Number Of Nonconformities Research Articles

Most powerful lot acceptance test plans from dispersed nonconformity counts

Optimal inspection schemes based on dispersed nonconformity count data are derived to properly discriminate between satisfactory and unsatisfactory batches. The Conway-Maxwell-Poisson distribution is adopted to describe the stochastic behavior of the number of nonconformities per sampled unit. A mixed integer nonlinear programming problem is stated in order to determine the lot sampling plan with a minimal sample size and limited producer and consumer risks. Explicit approximations of the smallest number of units to be tested per lot and the maximum tolerable nonconformity score are presented. A Monte Carlo simulation approach is then used to find the most powerful decision rule for lot disposition. In case of over-dispersion, the suggested perspective allows the practitioners to greatly reduce the required sample size for lot sentencing. The developed methodology is applied to the manufacturing of glass for illustrative and comparative purposes.

Controlling posterior producer and consumer risks in lot reinspection

Assuming that maximum tolerable posterior risks are specified for both producer and consumer, an integer nonlinear programming problem is formulated and solved in order to determine the optimal defects-per-unit acceptance sampling plan when lots found unacceptable may be resubmitted for reinspection. The number of nonconformities per inspected item follows a Poisson distribution. A computational algorithm is proposed to solve the underlying constrained minimization problem. The suggested procedure simplifies and quickens the determination of the inspection scheme for resubmitted lot acceptance with limited posterior risks that minimizes the expected number of sampled items per lot. An application to the manufacturing of paper is considered to illustrate the methodology developed. The generalized truncated gamma distribution is used to describe the prior uncertainty about the incoming defect rate per unit. The degree of similarity between the available previous information and the current study is also evaluated. Suitable ways are provided to assume a reduced parameter space for the defect rate and to update the prior model using past performance of the acceptance plan. The incorporation of lot resubmissions, as well as previous defect count data and expert opinions, into the decision process often yields appreciable savings in sampling effort.

Simplified resubmitted lot inspection from defect counts

Nowadays, as low defect rates per item are often expected in practice, conventional single sampling for lot acceptance purposes is rendered inefficient or unduly expensive. For specific producer’s and consumer’s quality and risk requirements, resubmitted lot sampling usually needs, on the average, less inspection effort than single sampling to properly discriminate between satisfactory and unsatisfactory batches. An integer nonlinear programming problem is stated in order to determine the optimal resubmitted lot sampling plan based on defect count data with limited producer and consumer risks. Nonaccepted lots may be resubmitted for sampling inspection a certain number of times. The number of nonconformities per sampled unit is assumed to follow a Poisson distribution. Quasi-optimal inspection schemes for screening submitted lots of manufactured material are derived in closed-forms by using a normal approximation of the incomplete gamma ratio function. Explicit and quite accurate approximations of the smallest number of units to be tested per lot and the maximum tolerable number of nonconformities in the selected sample are presented. The number of resubmissions with minimal inspection effort and controlled risks is also computed. An application to the manufacturing of glass is provided for illustrative purposes.

Case Study on Failures of Thermoplastics Pipeline Systems

The paper presents some of the most significant situations of tests realised on high density polyethylene pipeline networks from Romania, designed for fluids and gases, which failed during 2008-2014. The inspected objects were assemblies or welded components made of pipes and fittings, as parts of the natural gas and potable water pipeline. The inspections on various assemblies and weldments have identified a number of nonconformities, which have led to failures, generally recorded after welding, during operation. Based on the investigation results, a number of comments and recommendations have emerged, useful for manufacturing companies and for the clients, which could ensue increasing the safety in operation of the high density polyethylene pipeline systems.

