Fraction Of Nonconforming Items Research Articles

Modified control chart for monitoring the variance

ABSTRACT.
 Goal: The main objective of this research paper is to propose a chart, named Modified Control Chart, where the process variance () is allowed to be larger than the in-control variance value () until a maximum value (), as long as the process remains capable, in the sense that it produces a specified (tolerated) small fraction of non-conforming items.
 Design / Methodology / Approach: The research methodology was quantitative approach with statistical analysis of simulated data, to assess the practical impact of variance increase in process control in terms of quality requirements.
 Results: The analysis of the simulated data showed that by using the proposed Modified Control Chart the number of unnecessary interventions in the process could be decreased, contributing to improve its efficiency.
 Limitations of the investigation: The analysis assumed mean and variance known, which is unlikely to occur in real applications. Research considering unknown parameters is also in progress.
 Practical implications: The S2 Modified Control Chart detects only genuinely increases in the process variance, which significantly increase the rate of non-conforming items being produced, preventing unnecessary process stop and assessment for assignable causes if only a small increase in the process variance occurs, contributing for higher process efficiency and reduce costs.
 Originality / Value: This paper introduces a new control chart to monitor the variance of quality characteristics being produced by capable processes, preventing process overcontrol.

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.

Effect of warranty and quantity discounts on a deteriorating production system with a Markovian production process and allowable shortages

This paper explores the retailer's optimal lot sizing and quantity backordering for a deteriorating production system with a two-state Markov production process in which quantity discounts are provided by the supplier. The products are sold with the policy of free reasonable repair warranty employing the fraction of nonconforming items in a lot size. Unlike the traditional economic production quantity (EPQ) model with warranty policy based on the elapsed time of the system in the control state follows an exponential distribution, this paper not only constructs an alternative mathematical model for EPQ model based on the fraction of nonconforming items in a lot size for an imperfect production system but also extends the topics of optimal quantity and shortage to a wider scope of academic research and further finds that some results are different from the traditional EPQ models. We seek to minimize the expected total relevant cost through optimal lot sizing and quantity backordering. We also demonstrate that the optimal lot size is bounded in a finite interval. An efficient algorithm is developed to determine the optimal solution. Moreover, a numerical example is given and sensitivity analysis is conducted to highlight management insights.

Comparative Statistical Analysis of Selected Control Charts for Highly Capable Processes

When a high-quality process is to be controlled by 100% inspection and yes-no decision is employed, several types of charts come into account, e.g. CCC, CCC-r or geometric CUSUM (CCC-CUSUM). The aim of the paper is to examine performance of these charts so that a suitable one can be chosen for a given process. The charts are compared according to the quickness with which the upward shift in the fraction of nonconforming items is detected. The average number of observations to signal (ANOS) instead of the usual average run length (ARL) is determined. While ANOS for CCC or CCC-r charts can be easily calculated based on a geometric or a negative binomial distribution, its computation is quite diffi cult in the case of CCC-CUSUM chart. The corrected diffusion (CD) approximation was used to determine ANOS and the results were verifi ed by Monte Carlo simulation. Zero-state and steady-state (both fi xed-shift and random-shift model) analyses were performed to take different scenarios of the process shift occurrence into account. CCC-3 or CCC-2 and CCC-CUSUM charts were compared. The order r for CCC-r chart was chosen as an optimal value for the given process based on the semi-economic model suggested in Brodecka (2013). Our study revealed that for in-control p0 equal to 0.0002 the CCC-CUSUM chart performs best especially for shifts around the pre-specifi ed out-of-control fraction nonconforming. The CCC-r chart may be comparable or even better in detecting larger shifts. The results of the comparative study were utilized for the choice of the most suitable and best performing control chart to control the high-yield process producing ERG (Exhaust Gas Recirculation) sensors. Comparisons of CCC-r and CCC-CUSUM charts can be found elsewhere in literature, but conclusions seem to be rather inconsistent. To our best knowledge no study dealing with such small in-control fraction nonconforming together with the low risk of false alarm has been published yet. The choice of CUSUM’s parameters and consequent values of ANOS can help practitioners who need to control high-quality processes.

DETERMINATION OF QUICK SWITCHING DOUBLE SAMPLING SYSTEM BY ATTRIBUTES UNDER FUZZY BINOMIAL DISTRIBUTION – SAMPLE SIZE TIGHTENING

Acceptance sampling is concerned with norms of deciding about the acceptance or rejection of the lots based on the quality of the product during inspection. Dodge and Romig popularized the acceptance sampling as a major field of SQC. Various Sampling plans, systems and schemes are developed as per the need of the industry. Quick Switching Systems is a system which requires fewer samples for processes running at low levels of defects. Quick Switching Systems are compared with single, double, multiple, chain and variable sampling plans as well as MIL STD 105 E switching systems and concluded its advantages. This article presents the Quick Switching Double Sampling System (QSDSS) when the fraction of non-conforming items is a fuzzy number and being modeled based on the fuzzy Binomial distribution. Operating Characteristic (OC) curves of the fuzzy system is like a band having high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Tables are constructed and numerical illustrations are given to describe the determination of QSDSS for sample size tightening with fuzzy Binomial distribution with its OC curve.

A comparative study of two proposed CCC-r charts for high quality processes and their application to an injection molding process

ABSTRACTHigh-quality industrial processes, characterized by a low fraction of non-conforming items, require paying special attention to the statistical control methods employed since traditional Shewhart's control charts are no longer suitable. In this article, CCC-r charts are considered based on the cumulative count of conforming items inspected until r non-conforming items are observed. However, even though these charts have shown to be useful for high-quality processes, they are characterized by a biased average run length (ARL). In order to help engineers interested in this control methodology to select the best option, a computational study of statistical validation was performed to compare the two most outstanding procedures for the cases r = 2, 3, and 4. The performance was evaluated based on the ARL under control. The application of the CCC-r chart to a real process is shown with data from an automobile parts plant. Finally, analysis and discussion of the results are presented.

