Nonconforming Units Research Articles

Designing Accurate Control Charts Based on the Geometric and Negative Binomial Distributions

Attribute control charts are used effectively to monitor for process change. Their accuracy can be improved by judiciously selecting the sample size. The required sample sizes to achieve accuracy can be quite restrictive, especially when the nominal proportions of non-conforming units are quite small. The usual attribute control chart has a set sample size and the number of non-conforming units in the sample is plotted. If, instead of setting a specific sample size the number of non-conforming units is set, an alternative monitoring process is possible. Specifically, the cumulative count of conforming (CCC-r) control chart is a plot of the number of units that must be tested to find the rth non-conforming unit. These charts, based on the geometric and negative binomial distributions, are often suggested for monitoring very high quality processes. However, they can also be used very efficiently to monitor processes of lesser quality. This procedure has the potential to find process deterioration more quickly and efficiently. Xie et al. (Journal of Quality and Reliability Management 1999; 16(2):148–157) provided tables of control limits for CCC-r charts for but focused mainly on high-quality processes and the tables do not include any assessments of the risk of a false alarm or the reliability of detecting process change. In this paper, these tables are expanded for processes of lesser quality and include such assessments using the number of expected monitoring periods (average run lengths (ARLs)) to detect process change. Also included is an assessment of the risk of a false alarm, that is, a false indication of process deterioration. Such assessments were not included by Xie et al. but are essential for the quality engineer to make sound decisions. Furthermore, a hybrid of the control charts based on the binomial, geometric and negative binomial distributions is proposed to monitor for process change. Copyright © 2005 John Wiley & Sons, Ltd.

Artificial neural networks to classify mean shifts from multivariate χ2 chart signals

A traditional multivariate control chart is shown to be effective in monitoring a multivariate process to signal the out-of-control condition that arises when mean shifts occur. The immediate classification of the signals associated with mean vector shifts can greatly narrow down the set of possible assignable causes, facilitating rapid analysis and corrective action by a technician before numerous nonconforming units have been manufactured. A persistent problem presented by such multivariate control charts, however, concerns the analysis of signals and the provision of any shift-related information. This study develops an artificial neural network-based model to supplement the multivariate χ2 chart. The method not only identifies the characteristic or group of characteristics that cause the signal but also classifies the magnitude of the shifts when the χ2-statistic signals that mean shifts have occurred. The method is described from the perspectives of training and classification. An example of the application of the proposed method is provided. The results demonstrate that the proposed method provides an excellent rate of classification and the output generated by trained network is very strongly correlated with the corresponding actual target value for every quality characteristic. Additionally, general guidelines for the proper implementation of the proposed method are provided.

Modified CSP-C Continuous Sampling Plan for Consumer Protection

Dodge (1943) introduced a single level attribute continuous sampling plan designated as CSP-1 for the application of continuous production processes. Govindaraju & Kandasamy (2000) developed a new single level continuous sampling plan whose sampling inspection phase is characterized by a maximum allowable number of non-conforming units c, and a constant sampling rate f and was designated as CSP-C. In this paper, a modification is proposed on the CSP-C continuous sampling plan. In this modified plan, sampling inspection is continued until the occurrence of c+1 non-conforming units, provided the first m sampled units have been found conforming during the sampling phase. Using a Markov chain model, expressions for the performance measures of the modified CSP-C plan are derived. The main advantage of the modified plan is that it is possible to lower the average outgoing quality limit.

RUNS RULES AND P-CHARTS FOR MULTISTREAM BINOMIAL PROCESSES

ABSTRACT Process control schemes for multistream binomial processes are described. A multistream process is one in which the streams are uncorrelated or very weakly correlated. When each of the J streams are identical (a homogeneous multistream process) one can use a group control chart (a k-sigma p-chart on which only the largest and smallest of the J sample proportions nonconforming are plotted). A test (runs rule) that signals when the same stream produces the largest proportion nonconforming R consecutive times is investigated. Methods using Markov chains are developed for determining the average run length (ARL) of a runs test. ARL tables useful for designing runs rule control schemes are provided for selected values of J, stream sample size n, proportion of nonconforming units p, and R.