Quantitative Analysis of Supplier Quality Surveillance Practices in EPC Projects

AbstractThis study was funded by the Construction Industry Institute (CII) to investigate effective supplier quality practices that can reduce rework associated with supplied components in engineering-procure-construct (EPC) projects. The motivation was to analyze how the level and amplitude of inspection in different stages of a supply chain (from fabrication to mechanical completion) affect the resulting quality of products as measured by the number of nonconformances (NCs) found in its different stages. Quantitative data were collected using an instrument used by CII member organizations to submit data on actual purchase orders and analyzed using the Mann-Whitney (M-W) test on the nonparametric set of data obtained. Following the statistical analysis, interviews with subject matter experts, face-to-face presentations, and sharing of reports with the research team were used to clarify questions, interpret the data, and validate conclusions. The results provide insights regarding where inspection is most...

Evaluating multi-objective economic-statistical design of attribute C control charts for monitoring the number of non-conformities

The C control chart is mostly used to monitor the number of non-conformities per inspection unit of constant size. It is known that the classic C-chart control limits often experience a high false alarm rate and thus lead to the increase of unnecessary costs of inspection. Among many works performed to improve C-charts, this paper presents the optimised control limits approach to the C-chart. In addition, different C-charts are evaluated through factors related to the design of the control chart. Optimally selecting design parameters depends on several process parameters from statistical and/or economic aspects in the literature. This study presents multi-objective economic-statistical design of different C control charts under single assignable cause. An algorithm using the data envelopment analysis (DEA) is employed to solve the models. A numerical example is used to illustrate the algorithm procedure and to evaluate the performances of different designs.

Selection of single sampling plans by attributes under the conditions of zero-inflated Poisson distribution

Purpose– The purpose of this paper is to determine single sampling plans (SSPs) by attributes when the number of nonconformities is distributed according to a zero-inflated Poisson (ZIP) distribution.Design/methodology/approach– Manufacturing processes have now-a-days been aligned properly and are monitored well, so that the occurrence of nonconformities would be a rare phenomenon. The information related to number of nonconformities per product will have more number of zeros. Under such circumstances, the appropriate probability distribution of the number of nonconformities is a ZIP distribution. The operating characteristic function of the sampling plan is derived.Findings– Parameters of the sampling plans are obtained for some sets of values of (p1,α,p2,β). Numerical examples are given to illustrate the selection of SSPs under ZIP distribution and to study its advantages over Poisson SSP.Originality/value– Results obtained in this paper are original and has been done for the first time in this regard. Parameters of the sampling plans are essential to make decisions either to accept or reject the lots based on the inspection of the samples.

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.

Optimal Defects-Per-Unit Acceptance Sampling Plans Using Truncated Prior Distributions

Optimal sampling inspection plans for defects per unit with fixed acceptance numbers and limiting quality levels are developed to provide the appropriate protection to customers when the number of nonconformities per sampled item follows a Poisson distribution. The best inspection scheme assures the customer, who has to judge the quality of the submitted material, that a supplier's lot is released only when there is conclusive evidence that it is satisfactory. The underlying integer nonlinear programming problem is formulated and solved in the frequentist setting, and a practically exact approximation to the minimum sample size is presented. Because there is often no reason to assume that the process average is constant, the classical perspective is then extended to those situations in which there is substantial prior information on the supplier's process. A family of generalized truncated gamma models and several restricted maximum entropy distributions satisfying typical constraints are adopted to describe the stochastic fluctuations in the process average. Optimal defects-per-unit acceptance plans are determined by solving the corresponding constrained minimization problems. Lower and upper bounds on the required sample size are deduced in closed-forms. A general procedure based on Taylor series expansions of the operating characteristic function around the mean quality level of the rejectable lots is proposed to derive an explicit, accurate, easily computable approximation to the smallest sample size that provides the required average customer protection. This procedure greatly simplifies the determination of optimal plans from defect or failure count data and prior knowledge, and also requires little prior information, namely the prior mean and variance of the quality level of the rejectable lots, which could be estimated from past data and expert opinions. The suggested methodology is applied to the manufacturing of paper and glass for illustrative purposes. Our approach allows the practitioners to incorporate into the quality analysis a reduced parameter space for the process average. Furthermore, the proposed sampling plans are reasonably insensitive to small disturbances in the prior knowledge on the process average, and the effective use of the available information on the supplier's process provides a more realistic assessment of the actual customer protection, as well as considerable savings in testing time and sample size.

