Variable Sampling Interval Scheme Research Articles

A variable sampling interval EWMA control chart for urinary tract infections data

Control chart is an important method in Statistical Process Control, which is used to study how a process changes over time. The exponential distribution is one of the commonly used models for fitting data, especially in areas such as component life, aviation accidents, or health-care processes. In order to further improve the sensitivity of the control chart, we propose an exponentially weighted moving average control chart with a variable sampling interval scheme, denoted as VSIEWMA-T control chart, for monitoring exponentially distributed quality characteristics (e.g. Urinary Tract Infections data). In this paper, the average time to signal property of the proposed control chart is investigated using the Markov chain method. In addition, parameter optimization algorithms for known or unknown shift levels are provided. Subsequently, numerical analysis shows that the proposed control chart outperforms other competitive control charts. Finally, an example of urinary tract infections data is provided for illustration.

An enhanced EWMA chart with variable sampling interval scheme for monitoring the exponential process with estimated parameter

Control charts have been used to monitor product manufacturing processes for decades. The exponential distribution is commonly used to fit data in research related to healthcare and product lifetime. This study proposes an exponentially weighted moving average control chart with a variable sampling interval scheme to monitor the exponential process, denoted as a VSIEWMA-exp chart. The performance measures are investigated using the Markov chain method. In addition, an algorithm to obtain the optimal parameters of the model is proposed. We compared the proposed control chart with other competitors, and the results showed that our proposed method outperformed other competitors. Finally, an illustrative example with the data concerning urinary tract infections is presented.

Joint Design of Control Chart, Production Cycle Length, and Maintenance Schedule for Imperfect Manufacturing Systems with Deteriorating Products under Stochastic Shift Size

This paper presents a hybrid model based on the integration of three interrelated topics including statistical process monitoring (SPM), production cycle length, and maintenance scheduling for imperfect production systems. The proposed model takes both process deterioration and product deterioration into account i.e., the process can go out of control and the products can deteriorate over time. In this regard, a nonuniform sampling strategy is presented for calculating the sampling intervals to avoid exceeding the hazard rate from a threshold value. Moreover, in order to make the model more adapted to real industrial systems, the shift magnitude in the mean parameter of quality characteristic is considered as a stochastic variable. To elaborate the model effectiveness, three comparative studies and a sensitivity analysis are presented. The first comparison shows that by using the variable sampling interval scheme instead of the fixed one, the ratio of in-control time interval to the whole production cycle increases dramatically. Moreover, the use of variable sampling interval scheme leads to a significant cost savings and decreases the out-of-control time interval. The second comparative study indicates that although using statistical considerations in establishment of the control chart imposes a higher cost on the manufacturer, both values of the in-control average run length ([Formula: see text]) and out-of-control average run length ([Formula: see text]) improve significantly. In other words, the use of economic-statistical model reduces the amount of non-conforming products as well as the risk of issuing a false alarm by the control chart. The third comparative study indicates that, in terms of total inventory holding cost, the proposed model performs better than the model without considering deterioration possibility due to the significant reduction in the deterioration cost.

Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling

AbstractIn this paper, we design an attribute np control chart using multiple deferred state (MDS) sampling under Weibull distribution based on time truncated life test. This chart is constructed for monitoring the variation of mean life of the product in a manufacturing process. The optimal parameters of MDS sampling and the control limit coefficients are determined so that the in‐control average run length (ARL) is as close as to the target ARL. The optimal parameters of MDS sampling are sample size and number of successive subgroups required for declaring the current state of process. Out‐of‐control ARL is considered as a measure of the performance of proposed chart and reported with determined optimal parameters for various shift constants. The out‐of‐control ARL of the proposed chart obtained under various distributions is compared with each other. The performance of proposed control chart is compared with the performance of the existing control chart designed under single sampling. In addition, the economic design of proposed chart using variable sampling interval scheme is discussed, and sensitivity analysis on expected costs is also investigated.

