A study of economic design of control charts for cumulative count of conforming items

In this paper the economic design of Cumulative Count of Conforming (CCC) control charts to maintain the current control of fraction nonconforming of a process is studied. CCC chart is an attribute chart for monitoring high quality processes by plotting the cumulative count of conforming items between two nonconforming ones on a suitable chart. A process model is proposed to obtain an appropriate loss function. An alogorithm to search for the optimal setting of the sampling and control parameters is derived. Numerical illustrations of the method and some properties of the optimal economic design are provided.     

An economic rectification plan for a process subject to a random shift into a persistent defective state

A rectification strategy is considered for a process which is subject to a random shift into a persistent defective state. The expected costs associated with plans other than the basic retrospective unit by unit procedure are considered and a simple criterion is derived to identify that with approximate minimum expected cost. The validity of the application is discussed and an example is given to illustrate the inductive nature and simplicity of the technique.     

An economic model for clinical quality control

With increased focus on reducing costs in the healthcare industry, the economic aspects of quality control for clinical laboratories must be addressed. In order to evaluate the economic performance of statistical quality control approaches used in the clinical setting, an economic model is developed. Although the economic model is applied specifically to the clinical laboratory in this research, it is easily generalized for use in a wide variety of industry applications. Use of the economic model is illustrated through the comparison of traditional approaches to clinical quality control. Recommendations concerning the performance of the traditional approaches to clinical quality control are provided.     

Online control by attributes in the presence of classification errors with variable inspection interval

ABSTRACT

The procedure for online control by attribute consists of inspecting a single item at every m items produced (m ≥ 2). On each inspection, it is determined whether the fraction of the produced conforming items decreased. If the inspected item is classified as non conforming, the productive process is adjusted so that the conforming fraction returns to its original status. A generalization observed in the literature is to consider inspection errors and vary the inspection interval. This study presents an extension of this model by considering that the inspected item can be rated independently r (r ≥ 1) times. The process is adjusted every time the number of conforming classifications is less than a, 1 ≤ a ≤ r. This method uses the properties of an ergodic Markov chain to obtain the expression for the average cost of this control system. The genetic algorithm methodology is used to search for the optimal parameters that minimize the expected cost. The procedure is illustrated by a numerical example.     

Continuous inspection of Markov processes with a clearance interval

Dodge's continuous sampling plan-1 (CSP-1) with clearance interval zero may be inefficient if there is serial correlation between successive units which are Markov dependent and a clearance interval greater than zero is appropriate. For such a situation, the average outgoing quality limit (AOQL) expression has been obtained and, when the serial correlation coefficient of the Markov chain is assumed to be known a priori, it is numerically demonstrated that smaller AOQL values are achieved numerically for values of the clearance interval from 1 to 4, by improving the perform-ance ofCSP-L     

An economic statistical design of the Poisson EWMA control charts for monitoring nonconformities

An economic statistical model of the exponentially weighted moving average (EWMA) control chart for the average number of nonconformities in the sample is proposed. The statistical and economic performance of proposed design are evaluated using the average run length (ARL) and the hourly expected cost, respectively. A Markov chain approach is applied to derive expressions for ARL. The cost model is established based on the general cost function given in Lorenzen and Vance [The economic design of control charts: a unified approach. Technometrics. 1986;28:3–11]. An example is provided to illustrate the application of the proposed model. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design by using the design of experiments (DOE) technique.     

An integrated model for economic design of chi-square control chart and maintenance planning

Considered process in this article is a two-stage dependent process. Each item in this process has two quality characteristics as x and y while x and y are related to the stage 1 and 2, respectively. Each stage has two operational states as the in-control state and out-of-control state and transition time from the in-control state to the out-of-control state follows a general continues distribution function. The process is monitored using a chi-square control chart. An integrated model that coordinates the decisions related to the economic design of the used control chart and maintenance planning is presented. For the evaluation of the integrated model performance, a stand-alone maintenance model is also presented, and the performance of these two models is compared with each other.     

An improved score interval with a modified midpoint for a binomial proportion

One of the most basic and important problems in statistical inference is the construction of the confidence interval (CI). In this paper, we propose a novel CI for a binomial proportion by modifying the midpoint of the score interval. The proposed modified interval can solve the ‘downward spikes’ problem of the score interval without enlarging the interval length. Simulation studies are carried out to illustrate the performance of the modified interval. With regard to the criterions of coverage probability, mean absolute error and expected length, our method is competitive among the several commonly used methods for constructing a CI. A real data example is also presented to show the application of our method.     

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.     