ZIP 공정을 관리하는 GLR 관리도

단위 영역의 결점수는 일반적으로 Poisson 분포를 가정한다. 이 Poisson 분포의 확장된 형태로 ZIP(zero-inflated Poisson) 분포를 고려할 수 있는데, 이 모형은 데이터에 0이 많이 관측되는 경우 잘 적합된다고 알려져 있다. 이 논문에서는 ZIP 분포를 따르는 공정을 관리하는 GLR(generalized likelihood ratio) 관리도 절차를 제안하고 있다. 또한 제안된 GLR 관리도의 효율을 기존에 제안된 CUSUM 관리도들과 비교하였다. 그 결과 제안된 GLR 관리도는 모수의 다양한 변화에 대해 효율이 좋거나 또는 효율이 크게 떨어지지 않았고, 특히 CUSUM 관리도에서 모수가 미리 설정한 방향과 다르게 변화했을 때 효율이 크게 나빠지는 문제를 해결할 수 있는 대안이라는 결론을 얻을 수 있었다. The number of nonconformities in a unit is commonly modeled by a Poisson distribution. As an extension of a Poisson distribution, a zero-inflated Poisson(ZIP) process can be used to fit count data with an excessive number of zeroes. In this paper, we propose a generalized likelihood ratio(GLR) chart to monitor shifts in the two parameters of the ZIP process. We also compare the proposed GLR chart with the combined cumulative sum(CUSUM) chart and the single CUSUM chart. It is shown that the overall performance of the GLR chart is comparable with CUSUM charts and is significantly better in some cases where the actual directions of the shifts are different from the pre-specified directions in CUSUM charts.

Design and Construction of a Variables Repetitive Group Sampling Plan for Unilateral Specification Limit

This paper attempts to develop a repetitive group sampling (RGS) plan by variables inspection for controlling the process fraction defective or the number of nonconformities when the quality characteristic follows a normal distribution and has only the lower or upper specification limit. The proposed sampling plan is derived by the exact sampling distribution rather than the approximation approach. The plan parameters are solved by a nonlinear optimization model which minimizes the average sample number required for inspection and fulfills the classical two-point conditions on the operating characteristic (OC) curve. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. The results indicate that the proposed variables RGS plan could significantly reduce samples required for inspection compared to the traditional variables single sampling plan.

On-Line Process Control of the Number of Non-Conformities in the Inspected Item

Generally, production systems that use automatic control as automatic welding process, production of ceramic products, making clothes use on-line process control to evaluate the quality of their production processes. The control system consists of a periodic inspection of one item after every m produced items. If the number of non-conformities meets the control limit then it is decided that the process is in-control, otherwise the process is stopped for adjustment. The process starts in-control with a non-conformities rate and, after an assignable cause, this rate increases leading the system to operate out of control. The process remains in these conditions until the change is detected and the process adjusted. After adjustment, the process returns to operate in-control. The aim of this paper is to present an economic approach to monitor the rate of non-conformities in a production by on-line process control. To design such type of process, an average cost per item produced is achieved through the properties of an ergodic Markov chain and the two required parameters: the inspection interval and the upper control limit are obtained by minimizing the average cost per produced item. A numerical example illustrates the proposed procedure.

Construction of tightened-normal-tightened schemes indexed through Six Sigma quality levels

'Six Sigma is a tool used to convert management problem into a statistical problem and to find a statistical solution then it converts into a management solution'. Six Sigma is a set of practices originally developed by Motorola to systematically improve processes by eliminating non-conformities. The term Six Sigma refers to the ability of highly capable processes to produce outputs within specification. In particular processes that operate with Six Sigma quality produce 3.4 or less number of non-conformities per one million opportunities (dpmo). This Six Sigma concept can be applied in the construction of sampling plans also. In this paper a new procedure for the construction and selection of tightened-normal-tightened scheme [TNT-(n; c1, c2)] with c1 = 0 and c2 = 1 indexed through Six Sigma quality level-1 (SSQL-1) and Six Sigma quality level-2 (SSQL-2) are presented. Tables are also constructed and presented for the easy selection of the schemes. These schemes can be used by the companies which practice Six Sigma initiatives in their organisations.