Economic and economic–statistical designs of VSI Bayesian control chart using Monte Carlo method and ABC algorithm

ABSTRACTThe usual practice in using a Bayesian control chart to monitor a process is done by taking samples from the process with fixed sampling intervals. Recent studies on traditional control charts have shown that variable sampling interval (VSI) scheme compared to classical scheme (fixed ratio sampling, FRS) helps practitioners to detect process shifts more quickly. In this paper, the effectiveness of VSI scheme on performance of Bayesian control chart has been studied, based on economic (ED) and economic–statistical designs (ESD). Monte Carlo method and artificial bee colony algorithm have been utilized to obtain optimal design parameters of Bayesian control chart (sample size, sampling intervals, warning limit and control limit) since the statistic of this approach does not have any specified distribution. Finally, VSI Bayesian control chart has been compared to FRS Bayesian and VSI X-bar approaches based on ED and ESD, separately. According to the results, it has been found that the performance of VSI Bayesian scheme is better than FRS Bayesian and VSI X-bar approaches.

A modified variable sample size and sampling interval controlchart

In this article, a modified version of variable sample size and sampling interval chart using three sampling intervals and two sample sizes, called the VSSIt control chart, is proposed to overcome the weakness of the standard Shewhart (SS) control chart in detecting small and moderate shifts. In order to evaluate the performance of the proposed scheme, average time to signal (ATS), average number of observations to signal (ANOS), and average number of samples to signal (ANSS) are used. Using this control chart can reduce the ATS value around 68, 27, 7, and 1.83 time unit (sampling interval of the SS chart) in detecting shift of size 0.25, 0.5, 0.75, and 1 standard deviation, respectively. The performance of the constructed adaptive chart is compared with various adaptive charts such as variable sample size (VSS), variable sampling interval (VSI), variable sample size and sampling interval (VSSI), and special variable sample size and sampling interval (SVSSI) \( \overline{x} \) control chart. It is shown that the proposed chart always outperforms SS, VSI, VSS, and VSSI schemes. It also can detect shift of size 0.25 standard deviation quicker than SVSSI scheme. Finally, the optimal parameters of the proposed chart are recommended.

Comparison of two sampling intervals and three sampling intervals VSI charts for monitoring both means and variances

In industrial quality control, when engineers use VSI control procedure they should consider both required time to signal and switching behaviors together in the case of production process changed. Up to the present, many researchers have studied fixed sampling interval (FSI) chart and variable sampling interval (VSI) chart in the points of average number of samples to signal (ANSS) and average time to signal (ATS). However, ANSS and ATS do not provide any switching information between different sampling intervals of VSI schemes. In this study, performances of two sampling intervals VSI chart and three sampling intervals VSI chart are evaluated and compared. The numerical results show that ANSS and ATS values of two sampling intervals VSI chart and three sampling interval VSI chart are similar regardless the amount of shifts. However, the values of switching behaviors including ANSW are less efficient in three sampling intervals VSI charts than in two sampling intervals VSI chart.

Economic design of moving average control chart for non-normal data using variable sampling intervals

In this article, we propose an economic design of moving average control chart for non-normal quality characteristics using variable sampling intervals (VSI) policy. An expression for expected loss cost function is derived for continued and ceased process designs. The performance of two operational modes is compared numerically and the comparison between fixed sampling interval (FSI) and VSI control schemes is carried out. The VSI scheme is found to be superior to FSI scheme. As the number of sampling intervals increases, percentage saving in cost with respect to FSI design increases. The ceased VSI production process shows more saving with respect to continuous VSI production process. Percentage saving due to ceasing increases with increasing shift in the process. Also, the sample size increases with the decreasing values of shift. Overall, the ceased VSI moving average process design seems to be economically superior to other process designs.

Evaluation of the economic statistical design of the multivariate T2 control chart with multiple variable sampling intervals scheme: NSGA-II approach

The economic and statistical merits of a multiple variable sampling intervals scheme are studied. The problem is formulated as a double-objective optimization problem with the adjusted average time to signal as the statistical objective and the expected cost per hour as the economic objective. Bai and Lee's [An economic design of variable sampling interval ¯X control charts. Int J Prod Econ. 1998;54:57–64] economic model is considered. Then we find the Pareto-optimal designs in which the two objectives are minimized simultaneously by using the non-dominated sorting genetic algorithm. Through an illustrative example, the advantages of the proposed approach are shown by providing a list of viable optimal solutions and graphical representations, which indicate the advantage of flexibility and adaptability of our approach.

