Optimum time-censored lot sampling inspection based on type-I half-logistic Nadarajah-Haghighi-percentile lifetimes

Design of economically optimal acceptance sampling plans with inspection error

This paper presents a comparative study of classical and Bayesian risks in the design of optimal failure-censored sampling plans for lognormal lifetime models. The analysis focuses on how variations in prior distributions, specifically the beta distribution for defect rates, influence the producer's and consumer's risks, along with the optimal sample size. We explore the sensitivity of the sampling plan's risks to changes in the prior mean and variance, offering insight into the impacts of uncertainty in prior knowledge on sampling efficiency. Classical and Bayesian approaches are evaluated, highlighting the trade-offs between minimizing sample size and controlling risks for both the producer and the consumer. The results demonstrate that Bayesian methods generally provide more robust designs under uncertain prior information, while classical methods exhibit greater sensitivity to parameter changes. A computational procedure for determining the optimal sampling plans is provided, and the outcomes are validated through simulations, showcasing the practical implications for quality control in reliability testing and industrial applications.

In manufacturing industries, sampling inspection is a common practice for quality assurance and cost reduction. The basic decisions in sampling inspection are how many manufactured items to be sampled from each lot and how many identified defective items in the sample to accept or reject each lot. Because of the combinatorial nature of alternative solutions on the sample sizes and acceptance criteria, the problem of determining an optimal sampling plan is NP-complete. In this paper, a neurally-inspired approach to generating acceptance sampling inspection plans is proposed. A Bayesian cost model of multi-stage-multi-attribute sampling inspections for quality assurance in serial production systems is formulated. This model can accommodate various dispositions of rejected lott such as scraping and screening. The model also can reflect the relationships between stages and among attributes. To determine the sampling plans based on the formulated model, a neurally-inspired stochastic algorithm is developed. This algorithm simulates the state transition of a primal-dual stochastic neural network to generate the sampling plans. The simulated primal network is responsible for generation of new states whereas the dual network is for recording the generated solutions. Starting with an arbitrary feasible solution, this algorithm is able to converge to a near optimal or an optimal sampling plan with a sequence of monotonically improved solutions. The operating characteristics and performance of the algorithm are demonstratedvia numerical examples.

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.

We consider the problem of designing single and the double sampling plans for monitoring dependent production processes. Based on simulated samples from the process, Nelson proposed a new approach of estimating the characteristics of single sampling plans and, using these estimates, designing optimal plans. In this paper, we extend his approach to the design of optimal double sampling plans. We first propose a simple methodology for obtaining the unbiased estimators of various characteristics of single and double sampling plans. This is achieved by defining the various characteristics of sampling plans as explicit random variables. Some of the important properties of the double sampling plans are established. Using these results, an efficient algorithm is developed to obtain optimal double sampling plans. A comparison with a crude search shows that our algorithm leads to about 90% savings, on the average, in computational timings. The procedure is also explained through a suitable example for the ARMA(1,1) model. It is observed, for instance, that an optimal double sampling plan leads to about 23% reduction in average sample number, compared to an optimal single sampling plan. Tables for choosing the optimal plans for certain auto regressive moving average processes at some practically useful values of acceptable quality level and rejectable quality level are also presented.

Bayesian models for multiattribute acceptance sampling have been developed under the assumption that sampling inspection is carried to completion. A Bayesian multiattribute model for stepwise sampling inspection is proposed, whereby sampling inspection is terminated as soon as the disposition of the inspection lot is determined. An iterative solution procedure is developed for obtaining optimal or near-optimal multiattribute acceptance sampling plans under stepwise sampling inspection. The effect of stepwise sampling inspection on the characteristics of an optimal sampling plan is investigated. It is shown that stepwise sampling inspection achieves a sampling plan with lower total expected cost than complete sampling inspection. In addition, it is shown that the sequence of attributes in a stepwise sampling inspection substantially affects the sampling plan and resultant expected cost. The proposed methodology is used to evaluate various heuristics which may be used to determine the sequence of attributes in a stepwise inspection procedure.

Optimal acceptance sampling plans for log-location–scale lifetime models using average risks

Supply Chain Management, which is concerned with material and information flows between facilities and the final customers, has been considered the most popular operations strategy for improving organizational competitiveness nowadays. With the advanced development of computer technology, it is getting easier to derive an acceptance sampling plan satisfying both the producer's and consumer's quality and risk requirements. However, all the available QC tables and computer software determine the sampling plan on a noneconomic basis. In this paper, we design an economic model to determine the optimal sampling plan in a two-stage supply chain that minimizes the producer's and the consumer's total quality cost while satisfying both the producer's and consumer's quality and risk requirements. Numerical examples show that the optimal sampling plan is quite sensitive to the producer's product quality. The product's inspection, internal failure, and postsale failure costs also have an effect on the optimal sampling plan.

