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.     

A likelihood ratio test for the equality of proportions of two normal populations

In sampling inspection by variables, an item is considered defective if its quality characteristic Y falls below some specification limit L₀. We consider switching to a new supplier if we can be sure that the proportion of defective items for the new supplier is smaller than the proportion defective for the present supplier.

Assume that Y has a normal distribution. A test for comparing these proportions is developed. A simulation study of the performance of the test is presented.     

The geometric CUSUM chart with sampling inspection for monitoring fraction defective

The detection of an upward shift in the fraction defective of a repetitive process is considered using the geometric CUSUM. This CUSUM makes use of the information provided by the run-lengths of non-defective items between successive defective items, and was initially developed for the case of 100% inspection. This paper considers the geometric CUSUM under sampling inspection, and emphasizes that the pattern of sampling inspection can be quite haphazard without causing any difficulty for the operation of the CUSUM. Two separate mechanisms for the occurrence of a shift are considered. Methods for evaluating zero-state and steady-state ARL are presented for both 100% inspection and sampling inspection. Parameter choice is also considered, and recommendations made. Comparisons with some np -charts are provided.     

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.     

A New Acceptance Sampling Policy Based on Number of Successive Conforming Items

In an acceptance-sampling plan, where items of an incoming batch of products are inspected one by one, if the number of conforming items between successive non conforming items falls below a lower control threshold, the batch is rejected. If it falls above an upper control threshold, the batch is accepted, and if it lies within the thresholds then the process of inspecting the items continues. The purpose of this article is to develop an optimization model to determine the optimum values of the thresholds such that constraints on the probability of Type I and Type II errors are satisfied. This article starts by developing a Markovian model to derive the expected total cost of the inspection problem containing the costs of acceptance, rejection, and inspection. Then, the optimum values of the thresholds are selected in order to minimize the expected cost. To demonstrate the application of the proposed methodology, perform sensitivity analysis, and compare the performance of the proposed procedure to the one of another method, a numerical example is given at the end and the results are reported.     

Online control by attributes in the presence of classification errors with variable inspection interval

ABSTRACT

The procedure for online control by attribute consists of inspecting a single item at every m items produced (m ≥ 2). On each inspection, it is determined whether the fraction of the produced conforming items decreased. If the inspected item is classified as non conforming, the productive process is adjusted so that the conforming fraction returns to its original status. A generalization observed in the literature is to consider inspection errors and vary the inspection interval. This study presents an extension of this model by considering that the inspected item can be rated independently r (r ≥ 1) times. The process is adjusted every time the number of conforming classifications is less than a, 1 ≤ a ≤ r. This method uses the properties of an ergodic Markov chain to obtain the expression for the average cost of this control system. The genetic algorithm methodology is used to search for the optimal parameters that minimize the expected cost. The procedure is illustrated by a numerical example.     

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.     

Dorfman-sterrett screening (group testing) schemes and the effects of faulty inspection

The Dorfman screening procedure is based on first testing a group of items as a whole, proceeding to individual testing only if the group-test indicates existence of at least one nonconforming item. A modification suggested by Sterrett allows for reintroduct-ion of group testing of all items, not yet tested individually, when an item is classified as nonconforming by an individual test. Effects of faulty test inspection on the properties of the modified procedures are studied.     

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.     

An inspection procedure for radio frequency repeaters using a multiple linear regression method

Abstract

A radio frequency (RF) repeater is a wireless electronic device that transmits signals from a base transceiver station to a mobile station. When inspecting RF repeaters, various items are required to be tested to ensure their quality. In this paper, we propose a systematic procedure for the inspection by using a multiple linear regression method. The basic idea is to predict the inspection result without real inspection. In particular, a multicollinearity problem is considered in the regression analysis. Two case studies are conducted for validating the proposed method with an RF repeater production company in Korea.     

A bayesian analysis of imperfect inspection models

An examination of sampling inspection models is provided for the case where inspection is not perfect and classification errors can be made. The conjugate family of distributions is obtained under t h e assumption that defective items are generated according to a Bernoulli process. To simplify analysis, the use of a single beta prior distribution is considered. Relevant predictive distributions are obtained.     

An investigation of the effects of inspection errors on the run-length control charts

For continuous inspection schemes in an automated manufacturing environment, a useful alternative to the traditional p or np chart is the Run-Length control chart, which is based on plotting the run lengths (the number of conforming items) between successive nonconforming items. However, its establishment relies on the error-free inspection assumption, which can seldom be met in practice. In this paper, the effects of inspection errors on the Run-Length chart are investigated based on that these errors are assumed known. The actual false alarm probability and the average number inspected (ANI) in the presence of inspection errors are studied. This paper also presents the adjusted control limits for the Run-Length chart, which can provide much closer ANI curves to the ones obtained under error-free inspection.     

