Bayesian Acceptance Sampling Plans Research Articles

Design and Evaluation of Bayesian Dependent State Sampling Inspection Plans

Abstract The theory of sampling inspection procedures by attributes is built upon the general assumptions that the manufacturing process from which lots are formed is stable and that the lot or process fraction nonconforming is a constant. However, in practice, the lots formed from any production process will have quality variations, which occur due to random fluctuations. When quality variations are present in a process, the proportion of nonconforming units in the lots will vary continually. In such cases, Bayesian acceptance sampling plans (BASP), which use prior information on the process variation for taking decisions about the submitted lots, can be employed as an alternative to conventional plans. This paper focuses on the concept of dependent state sampling inspection plans by attributes for continuous production with small acceptance numbers under Bayesian perspective and highlights the properties of its characteristic curves with reference to various parameters. A procedure for determining the parameters of such plans for two specified points on the operating characteristic curves under the conditions of gamma-Poisson distribution is discussed with illustrations. The closed form expressions for the parameters of the plans are also derived.

Bayesian Design of Special Type of Double Sampling Plans for Compliance Testing

Bayesian acceptance sampling plans, which utilize prior information on the process variation, can be employed as an alternative to conventional types of plans for taking decisions on the disposition of submitted lots. A special type of double sampling inspection plans by attributes with small acceptance numbers using Bayesian methodology is presented in this paper emphasizing its significance over small acceptance number single sampling plans. The procedures for designing such sampling plans for specified degree of discrimination which would ensure protection to the producer and consumer are discussed with illustrations under the conditions for the application of gamma-Poisson distribution.

Risk-embedded Bayesian acceptance sampling plans via conditional value-at-risk with Type II censoring

An acceptance sampling plan is usually determined by minimizing the expectation of the sum of the relevant costs involved. This expected cost minimization approach, however, could result in a great cost at a probability that is unacceptable to a decision maker. This study therefore develops a risk-embedded model via conditional value-at-risk that allows a decision maker to choose an acceptance sampling plan with minimal expected excess cost in accordance with his or her attitude towards risk. We focus in this study on Bayesian acceptance sampling under Type II censoring for Weibull distributed product lifetime with known shape parameter and products being sold with a general rebate warranty. We explore, through numerical analysis, the individual effects and cross-effects of a decision maker’s attitude towards risk and various unit costs on the Bayesian acceptance sampling plans, aiming to gain insights into the role of a decision maker’s risk aversion in the determination of Bayesian acceptance sampling plans.

Selection of Bayesian Single Sampling Plans by Attributes with Desired Discrimination

Acceptance sampling is one of the celebrated techniques in quality assurance. The application of acceptance sampling methodology has been widespread in the industrial environment and the concept is being used primarily for incoming or receiving inspection. It is concerned with inspection of one or more samples drawn randomly from a lot or lots of finished products or materials and with decision making regarding lots on the basis of the information contained in the sample(s) about the quality of the products. A sampling plan under acceptance sampling is a rule that precisely specifies the parameters of the sampling process and acceptance/rejection criteria and may be one of two categories, viz., attributes and variables. The theory of acceptance sampling plans by attributes is based on the implicit assumption that the production process from which lots are formed is stable and the lot or process fraction nonconforming is a constant. However, the lots formed from a process, in practice, have quality variations, which occur due to random fluctuations, and thereby the proportion of non-conforming units in the lots will vary continuously. Hence, in such cases, a framework of Bayesian methodology, which uses prior information on the process variation for making decisions about the submitted lots, can be employed as an alternative to conventional plans. Such plans are called Bayesian acceptance sampling plans. In this paper, Bayesian single sampling plans by attributes are developed under the conditions of Poisson distribution for sampling information and gamma distribution for prior process information. The methodology for determining the plan parameters based on unity values with operating ratio as a measure of discrimination is discussed. The procedures for the determination of an optimum plan and for the construction of operating characteristic curve are also presented. The Bayesian plans are compared with the plan under conventional method through an illustration.

Chain Sampling Inspection Plans Based on Bayesian Methodology

Acceptance sampling in quality control is a statistical methodology and consists of procedures for sentencing one or more incoming lots of finished products based on the inspection of sampled items drawn randomly from the lots. The theory of such procedures by attributes is often built upon the assumptions that the production process from which lots are formed is stable and that the lot or process fraction nonconforming is a constant. However, in practice, any production process exhibits quality variations, which occur due to random fluctuations. When the quality variations are present in a process, the proportion of nonconforming units in the lots will vary continually. In such cases, for sentencing the processes generating the lots, Bayesian acceptance sampling plans, which use prior information on the process variation, can be employed as an alternative to conventional plans. This paper presents the concept of chain sampling inspection plans by attributes for continuous production using Bayesian methodology. The operating characteristic (OC) function of Bayesian chain sampling plans as a measure of performance is defined and the properties of OC curves of the plans with reference to their parameters are studied empirically. A procedure for determining the parameters of such plans for two specified points on the operating characteristic curves under the conditions of gamma-Poisson distribution is discussed. The closed form expressions for the parameters of the plans are derived.

