Effects Of Inspection Errors Research Articles

Effect of Inspection Error on CUSUM Chart for Truncated Negative Binomial Distribution


 In this paper, a mathematical investigation has been done for Cumulative Sum control Chart (CSCC) of
 Truncated Negative Binomial Distribution (TNBD) under inspection error using the sequential probability
 ratio test (SPRT). Average Run Length (ARL), d (lead distance) and \(\phi\) (angle of the mask) is calculated for
 different values of error rates and different values of parameter of the distribution.

Effect of inspection errors on imperfect production inventory model with warranty and price discount dependent demand rate

This paper deals with selling price-discount and warranty period dependent demand in an imperfect production inventory model under the consideration of inspection errors and time dependent development cost. Normally, due to long-run, a production process deteriorates with time and here we assume that the process shifts from "in-control" to "out-of-control" state at any random time. A time dependent development cost has been constructed to increase the reliability of the production systemi.e., to decrease the deterioration of the system during the production process. As a result, a few items are rejected. Here, two types of inspection errors such as Type-I error and Type-II error, have been considered during the period of product inspection process. In Type-I error, an inspector may choose falsely a defective item as non-defective and in Type-II error an inspector may choose falsely a non-defective item as defective. Due to these phenomena, the inspection process would consist of the following costs: cost of inspection, cost of inspection errors. The purpose of this paper is to investigate the effects of time dependent development cost on the defective items, selling price-discount and warranty policy on the market demand and finally optimize the expected average profit under consideration of such inspection costs in infinite time horizon. Some numerical examples along with graphical illustrations and sensitivity analysis are provided to test the feasibility of the model.

Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system

In many cases, the safety and the reliability of a warm standby system heavily rely on the successful activation and the subsequent operation of its standby components. Optimal inspection and maintenance schedule is one of the most common but essential activities in the real world applications to manage standbys effectively and efficiently. In this paper, we propose a novel state-based method by incorporating inspection activities into multiphase Markov process to model the dynamic behaviors of a general repairable k-out-of-n: G warm standby system with common-cause failures. Here the effects of inspection errors are taken into consideration. Then the expected total cost and the average unavailability of the system are expressed as exact closed formulas regarding the inspection interval (or inspection frequency) in a cycle. Finally, the inspection and maintenance optimization problem is formulated as a nonlinear optimization program which aims to find the optimal periodic inspection interval on a finite time horizon by minimizing the expected total cost while taking into account the limitation of the average unavailability. The proposed modeling approach can be used in various industrial systems, where inspections and standbys are especially necessary, e.g., a feedwater subsystem of a nuclear power plant. A simplified numerical example illustrates the models and the calculations with sensitivity analysis and Monte Carlo simulation.

The effect of inspection error on quality and producer losses: the case of nominal-the-best type quality characteristic and rework

In this study, the effect of inspection error (IE) on quality and producer losses is investigated for a nominal-the-best type quality characteristic determined by a manufacturing process centre with a separate rework unit. The probability distribution and the first two moments of the resulting quality characteristic values are derived and used together with Markov chain models and simulation to study the quality and producer losses and the related statistics for various processes and gage capability levels. The results of this study confirm with strong theoretical and empirical evidence that an effective way of achieving robustness to IE is to improve the process capability. This study provides benchmarks that support understanding and decision making of quality professionals.

Economic optimization for an imperfect process with inspection errors, inspection time and minimal repair

This paper extends an integrated model of production lot-sizing, maintenance and quality to consider the possibilities of inspection errors, inspection time and minimal repair for an imperfect process. These generalizations are importation because inspection might demand a considerable amount of time and there might be inspection errors due to human or technological limitations in the process of inspection. The production process is in either the in-control state or the out-of-controlstate. If the production process is judged in the in-control state, then when preventive maintenance is performed, system age and the level of maintenance performed will be related. If the production process is judged in the outof- control state, there might have two types. The fi rst type is a relatively mild production processshift, where minimal repair can restore the process to the in-control state. The second type is a more serious shift, where it interrupts the production cycle and the production has to be completely stopped. In this article, we derive the optimal solutions for the inspection interval, the number of inspections and the productionlot-sizing with two types of out-ofcontrol states and inspection errors. We use numerical examples to illustrate the eff ects of inspection errors, inspection time and minimal repair on the cost of production.