Impact of the Variable Sampling Intervals Scheme on the CQC Chart

The Cumulative Quantity Control (CQC) chart which is based on monitoring the cumulative quantity of product manufactured has been shown to be useful for monitoring high yield processes. However, this chart is not so sensitive to small process changes and the inspection cost could be high if the inspection is frequent. In this paper, a variable sampling interval procedure of the CQC chart is developed and studied. We compare the performance of the variable sampling interval CQC chart in terms of its average time to signal with the traditional CQC chart and prove that this new chart performs better than the traditional CQC chart. The use of variable sampling interval scheme could further enhance the efficiency of traditional CQC chart.

Cumulative conformance count charts with variable sampling intervals for correlated samples

The cumulative conformance count (CCC) control chart is often employed to monitor the fraction nonconforming of high-yield processes. Traditional CCC chart is used when the items from a process are inspected one-at-a-time following the production order. In recent years, the CCC chart has been generalized to accommodate some industrial practices where items from a process are inspected sample by sample and not according to the production order. In order to increase the sensitivity of the generalized CCC (GCCC) chart to changes in fraction nonconforming, the variable sampling interval (VSI) scheme is used in this study. The output characteristic within each sample is assumed with correlation. The statistical properties of the GCCC chart with the VSI scheme are deduced using the Markov chain method. In evaluating the usefulness of the VSI feature, GCCC charts with VSI and fixed sampling interval (FSI) schemes are compared in terms of their statistical properties. The comparison results show that using the VSI scheme can improve the speed of GCCC chart in detecting changes in fraction nonconforming. Finally, according to the comparison results, a design procedure is applied to an industrial example to validate its practicability.

A Design of s Control Charts with a Combined Double Sampling and Variable Sampling Interval Scheme

This study extended the idea of Carot et al. (2002) to combine double sampling and variable sampling interval s charts (DSVSI s chart) for improving efficiency in detection of small standard deviation shifts. The performance of DSVSI s charts in detecting small shifts was measured and compared with double sampling, variable sampling intervals, EWMA, and Cusum control charts. This comparative study presented found the DSVSI s chart to be efficient in detecting small shifts.

An effective joint X-bar and R chart to monitor the process mean and variance

When the shift occurs in both sample mean and standard deviation of a process, a joint X-bar and R charts can be used to monitor the process mean and variance. This paper deals with very simple and effective design of proposed X-bar and R charts to monitor the process mean and standard deviation. The concept of the proposed chart is based upon the sum of chi-square (χ) to compute and compare Average Run Length values (ARLs). Although Variable Sample Size (VSS), Variable Sampling Interval (VSI) and Variable Sample Size and Sampling Interval (VSSI) joint charts are very useful to catch the small shifts in the mean or standard deviation, they make the chart more complex and very difficult to use at shop-floor level. The performance of the proposed chart has been compared with VSS, VSI and VSSI joint schemes proposed by Costa (1999).

A synthetic control chart for monitoring process dispersion with sample range

A synthetic control chart for monitoring the changes in the standard deviation of a normally distributed process is proposed in this paper. The synthetic chart consists of the sample range (R) chart and the conforming run-length (CRL) chart. The R chart can be viewed as a special case of the synthetic chart. The operation, design and performance of this chart are described. Average run- length comparisons between other procedures and the synthetic chart are presented. It indicates that the synthetic chart is a good alternative for monitoring process dispersion. The variable sampling interval (VSI) schemes, as an enhancement to the synthetic chart, are discussed to further improve the chart performance. An example is presented to illustrate the application of synthetic chart and its VSI scheme.

A synthetic control chart for monitoring process dispersion with sample standard deviation

Some factors in manufacturing such as faulty raw material, unskilled/careless operators, and loosening of machine settings may lead to a change in process dispersion without necessarily influencing the level of the process mean. This paper proposes a synthetic control chart for monitoring the changes in the standard deviation of a normally distributed process. The synthetic chart is a combination of the sample standard deviation ( S ) chart and the conforming run length (CRL) chart. The S chart can be regarded as a special case of the synthetic chart. The operation, design, and performance of this chart are described. Average run length comparisons between other procedures and the synthetic chart are presented. It indicates that the synthetic chart is a good alternative for monitoring process dispersion. The variable sampling interval (VSI) schemes as an enhancement to the synthetic chart are discussed to further improve the chart performance. An example is presented to illustrate the application of synthetic chart and its VSI scheme.