Mean shifts detection and classification in multivariate process: a neural-fuzzy approach

For monitoring multivariate quality control process, traditional multivariate control charts have been proposed to detect mean shifts. However, a persistent problem is that such charts are unable to provide any shift-related information when mean shifts occur in the process. In fact, the immediate classification of the magnitude of mean shifts can greatly narrow down the set of possible assignable causes, hence facilitating quick analysis and corrective action by the technician before many nonconforming units are manufactured. In this paper, we propose a neural-fuzzy model for detecting mean shifts and classifying their magnitude in multivariate process. This model is divided into training and classifying modules. In the training module, a neural network (NN) model is trained to detect various mean shifts for multivariate process. Then, in the classifying module, the outputs of NN are classified into various decision intervals by using a fuzzy classifier and an additional two-point-in-an-interval decision rule to determine shift status. An example is presented to illustrate the application of the proposed model. Simulation results show that it outperforms the multivariate T2control chart in terms of out-of-control average run length under fixed type I error. In addition, the correct classification percentages are also studied and the general guidelines are given for the proper use of the proposed model.

A STUDY ON THE PRODUCTION SIMULATION UNDER THE CONSIDERATIONS OF OPERATION VARIATION AND LEARNING EFFECT

ABSTRACT The simulation of production system has a lot of benefits about the understanding of production conditions and the design of production system. In this paper, we simulate several kinds of learning conditions and production variations to evaluate the system performance, and search for optimal combinations to promote the production efficiency. The production conditions include following five types: 1. The operation time has no learning effect 2. The operation time has variation 3. The operation time has variation and the learning rate is deterministic 4. Both of operation time and learning effect have variation 5. Besides of condition 4, also have non-conforming units. Finally, we draw six conclusions for future applications and studies.

Quick switching variables single sampling (QSVSS) system indexed by AQL and AOQL

Procedures and tables are given for the selection of a 'Quick Switching Single Sampling Variable System' for given AQL and AOQL, whenever rejected lots are 100% inspected and for replacement of non-conforming units.

Bayesian Analysis of Quality Level Using Simulation Methods

This article demonstrates how Bayesian methods for making inferences about the number, or proportion, of nonconforming units in a quality control setting can be implemented using simulation techniques. Random draws from the posterior distribution of the target quantities of interest are used to construct the needed inferences. The same random draws from the posterior distribution are also used to perform model checking and sensitivity analysis. The methods are illustrated using two examples. The methods can be generalized to more complicated situations which are illustrated by discussing the extensions of both the examples.

Improved p charts to monitor process quality

It is a common practice to monitor the fraction p of non-conforming units to detect whether the quality of a process improves or deteriorates. Users commonly assume that the number of non-conforming units in a subgroup is approximately normal, since large subgroup sizes are considered. If p is small this approximation might fail even for large subgroup sizes. If in addition, both upper and lower limits are used, the performance of the chart in terms of fast detection may be poor. This means that the chart might not quickly detect the presence of special causes. In this paper the performance of several charts for monitoring increases and decreases in p is analyzed based on their Run Length (RL) distribution. It is shown that replacing the lower control limit by a simple runs rule can result in an increase in the overall chart performance. The concept of RL unbiased performance is introduced. It is found that many commonly used p charts and other charts proposed in the literature have RL biased performance. For this reason new control limits that yield an exact (or nearly) RL unbiased chart are proposed.

Improved p charts to monitor process quality

It is a common practice to monitor the fraction p of non-conforming units to detect whether the quality of a process improves or deteriorates. Users commonly assume that the number of non-conforming units in a subgroup is approximately normal, since large subgroup sizes are considered. If p is small this approximation might fail even for large subgroup sizes. If in addition, both upper and lower limits are used, the performance of the chart in terms of fast detection may be poor. This means that the chart might not quickly detect the presence of special causes. In this paper the performance of several charts for monitoring increases and decreases in p is analyzed based on their Run Length (RL) distribution. It is shown that replacing the lower control limit by a simple runs rule can result in an increase in the overall chart performance. The concept of RL unbiased performance is introduced. It is found that many commonly used p charts and other charts proposed in the literature have RL biased performance. For this reason new control limits that yield an exact (or nearly) RL unbiased chart are proposed.

