Single Sampling Inspection Plans Research Articles

Single acceptance sampling inspection plan based on transmuted Rayleigh distribution

Single acceptance sampling inspection plan based on transmuted Rayleigh distribution

Amputated Life Testing for Weibull-Fréchet Percentiles: Single, Double and Multiple Group Sampling Inspection Plans with Applications

When a life test is terminated at a predetermined time to decide whether to accept or refuse the submitted batches, the types of group sampling inspection plans (single, two, and multiple-stages) are introduced. The tables in this study give the optimal number of groups for various confidence levels, examination limits, and values of the ratio of the determined experiment time to the fixed percentile life. At various quality levels, the operating characteristic functions and accompanying producer's risk are derived for various types of group sampling inspection plans. At the determined producer's risk, the optimal ratios of real percentile life to a fixed percentile life are obtained. Three case studies are provided to illustrate the processes described here. Comparisons of single-stage and iterative group sampling plans are introduced. The first, second, and third sample minimums must be used to guarantee that the product's stipulated mean and median lifetimes are reached at a certain degree of customer trust. The suggested sample plans' operational characteristic values and the producer's risk are given. In order to show how the suggested approaches based on the mean life span and median life span of the product may function in reality, certain real-world examples are examined.

Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.

An Application of Time Truncated Single Acceptance Sampling Inspection Plan Based on Generalized Half-Normal Distribution

In this paper, single acceptance sampling inspection plan for generalized half-normal distribution when the lifetime experiment is truncated at a pre-fixed time is introduced. For the propose plan, ratio of true mean life time to specified mean life time for different choices of confidence level are provided. Minimum sample size which is necessary to ensure a certain specified lifetime are obtained. Operating characteristic values of the proposed plan are also presented. A real life example is considered to show the applicability of the proposed sampling plan.

Optimum process mean setting based on variable sampling plan with producer’s and consumer’s risks

In this paper, the author applies a variable sampling inspection plan with the producer’s and consumer’s risks on the operational characteristic curve for setting the optimum process mean. Assume that the quality characteristic of a one-sided lower specification limit product is normally distributed. The process standard deviation is known but the process mean is unknown. The rectifying inspection plan is adopted when the lot of product is rejected. The optimum process mean and the parameters of single variable sampling inspection plan are simultaneously determined by maximizing the expected total profit per unit under the specified producer’s and consumer’s risks. The numerical results show that (1) the unit price of product for the accepted lot, the production cost per unit, and the specification limit have a major effect on the expected total profit per unit; (2) the process standard deviation and the lot tolerance percent defective have a moderate effect on the expected total profit per unit

Optimum process mean setting with specified average outgoing quality limit protection for variable single sampling plan

The average outgoing quality limit (AOQL) is a major performance evaluation for assuring the quality of product lot. The process mean setting is an important topic for statistical process control. In this paper, the author applies a variable single sampling inspection plan with the AOQL protection on the consumer for determining the optimal process mean and the parameters of sampling plan. The quality characteristic is considered with one-side lower specification limit and it is normally distributed with known standard deviation and unknown mean. The 100% inspection is adopted when the product lot is rejected. The optimum process mean and parameters of inspection plan are simultaneously determined by maximizing the expected total profit per unit under the specified AOQL value. The numerical example and sensitivity analysis of parameters are provided for illustration.

Economic aspects of the LTPD single sampling inspection plans

The paper deals with the LTPD (Lot Tolerance Percent Defective) single sampling plans when the remainder of rejected lots is inspected. There are considered two types of the LTPD plans - for inspection by variables and for inspection by variables and attributes (all items from the sample are inspected by variables; the remainder of rejected lots is inspected by attributes). These plans were created by the author of this paper and published in the Statistical Papers. These new plans were compared with the corresponding Dodge-Romig LTPD plans for the inspection by attributes from the economic point of view. From the results of the numerical investigations, it follows that under the same protection of consumer the LTPD plans for the inspection by variables are in many situations more economical than the corresponding Dodge-Romig attribute sampling plans (saving of the inspection cost is 80% in any cases). The dependence of the saving of the inspection cost on the acceptance sampling characteristics is analyzed in the paper.