Minimum Size Double Sampling Plans for Large Isolated Lots

A common approach to the design of an acceptance sampling plan is to require that the operating characteristic (OC) curve should pass through two designated points that would fix the curve in accordance with a desired degree of discrimination. This paper presents a search procedure for the selection of double sampling inspection plans of type DSP - (0, 1) for specified two points on the OC curve, namely acceptance quality limit, producer's risk, limiting quality and consumer's risk. Selection of the plans is discussed for both the cases of fraction non-conforming and the number of non-conformities per unit.

The Effect of Estimated Parameters on Poisson EWMA Control Charts

Performance of control charts is generally evaluated with the assumption that the process parameters are known. In many control chart applications, however, the process parameters are rarely known and their estimates from an in-control reference sample are used instead. In such cases, the moments of the run length distribution depend on the values of the estimated parameters. The Poisson exponentially weighted moving average (EWMA) is an effective control chart in situations where the number of nonconformities per unit from a repetitive production process is monitored. The objective of this paper is to study the effect of estimating the mean on the performance of the Poisson EWMA control chart. We make use of the Markov Chain approach. Sample-size recommendations and some concluding comments are provided.

On Control Charts Based on the Generalized Poisson Model

The Poisson distribution is widely used to fit count data such as the number of nonconformities in a product unit. However, this distribution fails to fit the defect data in a high-quality manufacturing environment when over-dispersion occurs. In this paper, the generalized Poisson distribution is studied as an alternative distribution. The generalized Poisson distribution is flexible and capable of dealing with over-dispersed data. In particular, the interpretation of parameters is discussed and statistical monitoring procedures for count data that can be modeled by the generalized Poisson distribution are studied. Based on the generalized Poisson distribution, two different procedures are discussed for an effective process monitoring. Sensitivity analyses of the two monitoring procedures are also presented. To validate the use of the generalized Poisson distribution, three statistical tests for testing the Poisson distribution against the generalized Poisson alternative are also investigated and compared.

Poisson Moving Average Versus c Chart for Nonconformities

The c chart is often used to monitor the number of nonconformities in an inspection unit of product, especially when the chance of an occurrence of a nonconformity is relatively small. However, the c chart is slow in detecting small shifts. In this article, a more efficient alternative based on the construction of a Poisson moving average control chart for the number of nonconformities is suggested. Comparisons between the performances of the new approach in terms of its average run length (ARL) profiles and that of the classical c chart show that the new approach provides faster detection of out-of-control conditions while maintaining a longer in-control ARL. Two examples are given to show how the new approach is put to work in real situations. The first example deals with the case where the standard value for the number of nonconformities; i.e., the mean of the Poisson distribution, c, is known while in the second example, c is unknown and hence is estimated from a preliminary sample of inspection units.

Acceptance Sampling with Rectification When Inspection Errors are Present

In this paper we consider the problem of estimating the number of nonconformances remaining in outgoing lots after acceptance sampling with rectification when inspection errors can occur. We show that inspection errors can have a serious biasing effect on the predictor that Greenberg and Stokes (1992) propose for the number of undetected nonconformances. We develop a new bias-corrected predictor of this quantity. A simulation study shows that this predictor performs well with respect to mean square error under a wide range of scenarios. We also propose a predictor for the number of conforming items rejected.

DISTRIBUTION OF RUNS IN A TWO-STAGE PROCESS MONITORING MODEL

In statistical process control, procedures similar to double sampling technique can be used to incorporate information from two observations. This leads to the study of the distribution of runs. In this paper, a run is defined as the number of nonconformities observed until an alarm when the two stage procedure is used. The exact distribution of run and the average quantity inspected between alarms are derived and we also obtain some analytical results concerning the expected value of some interesting related quantities.

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 ...