Group testing with test error as a function of concentration

A common assumption in group testing applications is that there is no test error, i.e., misclassification of a single item or a group of items cannot occur. Graff and Roeloffs ( 1972 ) have proposed a procedure applicable when there is a known probability of misclassification. We generalize their results to the situation where the probability of misclassification depends on the proportion of defective items in the group.     

Optimal sampling op hierarchical screening with inspection errors

For the multi-stage hierarchical Dorfman group testing problem, where inspection errors exist, we provide a simple procedure to determine the number to stages, the number of subgroups of each stage and sample size of each subgroup simultaneously. The optimal group testing plan established by this procedure minimizes the expected number of tests per item. This result can be easily extended to more general applications.     

Factors causing occurrence of artificial dif: A simulation study for dichotomous data

ABSTRACT

In modern test theory, differential item functioning (DIF) appears where respondents from two different groups have the same ability but different probability to respond to an item correctly. If some items favouring one group lead to the appearance of DIF in any other item favouring the other group, this type of problem is called artificial differential item functioning (A-DIF). The purpose of this paper is to deal with the effect of different factors causing A-DIF under the Rasch theoretical model for dichotomous responses. A simulation study was conducted to explore how various factors affect real DIF and simultaneous A-DIF expected proportion including total sample size, percentage of individuals in focal and reference groups, percentage of items exhibiting real DIF and DIF magnitude for two item sets including 10 and 20 items. It is concluded that DIF magnitude is the most essential factor while evaluating A-DIF for each item set. This is followed by percent of items exhibiting real-DIF.     

On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

On-line process control consists of inspecting a single item for every m (integer and m ≥ 2) produced items. Based on the results of the inspection, it is decided whether the process is in-control (the fraction of conforming items is p ₁; State I) or out-of-control (the fraction of conforming items is p ₂ < p ₁; State II). If the inspected item is non conforming, it is determined that the process is out-of-control, and the production process is stopped for an adjustment; otherwise, production continues. As most designs of on-line process control assume a long-run production, this study can be viewed as an extension because it is concerned with short-run production and the decision regarding the process is subject to misclassification errors. The probabilistic model of the control system employs properties of an ergodic Markov chain to obtain the expression of the average cost of the system per unit produced, which can be minimised as a function of the sampling interval, m. The procedure is illustrated by a numerical example.     

Effect of Inspection Error on Out-of-Control Average Run Length of CUSUM Charts

The cumulative sum (CUSUM) chart is commonly used for detecting small or moderate shifts in the fraction of defective manufactured items. However, its construction relies on the error-free inspection assumption, which can seldom be met in practice. In this article, we discuss the construction of an upward CUSUM chart in the presence of inspection error, study the effects of inspection error on the out-of-control ARL of the CUSUM chart, and present a formula for determining the sampling size that compensates for the effect of inspection error on the out-of-control ARL.     

Collaborative filtering for massive multinomial data

Content recommendation on a webpage involves recommending content links (items) on multiple slots for each user visit to maximize some objective function, typically the click-through rate (CTR) which is the probability of clicking on an item for a given user visit. Most existing approaches to this problem assume user's response (click/no click) on different slots are independent of each other. This is problematic since in many scenarios CTR on a slot may depend on externalities like items recommended on other slots. Incorporating the effects of such externalities in the modeling process is important to better predictive accuracy. We therefore propose a hierarchical model that assumes a multinomial response for each visit to incorporate competition among slots and models complex interactions among (user, item, slot) combinations through factor models via a tensor approach. In addition, factors in our model are drawn with means that are based on regression functions of user/item covariates, which helps us obtain better estimates for users/items that are relatively new with little past activity. We show marked gains in predictive accuracy by various metrics.     

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.     

Bayes and Empirical Bayes Two-Stage Procedures for Sampling Inspection

A batch of M items is inspected for defectives. Suppose there are d defective items in the batch. Let d ₀ be a given standard used to evaluate the quality of the population where 0 < d ₀ < M. The problem of testing H ₀: d < d ₀ versus H ₁: d ≥ d ₀ is considered. It is assumed that past observations are available when the current testing problem is considered. Accordingly, the empirical Bayes approach is employed. By using information obtained from the past data, an empirical Bayes two-stage testing procedure is developed. The associated asymptotic optimality is investigated. It is proved that the rate of convergence of the empirical Bayes two-stage testing procedure is of order O (exp(? c? n)), for some constant c? > 0, where n is the number of past observations at hand.