed based on the total expected loss. In order to illustrate the application of the proposed model, an example is presented. In addition, the effects of process parameters on the optimal solution and the total expected loss are studied by performing a sensitivity analysis. Finally, the efficiency of the proposed model is compared with the variables single sampling plan, the variables double sampling plan and the repetitive group sampling plan of Balamurali and Jun (2006) in terms of average sample number, total expected loss and its difference with ideal OC curve.     

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.     

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.     

Selection of csp-t plans

Various continuous sampling plans have been proposed for monitoring the quality of continuous production processes. The multi-level continuous sampling plan of MIL-STD-1235C (1988) is designated as CSP-T Plan. CSP-T plan is a three-level tightened continuous sampling plan. It requires a switch to 100% inspection, at any level, whenever a nonconforming unit is found. This provides quick rectification in the event of a shift in quality. In this paper certain performance characteristics of CSP-T plan are derived using the approach of Stephens (1979) under the assumption that the production process is in statistical control. For the selection of CSP-T plans, two tables are given. These tables can be used to obtain parameters i (clearance interval) and f (sampling fraction) of the CSP-T plan for given acceptable quality level (AQL) with producer’ risk α=0.05 or the limiting quality level(LQL) with consumer’ risk β=0.10 and the outgoing quality limit(AOQL). Two examples are also given to illustrate the selection of plans from these tables     

Designing an economic rectifying sampling plan in the presence of two markets

In this paper, an optimization model is developed for the economic design of a rectifying inspection sampling plan in the presence of two markets. A product with a normally distributed quality characteristic with unknown mean and variance is produced in the process. The quality characteristic has a lower specification limit. The aim of this paper is to maximize the profit, which consists the Taguchi loss function, under the constraints of satisfying the producer's and consumer's risk in two different markets simultaneously. Giveaway cost per unit of sold excess material is considered in the proposed model. A case study is presented to illustrate the application of proposed methodology. In addition, sensitivity analysis is performed to study the effect of model parameters on the expected profit and optimal solution. Optimal process adjustment problem and acceptance sampling plan is combined in the economical optimization model. Also, process mean and standard deviation are assumed to be unknown value, and their impact is analyzed. Finally, inspection error is considered, and its impact is investigated and analyzed.     

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.     

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.     

Modified chain sampling plans for lot inspection by variables and attributes

The purpose of acceptance sampling is to develop decision rules to accept or reject production lots based on sample data. When testing is destructive or expensive, dependent sampling procedures cumulate results from several preceding lots. This chaining of past lot results reduces the required size of the samples. A large part of these procedures only chain past lot results when defects are found in the current sample. However, such selective use of past lot results only achieves a limited reduction of sample sizes. In this article, a modified approach for chaining past lot results is proposed that is less selective in its use of quality history and, as a result, requires a smaller sample size than the one required for commonly used dependent sampling procedures, such as multiple dependent sampling plans and chain sampling plans of Dodge. The proposed plans are applicable for inspection by attributes and inspection by variables. Several properties of their operating characteristic-curves are derived, and search procedures are given to select such modified chain sampling plans by using the two-point method.     

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.     

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.     

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.     

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.     

Designing of a mixed-chain sampling plan based on the process capability index with chain sampling as the attributes plan

In this article, we propose a new mixed chain sampling plan based on the process capability index C_pk, where the quality characteristic of interest having double specification limits and follows the normal distribution with unknown mean and variance. In the proposed mixed plan, the chain sampling inspection plan is used for the inspection of attribute quality characteristics. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications by formulating the problem as a non linear programming in which the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.     

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.     

The Consumer’s Risk and Costs in Zero-Acceptance Number Sampling

The primary purpose of sampling inspection is the protection of consumer’s interests. Although under simple cost models, sampling inspection never serves the producer’s interest, some form of sampling inspection can be beneficial to the consumer under the same assumptions. We consider the case of isolated lot inspection and examine the consumer risk, economic sample design, and errors in the inspection process. Acceptance sampling is shown to be cost-effective to the consumer whenever the lot quality is less than perfect, and even for perfect lot quality in the presence of inspection errors.     

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.     

Efficient Bayesian sampling plans for exponential distributions with type-I-censored samples

The aim of this paper is to introduce an efficient Bayesian sampling procedure for exponential distribution with type-I censoring. An online inspection method is suggested to reach a Bayes decision prior the termination time of life test. Bayesian sampling plans (BSPs) with quadratic loss function are established to illustrate the use of the proposed method. Some BSPs are tabulated, and the performance of the proposed BSPs is compared with two existing competitive methods. Numerical results indicate that a significant reduction in the experimental time over the conventional BSP can be achieved when the online inspection method is applied.     

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.     

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.