With the advanced development of computer technology, it is getting easier to derive an acceptance sampling plan satisfying both the producer's and consumer's quality and risk requirements. However, all the available QC tables and computer software determine the sampling plan on a non-economic basis. In this paper, an economic model is designed to determine the optimal sampling plan that minimizing the producer's total cost while satisfying both the producer's and consumer's quality and risk requirements. Numerical examples show that the optimal sampling plan is quite sensitive to the producer's product quality. The product's inspection, internal failure, and post-sale failure costs also have an effect on the optimal sampling plan.

This paper presents the details of a study undertaken at the IBM wafer fabrication facility to determine the optimal in-line inspection sampling plan for poly process module. During the study several lots at multiple processing points were inspected. The data was collected and analyzed to characterize the process baseline and excursions. This was then used to determine the cost of current sampling plan and what the best sampling plan would be to both minimize risk to the product and minimize cost of doing inspections. The optimal sample plan was then modified to also minimize the cycle time through the inspection process. We also present the results of a new SPC model which explicitly accounts for the lot-to-lot and wafer-to wafer variations. We illustrate that the application of traditional policies could increase the lots-at-risk by as much as 17%.

Sampling plans play an important role in monitoring production systems and reducing quality- and maintenance-related costs. Existing sampling plans usually focus on one assignable cause. However, multiple assignable causes may occur, especially for a multistage production system, and the resulting process shift may propagate downstream. This article addresses the problem of finding the optimal sampling plan for an unreliable multistage production system subject to competing and propagating random quality shifts. In particular, a serial production system with two unreliable machines that produce a product at a fixed production rate is studied. It is assumed that both machines are subject to random quality shifts with increased nonconforming rates and can suddenly fail with increasing failure rates. A sampling plan is implemented at the end of the production line to determine whether the system has shifted or not. If a process shift is detected, a necessary maintenance action will be initiated. The optimal sample size, sampling interval, and acceptance threshold are determined by minimizing the long-run cost rate subject to the constraints on average time to signal a true alarm, effective production rate, and system availability. A numerical example on an automatic shot blasting and painting system is provided to illustrate the application of the proposed sampling plan and the effects of key parameters and system constraints on the optimal sampling plan. Moreover, the proposed model shows better performance for various cases than an alternative model that ignores shift propagation.

S.70-75

It is usually assumed that a quality characteristic in an item obeys a normal distribution in the case that the quality of items is evaluated based on the variable property. Then, the concept of Taguchi’s quality loss has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of nonconforming items. From this viewpoint, some variable sampling plans indexed by the quality loss have been investigated before now. As a study earliest among them, the variable single sampling plan based on operating characteristics (OC) indexed by the quality loss was considered. On the other hand, the attribute repetitive group sampling plan on OC was proposed for reducing the sampling number in the inspection. Recently, the variable repetitive group sampling (VRGS) plan on OC indexed by the quality loss has been considered. By the way, the rectifying inspection is known as one of the schemes of acceptance sampling inspection. Then, Dodge-Romig single sampling plans are known as the traditional rectifying inspection based on attribute sampling plans. Dodge-Romig rectifying attribute sampling plans provide the lot tolerance percent defective (LTPD) scheme on each lot and the average outgoing quality limit (AOQL) scheme for many lots. Furthermore, the rectifying variable single sampling (RVSS) plan indexed by the quality loss was investigated. In conformity with the traditional rectifying attribute sampling plans for the LTPD and AOQL schemes, the acceptance quality loss limit (AQLL) and specified permissible average outgoing surplus quality loss limit (PAOSQLL) schemes are respectively proposed in the RVSS plans indexed by the quality loss. In this article, we suppose that the quality characteristic in an item obeys a normal distribution. Under this condition, the rectifying variable repetitive group sampling (RVRGS) plan for AQLL is considered for the purpose of reducing the average total inspection (ATI). Specifically, the design procedure for finding out the required sample size and inspection criteria for satisfying the constraint of the quality assurance is derived. Lastly, it is shown that ATI of the RVRGS plan is reduced in comparison with that of the RVSS plan under the same condition.

Efficient Bayesian sampling plans for exponential distributions with random censoring

A methodology for determining optimal sampling plans for Bayesian multiattribute acceptance sampling models is developed. Inspections are assumed to be nondestructive and attributes are classified as scrappable or screenable according to the corrective action required when a lot is rejected on a given attribute. The effects of interactions among attributes on the resulting optimal sampling plan are examined and show that: (1) sampling plans for screenable attributes can be obtained by solving a set of independent single attribute models, (2) interactions of scrappable attributes on screenable attributes and conversely result in smaller sample sizes for screenable attributes than in single attribute plans, and (3) interactions among scrappable attributes result in either smaller sample sizes, lower acceptance probabilities or both, relative to single attribute plans. An iterative subproblem algorithm is developed, which is effective in finding near optimal multiattribute sampling plans having a large number of attributes.