Cumulative count of conforming chart with variable sampling intervals

The control chart with cumulative count of conforming (CCC) items has shown to be useful for process monitoring in automated and discrete manufacturing. It does not require a fixed sample size and can be useful for one-at-a-time data. The current research relies on data from the fixed sampling interval (FSI) scheme. In this paper, we investigate the use of the CCC chart when the variable sampling interval scheme is used. The average time to signal (ATS) is calculated, and its efficiency is compared with that of FSI CCC chart. The use of variable sampling interval scheme may further enhance the cost effectiveness of control chart implementation from a practical point of view.

Economic statistical design of adaptive control schemes for monitoring the mean and variance: An application to analyzers

Several individuals control chart schemes are contrasted for the problem of monitoring the mean and variance of a normal process variable, with special consideration given to monitoring process analyzers, such as electrochemical devices, chromatographs, potentiometers, refractometers, and spectrometers. The combination of the exponentially weighted moving average (EWMA) chart and the Shewhart X chart that uses a variable sampling interval (VSI) policy is shown to be very effective for this problem. We develop a comprehensive economic model for the design of control schemes based on this chart combination. The economic model expresses the long-run cost per time unit of operating the combined VSI EWMA and VSI X chart scheme as a function of its design parameters, the parameters that describe the behavior of the process, and the cost parameters associated with the operation of the scheme. This economic model can be used to quantify the cost reduction that can be achieved by using the combined VSI scheme instead of traditional control schemes that use fixed sampling rates. We show that the reduction in cost as well as gains in performance are substantial.

Steady-state-optimal adaptive control charts based on variable sampling intervals

Variable sampling interval (VSI) control charts vary the sampling rate adaptively as a function of the data coming from the process in order to reduce the detection delay of process changes. Zero-time performance refers to the detection delay of a process change that is present during the onset of the chart at time zero. Steady-state performance refers to the detection delay of a process change that occurs after the chart has been operating for some time. The zero-time performance of a VSI control chart can differ considerably from the chart's steady-state performance, which is generally more important than the zero-time performance. We develop an efficient quadratic-programming algorithm for the construction and investigation of steady-state-optimal sampling policies for various VSI charts. We show that a steady-state-optimal VSI scheme is fundamentally different from the respective zero-time-optimal VSI scheme, and recommend VSI policies based on two sampling intervals for the various types of control charts considered.

An Application of Variable Sampling Interval Control Charts

Variable Sampling Interval (VSI) control charts have been studied extensively, and it has been shown for Shewhart, cumulative sum (CUSUM), and exponentially weighted moving average (EWMA) charts that shifts in the process mean can be detected more quickly with no increase in the average in-control sampling or false alarm frequency relative to fixed interval charts. Applications of VSI charts in industry have been few, however, primarily due to logistical problems associated with a variable sample schedule. In this paper, we present an application of a VSI-EWMA chart at Monsanto's nylon fiber plant in Pensacola, Florida. Motivation for this implementation, instead of being quicker detection of shifts, was a significant decrease in laboratory cost with little adverse impact on control chart performance compared with the fixed-interval EWMA chart. The logistical problems were solved by employing a fixed time option with the VSI scheme (VSI-FT), where there is a fixed sample schedule for the long interval, and in-between samples are taken when warranted by the data.

The switching behavior of charts with variable sampling intervals

In a variable sampling interval control scheme the time interval between successive samples is allowed to vary depending on what is being observed from the data. It has been the practice to compare the average time to signal and the average run length of variable sampling interval schemes and the corresponding control procedures with fixed sampling intervals. Thus far design tables for control charts with variable sampling intervals have not considered the effect of the design parameters on the switching behavior of such control procedures. Frequent switches between the different sampling intervals can be a complicating factor in the application of control charts with variable sampling intervals. The problem of switches is addressed in this article and improved switching rules are presented and evaluated for Shewhart control procedures. Expressions for the average number of switches and the average time to signal are obtained. The proposed runs rules considerably reduce the average number of switches betw...