Synthetic double sampling np control chart for attributes

The quality of a product, based on the number of non-conforming items can be controlled using the np chart. This paper proposes a synthetic double sampling (DS) np chart which comprises two sub-charts, i.e. the DS np and conforming run length (CRL) sub-charts. For the zero-state case, the synthetic DS np chart surpasses its standard counterpart, i.e. the synthetic np and the basic DS np chart, and other np type charts like the standard np, combined synthetic and np (Syn-np), variable sample size (VSS) np, exponentially weighted moving average (EWMA) np and cumulative sum (CUSUM) np charts, for detecting increases in the fraction of non-conforming items p, for most shift sizes. The synthetic DS np chart also performs reasonably well in the steady-state case in comparison with other charts mentioned above. Thus, among the competing charts, the synthetic DS np chart stands out as one of the best charts.

Variable Sampling Interval Cumulative Count of Conforming Chart with Runs Rules

The cumulative count of conforming (CCC) chart is effective in detecting very low fraction of nonconforming items for high yield manufacturing processes. In this study, a combination of runs rules and variable sampling interval feature is proposed to a lower sided CCC chart by inspecting the items one by one. The performance measures of the control chart are derived by using the Markov chain approach. The numerical comparisons show that the performance of the CCC chart can be improved by adding the runs rules and varying the sampling interval.

Vendor-managed inventory models for items with imperfect quality

In this paper, two models for supply chain under VMI settings are developed when the incoming lot of items contains a fraction of non-conforming items. The first model is for a decentralised case where the vendor’s profit is maximised. However, there is significant extra profit to be realised by optimising the performance of the entire supply chain. Therefore, another model for centralised supply chain under VMI configuration is introduced. This model seeks to optimise the system total expected profit. The additional profit realised by implementing the integrated solution is distributed between vendor and retailer. The distribution scheme is according to some weight such that no party obtains less profit than that generated by decentralised VMI model. Usually, this weight reflects the bargaining positions of the vendor and retailer. The optimal solutions are characterised by finding all Karush-Kuhn-Tucker points of the profit functions. Based on these Karush-Kuhn-Tucker points, efficient algorithms are devised to solve the models.

Monitoring imprecise fraction of nonconforming items using p control charts

The quality characteristics, which are known as attributes, cannot be conveniently and numerically represented. Generally, the attribute data can be regarded as the fuzzy data, which are ubiquitous in the manufacturing process and cannot be measured precisely and often be collected by visual inspection. In this paper, we construct a p control chart for monitoring the fraction of nonconforming items in the process in which fuzzy sample data are collected from the manufacturing process. The resolution identity – a well-known theorem in the fuzzy set theory – is invoked to construct the control limits of fuzzy-p control charts using fuzzy data. In order to determine whether the plotted imprecise fraction of nonconforming items is within the fuzzy lower and upper control limits, we also propose a ranking method for a set of fuzzy numbers. Using the fuzzy-p control charts and the proposed acceptability function to classify the manufacturing process allows the decision-maker to make linguistic decisions such as rather in control or rather out of control. A practical example is provided to describe the applicability of the fuzzy set theory to a conventional p control chart.

Acceptance Single Sampling Plan By Using Of Poisson Distribution

This purpose of this paper is to present the acceptance single sampling plan when the fraction of nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have shown that the operating characteristic (OC) curves of the plan are like a band having 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. And then we compared the OC bands of using of binomial with the OC bands of using of Poisson distribution.

Parameter Estimation and Performance of the<tex>$p$</tex>-Chart for Attributes Data

Effects of parameter estimation are examined for the well-known <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> -chart for the fraction nonconforming based on attributes (binary) data. The exact run-length distribution of the chart is obtained for Phase II applications, when the fraction of nonconforming items, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> , is unknown, by conditioning on the observed number of nonconformities in a set of reference data (from Phase I) used to estimate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> . Numerical illustrations show that the actual performance of the chart can be substantially different from what one would nominally expect, in terms of the false alarm rate and/or the in-control average run-length. Moreover, the performance of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> -chart can be highly degraded in that an exceedingly large number of false alarms are observed, particularly when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> is estimated, unless the number of reference observations is substantially large, much larger than what might be commonly used in practice. These results are useful in the study of the reliability of products or systems that involve binary data.

Design of multiple run sampling plan

This paper studies the Multiple Run Sampling (MRS) plan introduced by Vance and Mc Donald (1979) which is useful for the initial stages of production. This plan accepts the process or a batch if a run of s conforming items is observed before the occurrence of k+1 non-conforming items. Formulae are given for the Operating Characteristic (OC) and Average Sample Number (ASN) of the plan along with tables useful for designing MRS plans when the fraction of nonconforming items is very low.

The AdjustedpChart anduChart for Varying Sample Sizes

It is common to have control charts for fraction of nonconforming items or number of nonconformities that are based on differing sample sizes for each observation. This paper presents a simple method for charting such data that is as easy to interpret a..

Plans for Very Low Fraction Nonconforming

Existing sampling plans are not very efficient in situations where the fraction of nonconforming items is near 0.0001. In such cases the statistician must resort to 100% inspection, which still will not guarantee 100% conforming product since inspection..

Rectifying Inspection for Nonconforming Items and the Hald Linear Cost Model

The Hald linear cost model is discussed with and without a beta prior for the distribution of the fraction of nonconforming items in a lot. For both situations, average outgoing quality limit plans, limiting quality level (lot tolerance percent defectiv..