Robust algorithms for economic designing of a nonparametric control chart for abrupt shift in location

The existing statistical process control procedures typically rely on the fundamental assumption of a parametric distribution of the quality characteristic. However, when there is a lack of knowledge about the underlying distribution (as full knowledge is not available in practice), the performance of these parametric charts is very likely to be heavily degraded. Motivated by this problem, a one-sided nonparametric monitoring procedure using the single sample sign statistic is proposed for detecting a shift in the location parameter of a continuous distribution. An economic model of the control chart is developed to optimize the sample size, sampling interval, and control limits. Three data-dependent estimation approaches for the unknown parameter are evaluated and discussed. Simulation results exhibit that our proposed procedure generally performs well under a great variety of continuous distributions and hence it is recommended as an alternative scheme especially when the knowledge of the underlying distribution is imperfect. Furthermore, beneficial recommendations of estimation approach selection are provided for practical implementation of the control chart.     

Sample size determination for quality control process using a multiple components tolerance interval

ABSTRACT

In the past, a tolerance interval was used for the statistical quality control process on raw materials and/or the final product. In the traditional concept of the tolerance interval, the variance from the measurements is a single component. However, we can find examples about several components that could vary in their measurements, so an approximate method must be found to modify the traditional tolerance interval. Now we employ a tolerance interval considering multiple components in the variance from the measurements to deal with quality control process. In our paper, the proposed method is used to solve the sample size determination for a two-sided tolerance interval approach considering multiple components on the variance of measurements.     

An inspection procedure for radio frequency repeaters using a multiple linear regression method

Abstract

A radio frequency (RF) repeater is a wireless electronic device that transmits signals from a base transceiver station to a mobile station. When inspecting RF repeaters, various items are required to be tested to ensure their quality. In this paper, we propose a systematic procedure for the inspection by using a multiple linear regression method. The basic idea is to predict the inspection result without real inspection. In particular, a multicollinearity problem is considered in the regression analysis. Two case studies are conducted for validating the proposed method with an RF repeater production company in Korea.     

A new economic scheme for CCC charts with run rules based on average number of inspected items

New statistical techniques and procedures have been developed to control high-yield processes along with looking for process improvement opportunities and minimizing production cost. Cumulative count of conforming control chart is generally a technique for high-quality processes, when nonconforming items are rarely produced. The objective of this study is to design control chart based on cumulative count of conforming items and run rules that develops an economic model based on the average number of inspected items to design m-of-m CCC chart in order to facilitate minimum average cost per item produced. The optimal design parameters for different values of nonconforming fraction and different cost parameters in each scenario are determined. Finally, to analyze the behavior of optimal economic solutions, sensitivity analysis of the model parameters is performed.     

Robust design of adaptive control charts for manual manufacturing/inspection workstations

Often the manufacturing and the inspection workstations in a manufacturing process can coincide: thus, in these workstations the statistical process control (SPC) procedure of collecting sample statistics related to a critical-to-quality parameter is a task required to be done by the same worker who has to complete the working operations on a part. The aim of this study is to design a local SPC inspection procedure implementing an adaptive Shewhart control chart locally managed by the worker within the manufacturing workstation: the economic design of the inspection procedure is constrained by the expected number of false alarms issued and is restricted to those designs feasible with respect to the available shared labour resource. Furthermore, a robust approach that models the shift of the controlled parameter mean as a random variable is taken into account. The numerical analysis allows the most influencing environmental process factors to be captured and commented upon. The obtained results show that a few process operating parameters drive the choice of performing a robust optimization and the selection of the optimal SPC adaptive procedure.     

A synthetic control chart for monitoring the small shifts in a process mean based on an attribute inspection

Abstract

In this paper, a synthetic control chart is proposed by integrating the salient features of the np_x chart and the CRL chart. The synthetic chart achieves higher detection effectiveness on both small and large mean shifts while retaining the operational simplicity of the attribute charts owing to only using attribute inspection. Both statistical and economic design of the synthetic chart are considered and numerical tests have indicated that the synthetic chart has a higher power for detecting mean shifts than the np_x chart, MON chart and CUSUM chart. In addition, sensitivity analyses are also performed under both the statistical and economic design model.     

Confidence sets in a linear regression model for interval data

The construction of confidence sets for the parameters of a flexible simple linear regression model for interval-valued random sets is addressed. For that purpose, the asymptotic distribution of the least-squares estimators is analyzed. A simulation study is conducted to investigate the performance of those confidence sets. In particular, the empirical coverages are examined for various interval linear models. The applicability of the procedure is illustrated by means of a real-life case study.     

Monitoring the coefficient of variation using a variable sample size and sampling interval control chart

This article proposes a CV chart by using the variable sample size and sampling interval (VSSI) feature to improve the performance of the basic CV chart, for detecting small and moderate shifts in the CV. The proposed VSSI CV chart is designed by allowing the sample size and the sampling interval to vary. The VSSI CV chart's statistical performance is measured by using the average time to signal (ATS) and expected average time to signal (EATS) criteria and is compared with that of existing CV charts. The Markov chain approach is employed in the design of the chart.