Fraction Of Defective Items Research Articles

Integrated control policies of production, returns’ replenishment and inspection for unreliable hybrid manufacturing-remanufacturing systems with a quality constraint

This paper deals with the production planning and control problem within unreliable Hybrid Manufacturing-Remanufacturing Systems (HMRSs) evolving in a stochastic and dynamic environment. The customer demand can then be fulfilled by either manufacturing of new units or remanufacturing of returned ones. However, both used materials and returns may contain a fraction of defective items. The paper investigates how companies could benefit from such integrated control policy to assist their managers in determining production rates, the sequence and the size of replenishment orders as well as their sample size to be inspected. The corresponding problem aims to propose an efficient control policy integrating four central decisions to coordinate remanufacturing, manufacturing, replenishment of returns and their quality control while minimizing the total cost and satisfying a quality constraint requested by customers. A simulation-based optimization approach is used to tackle the problem. It aims to determine the optimal values of control parameters of the proposed policy minimizing the total cost. The results provide relevant insights and bring effective solutions to help decision makers manage simultaneously manufacturing, remanufacturing, replenishment of returns and their quality control activities. A comparative study is also performed showing that our policy, based on sampling inspection of delivered returns, outperforms in terms of costs those most used in the literature where complete (i.e. 100%) or no inspection strategies are used.

Impact of Learning on the Inventory Model of Deteriorating Imperfect Quality Items With Inflation and Credit Financing Under Fuzzy Environment

The present paper contributes to a set of models capturing economic order quantity with learning effect and fuzzy environment for decaying defective quality items under the inflation condition and credit financing. In real-life situations, the demand is uncertain and is controlled with fuzzy numbers. When each item goes through inspection process, the screening rate is assumed to be more than the demand rate otherwise shortages may occur and this consideration also helps one to meet their demand parallel to the screening process, out of the items which are of perfect quality. Further, the defective items are sold immediately after the screening process as a single lot at a discounted price. Further, the fraction of defective items follows the S-shaped learning curve. An expression for the total fuzzy profit of the retailer has been de-fuzzified with the help of a signed distance method and maximizes the cycle length. Conclusively, sensitive analysis has been presented on the various effective parameters of the inventory model.

Sustainable production inventory model with greening degree and dual determinants of defective items

In the world of environmental scarcity, customers are keen to invest in a supply chain player who makes environmentally sound choices. Owing to this, the present study develops a production inventory model with demand dependent on greening degree and price. The production process is faulty and thereby some fraction of defective items gets piled up along with the perfect products. Efficient management of defectives is indeed crucial in achieving sustainable development goals. Thus, the proposed study develops two models to handle the fraction of defective goods. The first model considers the salvaging of the defectives, which is quite applicable to the goods that are not suitable for any further dispensation. The second model considers the reworking option, which is pragmatic for most of the reworkable inventory goods. A sustainability assessment of both models is done and findings suggest the better performance of the second model. Numerical analysis is presented to impart the validity of the proposed study. A comprehensive sensitivity analysis is also done to demonstrate model features. The developed study is inspired by the recent advancements in the global supply chains in terms of greening levels. The key contribution lies in the framework of decision-making of various manufacturers and analyzing the impact of greening degree and pricing. With dual maneuver options for the defective items, the problem throws thought-provoking insights into the strategies of manufacturers and their vital decisions. Lingo and Mathematica software are used to solve the developed model. The present study contributes to the burgeoning field of sustainable supply chains by incorporating green and price-sensitive demand, carbon emissions, and dual options for handling defectives.

Learning EOQ Model with Trade-Credit Financing Policy for Imperfect Quality Items under Cloudy Fuzzy Environment

An imprecise demand rate creates problems in profit optimization in business scenarios. The aim is to nullify the imprecise nature of the demand rate with the help of the cloudy fuzzy method. Traditionally, all items in an ordered lot are presumed to be of good quality. However, the delivered lot may contain some defective items, which may occur during production or maintenance. Inspection of an ordered lot is indispensable in most organizations and can be treated as a type of learning. The learning demonstration, a statistical development expressing declining cost, is necessary to achieve any cyclical process. Further, defective items are sold immediately after the screening process as a single lot at a discounted price, and the fraction of defective items follows an S-shaped learning curve. The trade-credit policy is adequate for suppliers and retailers to maximize their profit during business. In this paper, an inventory model is developed with learning and trade-credit policy under the cloudy fuzzy environment where the demand rate is treated as a cloudy fuzzy number. Finally, the retailer’s total profit is maximized with respect to order quantity. Sensitivity analysis is presented to estimate the robustness of the model.