Control chart for multivariate attribute processes

Many industrial processes are multivariate in nature since the quality of a product depends on more than one variable. Multivariate control procedures can be used to capture the relationship between the variables and to provide more sensitive control than that provided by the application of univariate control procedures on each variable. Much has been done on the multivariate variable processes, such as embodied in control procedures based on Hotelling's T 2 statistic. However, little work has been done to deal with the control of multivariate attribute processes, which is very important in practical production processes. In this paper, we develop a Shewhart-type control chart to deal with multivariate attribute processes, which is called the multivariate np chart (MNP chart). The control chart uses the weighted sum of the counts of nonconforming units with respect to all the quality characteristics as the plotted statistics. It enhances the efficiency of identifying the critical assignable cause when an out-of-control signal appears. It is also simple to interpret for out-of-control signals. The practical application of the MNP chart is also discussed in this paper with an example presented to demonstrate the approach of the MNP chart and to compare with the univariate np control charts which are commonly used in industry.

PRE-CONTROL AND SOME SIMPLE ALTERNATIVES

Pre-control, also called stoplight control, is a quality monitoring scheme similar to a control chart. However, the goal of Pre-control is the prevention of nonconforming units rather than the detection of a lack of stability. The appeal of Pre-control ..

Practical guidelines for process validation and process control of white cell-reduced blood components: report of the Biomedical Excellence for Safer Transfusion (BEST) Working Party of the International Society of Blood Transfusion (ISBT).

The increased use of white (WBC)-reduced blood components has prompted many institutions to develop quality assurance programs directed to such component preparation processes. For consistent preparation of WBC-reduced blood components that meet clinical needs as well as national standards, a program of process validation and control should be instituted. This involves controlling key factors that affect WBC reduction as well as periodic monitoring of the residual cellular content of components. Practical guidelines for the implementation of such a program are provided. A program involving three phases of monitoring was developed by individuals belonging to an international working party of the International Society of Blood Transfusion. The first phase, process validation, evaluates a minimum of 20 consecutive units (a minimum of 60 units when nonparametric measurements are used) to document the successful local implementation of a new or substantially modified process. Ongoing process control employing Levey-Jennings type control charts is used to demonstrate that the process remains stable over time. Process capability assessment and conformance with standards are evaluated once residual WBCs are counted in a sufficient number of units. This enables a facility to claim with a specified degree of confidence that a stated proportion of WBC-reduced units will meet national standards. Two approaches to determine the number of units that should be selected for counting are presented. The first approach considers units as either acceptable or not acceptable and assumes that the distribution of failed (or nonconforming) units approximates the Poisson distribution. The second approach takes into consideration the observed WBC content of the tested units, with the assumption that the residual WBC content in WBC-reduced components follows a lognormal distribution. A method to assess the lognormal distribution of residual WBCs is presented. Specific tables based on each of these approaches are provided to guide the reader in the design of a program that will verify conformance with any national standard at specific confidence levels. The approach can be generalized to other process control applications. Guidelines are presented for process validation, process control, and assessment of conformance in the production of WBC-reduced blood components. Policy makers retain the responsibility to establish, on the basis of the expected use of WBC-reduced components, requirements for the frequency of testing and for the proportion of prepared units that are expected with a stated degree of confidence to meet the standards. Facilities preparing WBC-reduced components can monitor key factors that influence the preparation of WBC-reduced blood, can periodically assess their conformance with the standards, and can intervene to correct adverse changes in the process. This approach can be used to ensure the consistent quality of WBC-reduced blood components.