The effect of inspection errors on the optimal batch size in reworkable production systems with scraps

The objective of this paper is to provide a framework to integrate the existence of products with imperfect-quality items, inspection errors, rework and scrap items into a single Economic Production Quantity (EPQ) model. To achieve this objective, a suitable mathematical model is defined and the optimal production lot size that minimises the total cost is obtained. Sensitivity analysis is carried out for this model. The sensitivity analysis results indicate that the model is very sensitive to defective proportions and type 1 errors of inspection. Nowadays, given the progress made, inspection errors are often ignored. But the findings of this study show that the values of EPQ and total cost are very sensitive to type 1 errors of inspection. If the existence of such errors is ignored, then the obtained results will differ considerably from the optimal outcome. This will impose additional costs to the system.

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.

Effect of inspection errors and preventive maintenance on a two-stage production inventory system

The effect of imperfect production processes on lot-sizing decisions has received a lot of attention in the literature. These efforts have mostly been confined to single-stage production systems. The issue of imperfect production processes has not been adequately addressed in the context of multistage production/inventory systems. In this paper, we propose a production inventory model that takes into account the effect of imperfect production processes, preventive maintenance and inspection errors. Numerical examples are presented for illustrative purposes.

Chain Sampling Scheme under Constant Inspection Errors

AbstractThe primary aim of this paper is to extend the inspection error consideration to chain sampling schemes, an area that has not been dealt with in the literature. A mathematical model is developed to investigate the performance of chain sampling schemes under constant inspection errors. Expressions of performance measures, such as operating characteristic function, average total inspection and average outgoing quality, are derived to aid the analysis of a general chain sampling scheme, ChSP‐4A ($c_1,\,c_2$) r, developed by Frishman. This study reveals that as Type I inspection error increases the probability of acceptance will decrease and as Type II inspection error increases the acceptance probability will increase. The effect of Type II error on the probability of acceptance is very marginal compared with that of Type I error, especially when the true fraction non‐conforming is small. In addition, the effects of inspection errors can be ‘eliminated’ by transforming to its equivalent perfect inspection counterpart, hence greatly reducing the complexity of the analysis. The effects of other sampling parameters are also studied to serve as a foundation for future plan designing purposes. Copyright © 2006 John Wiley & Sons, Ltd.

Impact of inspection errors on the lot size problem

Optimal production and product inspection policies for a deteriorating production system are considered. In theoretical investigations and practical applications using simplified models, inspection results may be assumed to be perfect. In this study, two kinds of inspection errors are considered. We first show that an inspection policy that does not inspect the first s produced items but inspects only those items from the ( s +1)th till the end of the production run is optimal. Two commonly used inspection strategies, no inspection and full inspection, are discussed. Next, we show how the optimal products inspection policy are incorporated into the determination of optimal lot size. Under the optimal inspection policy, the optimal production lot size is shown to be unique and bounded above by the traditional economic manufacturing quantity. Based on these findings, an efficient solution procedure is provided for the simultaneous determination of the optimal production lot size and its corresponding product inspection policy. Numerical examples are given to illustrate the model. Sensitivity analyses are performed to examine the effect of inspection errors on the solution.

Optimal lot-sizing, quality improvement and inspection errors for multistage production systems

We develop multistage lot-sizing models for imperfect production processes. The effect of inspection errors in screening non-conforming items at various stages has been incorporated. Inspection and restorstion of the processes at all stages have also been considered. Numerical examples are presented to illustrate various aspects of the models developed. It is shown that when inspection and restoration are introduced, lower costs are incurred and larger lot sizes are produced because of reductions in quality control costs.

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.