Optimal reorder level and lot size decisions for an inventory system with defective items

In this paper an (r,Q) stock policy is used to control an inventory system with deterministic demand and defective items. The fraction of defective items in a batch is a random variable whose variance maybe dependent and independent of the order quantity. Considering the numerous benefits of selling high quality items (noting the vital importance for firms like medical device companies), a full inspection of the order quantity is conducted. Although full inspection reduces returns, ensures high quality products and improves customer satisfaction, it requires a substantial inspection time. Consequently, during this time a non-zero probability of undesirable (unplanned) shortages exists. The dominant suggestion in the literature, is to set the reorder level equal to the total demand during inpection period. This paper suggests an alternative reorder level to prevent shortages during this period and to formulate the backlogging cost in the case that unplanned shortages are permitted. Then, theoretical results ensure the determination of the reorder level and the order quantity that minimize the average total cost of the inventory system. Comparisons, through numerical examples and simulation, demonstrate that the proposed model leads to significant reduction both in cost and probability of shortages (if allowed), in relation to other existing models.

Joint pricing and lot sizing model with statistical inspection and stochastic lead time

In many real-world situations, there are a fraction of defective items in a received lot whose quality should be evaluated before storage. In this article, we address the joint ordering, pricing, and inspection planning problem for a retailer facing price-sensitive demand and stochastic supply lead-time. The fraction of nonconforming items in a received lot follows a beta distribution and the buyer considers different kinds of inspection policies that include no inspection, inspection and sampling. Moreover, a novel non-linear optimization model is developed in order to determine optimal ordering, pricing and inspection policies. An analytical solution procedure based on mathematical properties of the model is proposed to find optimal decision variables. Numerical studies are conducted in order to show the applicability of the developed model and effectiveness of the proposed algorithms.

Some simultaneous progressive monitoring schemes for the two parameters of a zero-inflated Poisson process under unknown shifts

The zero-inflated Poisson (ZIP) distribution has been extensively studied in the literature during recent years. It is one of the most appropriate models for overdispersed data with an excessive number of zeros. Data of this type frequently arise in manufacturing processes with a low fraction of defective items. A ZIP model has two parameters; one presents the probability of extra zeros and the other stands for the expected Poisson count. In this article, we propose and study three new single control charts for detecting changes in either of the two parameters of a ZIP process. The performance of the schemes is studied via numerical simulation based on Monte-Carlo. We outline that all the existing control charts for monitoring ZIP processes are based on individual observations and assume that the shift sizes in either or both parameters are known. Our proposed schemes do not need any prior information related to shift size and can be used both for individual observations and subgroup samples. The results reveal that they are very effective in the detection of small and moderate shifts in process parameters. Practical implementation of the proposed schemes is also illustrated through an interesting real industrial data set on light emitting diodes (LED).

Modelling the newsvendor problem with a random fraction of defective items in the lot

An important assumption in deriving a formula for the optimal lot size newsvendor problem is that 100% of items in an ordered lot are assumed conforming to specifications. In real-life situations, however, this assumption may not hold for many production processes because of process deterioration and other factors. This paper develops a model for the newsvendor problem under the assumption that each ordered lot contains a random fraction of defective items which follows a beta distribution. The concavity of the expected total profit is established and the global optimal solution is determined by an algorithm based on Karush-Kuhn-Tucker conditions. Also, the effects of model's key parameters on the optimal solution are investigated using several case examples.

Retailer's ordering policy for deteriorating imperfect quality items when demand and price are time-dependent under inflationary conditions and permissible delay in payments

The present paper investigates an inventory model with unreliable supply, where each received lot may have a random fraction of defective items with known distribution. Thus, the inspection of lot becomes essential in almost all the situations, especially when the items are of deteriorating in nature. Moreover, in today's competition inherited business world, organisations use many promotional tools in order to increase their sales. One such tool is a permissible delay in payments, i.e., the buyer does not have to pay for the goods purchased immediately rather can defer the payment for a prescribed period given by the supplier. Further, in today's wobbling economy, especially for long-term investment, the effects of inflation cannot be disregarded as uncertainty about future inflation may influence the ordering policy. Being motivated by these aspects, the present paper investigates the impact of inspection on retailer's ordering policy for deteriorating items under permissible delay in payments when demand and price both varies with the passage of time. Finally, the model has been analysed and validated with the help of numerical examples. A comprehensive sensitivity analysis is also presented which provides important managerial implications.