A Markovian approach to determining optimum process means with inspection sampling plan in serial production systems

This paper develops Markovian-based models for determining the optimum process means with the consideration of an acceptance sampling plan in a serial production system. This paper studies a production system where products are produced continuously with specified lower and upper specification limits for each stage in the production system for quality assurance purposes. Considering the inherent variability in production processes, the quality characteristic(s) of a product might fall below the lower specification limit, resulting in scrap cost, or above the upper specification limit, resulting in rework costs. To study the dynamics of this problem, this paper first develops a Markovian-based model for the optimum process target level for a single quality characteristic assuming a single sampling inspection plan for both a single- and a two-stage production system. Then, the proposed model is extended for dual quality characteristics that are dependent for single- and two-stage production systems. Numerical examples and sensitivity analysis are performed to investigate the effect of different system parameters on the expected profit and optimum process means. The results showed that both single- and two-stage production systems have convex function for the expected profit. In addition, the results showed that the optimum process means are slightly larger than the average of the specification limits. Finally, the correlation between the quality characteristics affects the expected profit significantly.

Optimum process mean setting based on variable sampling plans with specified consumer’s risk

In the present paper, a new economic design with variable single sampling inspection plan for determining the optimal process mean is presented. The quality characteristic with the one-sided lower specification limit is assumed to be normally distributed with unknown mean and known standard deviation. The 100% rectifying inspection plan is adopted when the product lot is rejected. The optimum process mean and the parameters of sampling inspection plan are simultaneously determined by maximizing the expected total profit per unit and meeting the requirement of the specified consumer’s risk. Two numerical examples and sensitivity analyzes of parameters are provided for illustration. The numerical results show that, among the model parameters, the price of product for accepted lot, the processing cost per unit, and the lower specification limit significantly affect the expected total profit per unit.

Dodge-Romig LTPD Single Sampling Plan under Quality Investment and Inspection Error

In this study, the author proposes an economic design of quality investment for a Dodge-Romig single sampling inspection plan with inspection error. The optimal sampling inspection plan and quality investment level are jointly determined by minimizing the expected total cost of product under the specified consumer’s risk. Finally, the comparison of solution between the model with/without inspection error will be provided for illustration.

A Sampling Inspection Plan with Human Error: Considering the Relationship between Visual Inspection Time and Human Error Rate

Objective: The aim of this study is to design a sampling inspection plan with human error which is changing according to inspection time. Background: Typical sampling inspection plans have been established typically based on an assumption of the perfect inspection without human error. However, most of all inspection tasks include human errors in the process of inspection. Therefore, a sampling inspection plan should be designed with consideration of imperfect inspection. Method: A model for single sampling inspection plans were proposed for the cases that visual inspection error rate is changing according to inspection time. Additionally, a sampling inspection plan for an optimal inspection time was proposed. In order to show an applied example of the proposed model, an experiment for visual inspection task was performed and the inspection error rates were measured according to the inspection time. Results: Inspection error rates changed according to inspection time. The inspection error rate could be reflected on the single sampling inspection plans for attribute. In particular, inspection error rate in an optimal inspection time may be used for a reasonable single sampling plan in a practical view. Conclusion: Human error rate in inspection tasks should be reflected on typical single sampling inspection plans. A sampling inspection plan with consideration of human error requires more sampling number than a typical sampling plan with perfect inspection. Application: The result of this research may help to determine more practical sampling inspection plan rather than typical one.

Design of a Single Sampling Inspection Plan Utilizing Variables with a Specified Target Value

Design of a Single Sampling Inspection Plan Utilizing Variables with a Specified Target Value

A class of single sampling inspection plans based on possibilistic programming problem

The problem of designing the lot tolerance percent defective single sampling inspection plans is considered when the parameters cannot be known precisely. The parameters are assumed fuzzy variables so that the problem becomes a possibilistic programming problem. A solution procedure is developed to find a compromise plan. A numerical example and a sensitivity analysis are included.