Signal detection for human error correction in quality control

Acceptance sampling by attributes is now a universal and fundamental tool in statistical quality control. Among the various plans, single sampling has been recognized to offer significant cost savings and administrative simplicity. Single sampling by attributes is generally carried out or supervised by a human inspector. Unfortunately, human inspection error is another fact of life in industrial inspection. Two types of errors are possible. One is the Type 1 error, in which a good item is classified as defective (i.e., nonconforming); the other is the Type 2 error, in which a defective item is passed as good. Presently, little has been written on the effects of inspection errors on the outgoing quality and on how to compensate for these errors. The research objective of this paper is to show how a knowledge of the errors can be used to design compensating acceptance sampling plans for industrial quality control tasks. In contrast to the typical human inspection models in quality control, with fixed performance irrespective of incoming product quality, the model proposed here uses a form of signal detection theory (SDT) to predict inspector performance in order to improve system performance. The paper proposes the concept of lability, measured by a number ranging from 0 to 1, to characterize an inspector's ability to response to costs, rewards and probabilities involved in the inspection decision. This concept allows the modeling of both a constant-error inspector having a lability of 0, an SDT inspector having a lability of 1, and all those which fall within this range. Using this concept, the paper presents two models of the human inspector with considerations of: (a) constant Type 1 and Type 2 errors independent of the incoming fraction nonconforming, and (b) increasing Type 2 error and decreasing Type 1 error with increasing fraction nonconforming as specified by SDT. A general model covering these inspection errors is proposed. The paper shows that an imperfect inspector, who can detect the signal properly to adjust the decision criterion conservatively in the direction specified by the SDT, can compensate for the potential errors. A numerical example is proposed to illustrate the model application.

The Effects of Inspection Errors on Acceptance Sampling for Nonconformities

The effect of inspection errors on acceptance sampling when one is inspecting for the number of nonconformities per item is considered. Two types of inspection errors are defined. Formulas are derived for the AOQ and ATI for situations when these inspec..

Statistical Effects of Imperfect Inspection Sampling IV. Modified Dorfman Screening Procedures

This is the fourth and last in a series of papers on the effects of inspection errors on the properties of acceptance sampling procedures for attributes. This paper presents a study of some modified forms of hierarchal Dorfman screening procedures and a summary of all four papers.

Effect of Inspection Error on MIL STD 105D Sampling Plans: Some Observations

Inspection error has been and continues to be an important area of research particularly in statistical quality control. While considerable work has been reported on the effect of inspection error on different sampling plans and the implications thereof, very little seems to have been done to assess the effects of such errors on MIL STD 105D plans. In this article some aspects related to inspection errors and operation of MIL STD 105D plans have been studied. Based on this study some observations have been made which have led to the development of a few subtle practical guidelines that may prove helpful to the operating manager in administering such plans effectively.

Effects of Inspection Errors on Dorfman Screening Procedures with Random Group-Size: A Note on Kemp and Kemp’s ‘Simple Inspection Scheme for Two Types of Defect’

Effects of Inspection Errors on Dorfman Screening Procedures with Random Group-Size: A Note on Kemp and Kemp’s ‘Simple Inspection Scheme for Two Types of Defect’

Effects of Inspection Errors on Dorfman Screening Procedures with Random Group-Size: A Note on Kemp and Kemp's 'Simple Inspection Scheme for Two Types of Defect'

Effects of Inspection Errors on Dorfman Screening Procedures with Random Group-Size: A Note on Kemp and Kemp's 'Simple Inspection Scheme for Two Types of Defect'

Effects of Inspection Errors on Dorfman Screening Procedures with Random Group-Size: A Note on Kemp and Kemp's ‘Simple Inspection Scheme for Two Types of Defect’

Kemp and Kemp have proposed a scheme of inspection for two types (A and B) of non-conformity. There is serial inspection for type A, continuing until a sequence of k successive As is observed. These k items are discarded, and all previous items (since the last inspection for A) are subject to a Dorfman group-screening inspection procedure for B. We develop formulae for the properties of this scheme, when inspection (for both A and B) may not be perfect, allowing for both false negatives and false positives. Some numerical values given by the formulae are presented, with a view to assessing the robustness of Kemp and Kemp's scheme.

ThecControl Chart Under Inspection Error

The effects of inspection errors on the c chart, especially on the OC curves, are considered. Control limits based upon target values and those based upon historical data are both considered. An adjusted c chart is presented which provides OC curves und..