Dynamic lot-sizing with rework of defective items and minimum lot-size constraints

In most production processes, defective items may result from an imperfect production system and the need of reworking them is inevitable in many production environments. Despite the great importance of rework in real-world manufacturing, the body of literature is very limited. This paper deals with the effects of defective items and rework on the Capacitated Lot-Sizing Problem (CLSP). We present a mixed-integer programming formulation of the CLSP with rework of defective items and minimum lot-size constraints on production lots. The formulation describes an imperfect production process that leads to a fraction of defective items that have to be reworked before they can be sold to customers. Detailed numerical experiments show that while the occurrence of defective items significantly increases the computational times, reasonably sized minimum lot-size constraints, besides their practical importance, can be a good strategy to accelerate the solution process.

Economic production quantity (EPQ) models under an imperfect production process with shortages backordered

In this paper, we develop economic production quantity (EPQ) models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production γ. The paper considers different cases of the EPQ model depending on (1) whether γ is known with certainty or is a random variable, and (2) whether imperfect items are drawn from inventory (a) as they are detected, (b) at the end of each production period or (c) at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.

An Inventory Model with Price and Quality Dependent Demand Where Some Items Produced Are Defective

This paper analyzes an inventory system for joint determination of product quality and selling price where a fraction of items produced are defective. It is assumed that only a fraction of defective items can be repaired/reworked. The demand rate depends upon both the quality and the selling price of the product. The production rate, unit price, and carrying cost depend upon the quality of the items produced. Quality index is used to determine the quality of the product. An algorithm is provided to solve the model with given values of model parameters. Sensitivity analysis has also been performed.

Economic order and production quantity models without constraint on the percentage of defective items

The paper deals with a version of the economic order and production quantity models when the fraction of defective items is probability variable that either may vary from cycle to cycle, or remains the same as it was in the first period. We drop the well-known assumption intended to avoid shortages, and two lot sizing rules are derived. Relationships between the new and known lot sizing rules are analyzed and cases are identified when lot sizing rules give significantly different results.

ACCEPTANCE SINGLE SAMPLING PLAN WITH FUZZY PARAMETER

In this present paper we have argued the acceptance double sampling plan when the fraction of defective items is a fuzzy number. we have shown that the operating characteristic (oc) curves of the plan is like a band having a high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Finally we completed discuss opinion by a numerical example.

Inspection error and its effects on single sampling plans with fuzzy parameters

In this paper we have designed an acceptance single sampling plan with inspection errors when the fraction of defective items is a fuzzy number. We have shown that the operating characteristics curve of this plan is like a band having high and low bounds, its width depends on the ambiguity of proportion parameter in the lot when the samples size and acceptance numbers are fixed. A comparison of the single sampling plans with and without inspection errors was done to study the effects upon the characteristics. The results of this comparison show that in the sampling plan with inspection errors, there is a lower operating characteristics band in comparison to a sampling plan without inspection errors for good processing quality. We have also shown that the incorrect classification of a good item reduces the fuzzy probability of acceptance and incorrect classification of a defective item results in a higher fuzzy probability of acceptance.

Fuzzy EPQ models for an imperfect production system

Manufacturing uncertainties are inevitable as unexpected events may occur at any time. In this article, we consider an imperfect production system in which the production process may shift from the in-control state to the out-of-control state at any random time. We assume that the fraction of defective items produced after process shift is uncertain and can be characterised by a fuzzy number. In another attempt, we take the fraction of defective items produced as a random variable, which follows an exponential probability distribution with fuzzy parameter. The expected fuzzy cost per unit time is derived in each model and defuzzified by using centroid method to obtain crisp values that can be used for comparison purposes. Two numerical examples are taken to demonstrate the optimal results of the proposed fuzzy models numerically and to compare these results with the corresponding ones in crisp models.

SHARPER BOUNDS IN ADAPTIVE GROUP TESTING

Adaptive group testing in the presence of a large percentage of defectives is best done by individual testing rather than by pooling. The fraction of items which must be defective to make individual testing optimal remains unknown, and is conjectured to be 1/3. In this paper it is shown that when the number of items is sufficiently large, and the fraction of defective items is at least $1/\log_{3/2}3$, individual testing is optimal.

Problems Associated with Quality control Sampling in Modern IC Manufacturing

Existing sampling plans are not very efficient in situations when a fraction of defective items is on the order of 0.0001. They usually command a 100-percent inspection, but it still does not provide for 100percent quality since in semiconductor manufacturing the inspection is never totally reliable and can easily introduce an error of almost the same order as the fraction of defectives. Skip-lot strategies can rarely be used because most of the customers frequently require inspection of every shipped lot. An inspection policy is suggested which combines the ideas of various sampling strategies and provides a guarantee against undesirable levels of average outgoing quality as well as protection against poor quality on a lot-to-lot basis. The method is based on observing the number of good items between defective ones and shifting to a 100percent inspection when certain conditions are not met.