Sensitivity of Bayesian sampling inspection schemes to a non-normal prior distribution

summary In this paper we derive the predictive density function of a future observation under the assumption of Edgeworth-type non-normal prior distribution for the unknown mean of a normal population. Fixed size single sample and sequential sampling inspection plans, in a decisive prediction framework, are examined for their sensitivity to departures from normality of the prior distribution. Numerical illustrations indicate that the decision to market the remaining items of a given lot for a fixed size plan may be sensitive to the presence of skewness or kurtosis in the prior distribution. However, Bayes'decision based on the sequential plan may not change though expected gains may change with variation in the non-normality of the prior distribution.

Designing Sampling Inspection Plans When the Sample Size is Fixed

The readily available acceptance number value is revised in the form of three tables. From these tables it is possible to determine single or chain sampling inspection plans when the sample size is fixed. These tables replace the large number of existing tables in use.

Static Inventory Model with Unknown Proportion of Defectives in the Supplied Lot

A static inventory model where lots received (against orders) are accepted through a curtailed single sampling inspection plan has been considered. Since the proportion of non-defective units in a lot is not likely to be known in advance, a probability Jaw has been assumed for the same. The optimal order quantity has been obtained by maximizing the expected net profit, taking into account selling price, purchase cost, carrying cost, shortage cost, salvage cost and inspcctioo cost.

Equitable quality level and error-areas under the operating characteristic curves of normal single sampling inspection plans (with σ known)

This article assumes a continuous prior distribution for lot quality in the case of a normal single sampling inspection plan with known standard deviation. The definition of Equitable Quality Level (EQL) as given in this paper ensures that the proportion of lots of quality better than the EQL—as obtained under the prior distribution—is equal to the average probability of acceptance. The first kind of error-area at the quality levelp′ is the joint probability of producing a lot of quality equal to or better thanp′ and getting such a lot rejected by the plan whereas the second kind of error-area is the joint probability of producing a lot of quality worse thanp′ and getting it accepted. Certain measures of producer's and consumer's risks can therefore be defined in terms of error-areas. It is noted that the OC can be viewed as the upper cumulative distribution function of a hypothetical random variableY. It is shown that the EQL and the error-areas can be expressed in terms of the derivatives of the prior distribution and the moments ofY. The latter do not depend on the prior distribution. It is hinted how this technique can be used to construct plans having certain optimum properties and also to obtain approximations to compound distribution. The case of a normal prior distribution is fully dealt with.

The effects of inspection error on single sampling inspection plans : International Journal of Production Research, Jul. 1973, 11.3, 289–298

The effects of inspection error on single sampling inspection plans : International Journal of Production Research, Jul. 1973, 11.3, 289–298

The effects of inspection error on single sampling inspection plans

SUMMARY Acceptance sampling plans are designed under the assumption of perfect inspection. However, inspection tasks are not, even under ideal inspection conditions, free of error. In this paper we consider the effects of inspection error on probability of acceptance, average outgoing quality, and average total inspection. These measures are examined under both replacement and non -replacement assumptions. Also, a method is presented whereby an acceptance sampling plan may be designed which explicitly considers inspection error.

Verification Error in Single Sampling Inspection Plans for Processing Survey Data

Abstract This article deals with measurement error in single sampling inspection plans of the attributes type. Formulas are provided to assess the effect of inefficient inspection and correction on the power of the sampling plan to distinguish between acceptable and unacceptable quality levels, on average outgoing quality, and on costs. Emphasis is placed on the error of classifying defectives as nondefectives (Type II) made by both inspectors (called “verifiers”) of sample items and by correctors of items in rejected lots. Type I errors are mentioned under conditions peculiar to preparing data for machine processing in which nondefective items are regarded as defectives and changed to incorrect ones.