Selection of Bayesian Double Sampling Inspection Plans by Attributes with Small Acceptance Numbers

Sampling inspection is a product control technique and consists of rules or procedures for taking decisions on the disposition of lots of finished products based on the inspection of individual units in one or more random samples drawn from the lots. The basic assumption underlying the theory of such procedures by attributes is that the lot or process fraction nonconforming is a constant. Evidently, this assumption is not fulfilled, even if the production process is stable, i.e., if the nonconforming probability is a constant. However, in practice, the lots formed from a process will have different fractions nonconforming, which occur due to random fluctuations. In such cases, Bayesian acceptance sampling plans (BASP), which use prior information on the process variation for taking decisions about the submitted lots, can be employed as alternative to conventional plans. This paper presents a double sampling inspection plan by attributes with small acceptance numbers using the Bayesian methodology. The properties of its characteristic curves with reference to various parameters are highlighted. The design problem of selecting such sampling plans with reference to two prescribed points on the operating characteristic curve under the condition of gamma-Poisson distribution is addressed.

Bayesian acceptance sampling plans following economic criteria: An application to paper pulp manufacturing

The main purposes of this paper are to derive Bayesian acceptance sampling plans regarding the number of defects per unit of product, and to illustrate how to apply the methodology to the paper pulp industry. The sampling plans are obtained following an economic criterion: minimize the expected total cost of quality. It has been assumed that the number of defects per unit of product follows a Poisson distribution with process average 5 , whose prior information is described either for a gamma or for a non- informative distribution. The expected total cost of quality is composed of three independent components: inspection, acceptance and rejection. Both quadratic and step-loss functions have been used to quantify the cost incurred for the acceptance of a lot containing units with defects. Combining the prior information on 5 with the loss functions, four different sampling plans are obtained. When the quadratic-loss function is used, an analytical relation between the optimum settings of the sample size and the acceptance number is derived. The robustness analysis indicates that the sampling plans obtained are robust with respect to the prior distribution of the process average as well as to the misspecification of its mean and variance.

Monitoring Drug Use Using Bayesian Acceptance Sampling: The Illinois Experiment

Bayesian acceptance sampling was used to monitor illegal drug use in a population of probationers. The study utilizes an economic model of drug testing based on single-sample, single-attribute acceptance sampling. This approach reduces from 100% the amount of testing which must be done to monitor the use of illegal drugs in the population and provides a decision rule, vis-à-vis a sampling plan, that specifies under what sampling outcome the entire population must be tested. The objective is to minimize the expected total cost of a drug testing program while ensuring that the proportion of users in the population is not increasing over time. A field study of the acceptance sampling approach was conducted using probationers assigned to Intensive Drug Supervision Programs in six Illinois counties. The degree to which drug testing results were reported to probation officers was controlled during the experiment. Counties were assigned to receive: no feedback of drug-test results; random proportion of feedback using Bayesian acceptance sampling plans; and 100% feedback—the status quo situation. Results show that those counties using acceptance sampling could have reduced the number of drug tests performed without increasing drug use. In those counties with no feedback, there was an upward trend over time in the proportion testing positive for drug use. Acceptance sampling-based drug testing programs are now being implemented by Illinois probation offices.

Risk preference, multiple attributes, and multiple criteria in bayesian acceptance sampling plans

AbstractAlthough there has been considerable research directed toward developing Bayesian acceptance sampling plans, little consideration has been given to incorporating a decision‐maker's risk attitude or treating such problems in terms of multiple‐type defects and multiple criteria. We review our own work which is focused on the above issues. A model incorporating risk preference is shown to yield substantial differences in the characteristics of an optimal sampling plan relative to a typical Bayesian linear cost (risk neutral) model. Bayesian models and optimization schemes for a variety of multiple‐type defect plans are reviewed. A bicriterion acceptance model, employing average outgoing quality and average inspection cost is also formulated. Traditional versus interactive optimization procedures are compared empirically in terms of ease of use, satisfaction with solutions, and insight gained into the problem.

Multiattribute Bayesian Acceptance Sampling Plans for Screening and Scrapping Rejected Lots

Abstract A general model for multiattribute Bayesian acceptance sampling plans is developed which incorporates the multiattribute utility function of a decision maker in its design. The model accommodates various dispositions of rejected lots such as screening and scrapping. The disposition of rejected lots is shown to have a substantial impact on the solution approach used and on the ease of incorporation of multiattribute utility functions in terms of their measurement complexity, functional form, and parameter estimation. For example, if all attributes are screenable upon rejection, and the prior distributions of lot quality on each attribute are independent, then an optimal multiattribute sampling plan can be obtained simply by solving for an optimal single sampling plan on each attribute independently. A discrete search algorithm, based on pattern search, is also developed and shown to be very effective in obtaining an optimal multiattribute inspection plan when such separability cannot be accomplished.

On the Selection of a Prior Distribution in Bayesian Acceptance Sampling

Bayesian acceptance sampling plans, including the increasingly popular economically-based versions, require the specification of a prior distribution of defectives from lot to lot. This paper examines the relationship between defectives in the sampling ..