Filter effect in the use of control charts for productive process control

In this paper the author analyses the reduction of product nonconformity obtainable through the use of Shewhart control charts during the operative phase of a productive process. This result can be called of control charts. The author supplies a quantification of this effect by defining , in correspondence with a nonconformity input of the process, an approximate measure of the expected proportion of nonconforming units resulting from the use of control charts. The study is conducted both under the classic hypothesis of a single shift,which is constant over time, in the observed process parameter, and under the hypothesis of a uniformly progressive shift. The result obtained show that, at a given level of nonconformity input, the filter effect is more pronounced in the case of a progressive shift, and above all, that it is possible to quantify this effect at assigned levels of risk. It can be observed that the filter effect of a control chart increases when the nonconformity level of the process decreases. Therefore the filter effect is particularly remarkable when more time is needed to detect the process parameter and, consequently, there is a longer exposure to the resulting nonconformity.

Sample size determination for p-charts

Two types of decision errors can be made when using a quality control chart for non-conforming units (p-chart). A Type I error occurs when the process is not out of control but a search for an assignable cause is performed unnecessarily. A Type II error occurs when the process is out of control but a search for an assignable cause is not performed. The probability of a Type I error is under direct control of the decision-maker while the probability of a Type II error depends, in part, on the sample size. A simple sample size formula is presented for determining the required sample size for a p-chart with specified probabilities of Type I and Type II errors.

Estimating Nonconformance Rates after Zero-Defect Sampling with Rectification

Suppose a set of T lots has been subject to zero-defect acceptance sampling with rectification. A lot is accepted if there are no nonconforming units in a sample; otherwise there is 100% inspection of the lot and all nonconforming units are replaced with conforming ones. We introduce an estimator for the number of nonconformances that remain in those lots, using the data observed during acceptance sampling, including the rectification procedure. The estimator proposed is similar to a Horvitz-Thompson estimator in that it weights the number of detected nonconformances in a lot by the inverse of its detection probability. The mean squared error of this estimator is compared with several alternatives. The proposed estimator was found to perform well under a variety of models for the nonconformance process. Confidence interval procedures are given for the proposed estimator. A simulation study shows that coverage is less than the nominal level for few lots and small sample sizes. We observe that the coverage ...

EXPRESSING VARIABILITY AND YIELD WITH A FOCUS ON THE CUSTOMER

Click to increase image sizeClick to decrease image sizeKey Words: Q-yieldQuality lossInspection limitsCustomer functional limitsYield

Determination of single sampling attributes plans for given (aql. aoql)

This paper presents tables and a computer program for determining single sampling plans for given AQL, producer's risk and AOQL for the case of nonconforming units and nonconformities. Comparison with Soundararajan's (1981) procedures for selection of single sampling plans for given (AQL, AOQL) is also given

Single Sampling Plans for Variables Indexed by AQL and AOQL

Procedures and tables are given for the selection of single sampling plans for variables for given AQL and AOQL, whenever rejected lots are 100% inspected for replacement of nonconforming units...

The optimal location of inspection stations using a rule-based methodology

Abstract The location of inspection stations is a significant component of production systems. In this paper, a prototype expert system is designed for deciding the optimal location of inspection stations. The production system is defined as a single channel of n serial operation stations. The potential inspection station can be located after any of the operation stations. Non-conforming units are generated from a compound binomial distribution with known parameters at any given operation station. Traditionally Dynamic programming, Zero-one integer programming or Non-linear programming techniques are used to solve this problem. However a problem using these techniques is that the computation time becomes prohibitively large when the number of potential inspection stations are fifteen or more. An expert system has the potential to solve this problem using a rule-based system to determine the near optimal location of inspection stations. The prototype expert system is divided into a static database, dynamic database and knowledge base. Based on defined production systems, the sophisticated rules are generated by the simulator as part of a knowledge base. A generate-and-test inference mechanism is utilized to search the solution space by applying appropriate symbolic and quantitative rules. The goal of the system is to determine the location of inspection stations while minimizing total cost.