Repetitive Sampling Scheme Research Articles

Control charts using half-normal and half-exponential power distributions using repetitive sampling

This manuscript presents the development of an attribute control chart (ACC) designed to monitor the number of defective items in manufacturing processes. The charts are specifically tailored using time-truncated life test (TTLT) for two lifetime data distributions: the half-normal distribution (HND) and the half-exponential power distribution (HEPD) under a repetitive sampling scheme (RSS). To assess the effectiveness of the proposed control charts, both in-control (IC) and out-of-control (OOC) scenarios are considered by deriving the average run length (ARL). Various factors, including sample sizes, control coefficients, and truncated constants for shifted phases, are taken into account to evaluate the performance of the charts in terms of ARL. The behavior of ARLs is analyzed in the shifted process by introducing shifts in its parameters. The superiority of the HEPD-based chart is highlighted by comparing it with both the HND-based ACC and the ACC based on the Exponential distribution (ED) under TTLT using RSS. The results showcase the superior performance of the proposed HEPD-based chart, indicated by smaller ARL values. Additionally, the benefits of another proposed ACC using HND are compared with the ED-based ACC under RSS, further confirming the effectiveness of the HND-based approach through smaller ARLs Finally, the proposed control charts are evaluated through simulation testing and real-life implementation, emphasizing their practical applicability in real-world manufacturing settings.

Comparing the sequential and the repetitive Cpk sampling plans

AbstractThe index Cpk was created to quantify the ability of the process to produce products within the upper and lower specified limits (USL/LSL); but in the last two decades, the sample estimator of the capability index Cpk has also been used to decide whether a lot should be accepted or not; if the value of a sample of size n, randomly taken from the lot, is lower/larger than a threshold, then the lot is rejected/accepted. The sampling plan based on the value is known as the Cpk sampling plan. In recent publications, the Cpk sampling plan has been combined with the repetitive sampling scheme. In short, with the repetitive sampling scheme the Cpk sampling plan might be applied m times, consequently, the lot has m chances to be accepted; if the Cpk sampling plan is applied m times and the lot is not accepted, then the lot is finally rejected. The average number of inspected items per lot (ANI) the repetitive Cpk sampling plan (where m > 1) requires to decide whether the lot should be accepted or not is larger than the sample size n of the standard Cpk sampling plan (where m = 1), because of that the repetitive sampling strategy is not recommended. In this article, we propose the sequential Cpk sampling plan where the is compared with two thresholds (c1; c2) with c1 < c2; if the is lower (larger) than c1 (c2), then the lot is rejected (accepted); otherwise, the decision is left to the next sample. The ANI of the sequential Cpk sampling plan is a function of c1 and c2; depending on the choice of these two design parameters, the ANI of the sequential Cpk sampling plan is substantially lower than the sample size n of the standard Cpk sampling plan.

Enhanced Dispersion Monitoring Structures Based on Modified Successive Sampling: Application to Fertilizer Production Process

In this era of Industry 4.0, efficient and affordable monitoring solutions are needed for the surveillance of manufacturing/service operations. In general, memory-type control charts outperform memoryless control charts when it comes to determining the changes in location and dispersion parameters of symmetrically distributed processes. Before monitoring the process location, it is essential to monitor the process dispersion, since the latter presumes that the process variance remains stable. In practice, the modified successive sampling (MSS) mechanism is preferred over simple random sampling for its cost-effectiveness and efficiency. This study was designed in order to propose moving average and double moving average control charts based on the MSS mechanism for monitoring the dispersion parameter. The performance of the proposed charts is evaluated using run-length measures, and a comparison is made with an existing control chart based on MSS and repetitive sampling. Furthermore, the application of the designed moving and double moving average charts is demonstrated using a case study related to fertilizer production. It is observed that the proposed double moving average control chart performs better than the other control charts designed under the MSS and repetitive sampling schemes.

A New Hybrid Exponentially Weighted Moving Average Control Chart with Repetitive Sampling for Monitoring the Coefficient of Variation

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length.

On designing TEWMA-Tukey control charts for normal and non-normal processes using single and repetitive sampling schemes

Technology advancement and the need to produce quality products have necessitated the development of more efficient process monitoring schemes. In the form of a combined triple EWMA (TEWMA) and Tukey control chart (TCC), this study is an analogous attempt to develop a better charting framework for normal and non-normal data using single and repetitive schemes. The proposed and competing charts are compared based on average run length, standard deviation of the run length and median run length criteria under both zero-state and steady-state conditions. The proposed charts display dominance in detecting mean shifts in both directions not only for symmetric distributions but they are also robust for skewed distributions in that they are devoid of the average run length biased problem. The proposed charts beat the Tukey and Shewhart charts under the repetitive scheme. The TEWMA-TCC under the repetitive scheme has emerged as the best chart under all distributional setups. The steady-state findings of the TEWMA-TCC and its repetitive variant are as beneficial as those of the zero-state results, if not more. A practical application for the proposed designs in the surveillance of industrial production index data in the aerospace manufacturing is illustrated. The proposed charts issue more and earlier signals in the Phase-II process compared with their existing counterparts, most notably the two Tukey charts, i.e. the TCC and EWMA-TCC. Hence, quality and industrial engineers can rely on the proposed charts in process monitoring.

The effect of parameters estimation on the performance of variables control charts under repetitive sampling

The repetitive sampling scheme is utilized in control charts to enhance their detection ability in process shifts. Their performance is usually evaluated under the assumption that the process parameters are known. In this article, we investigate the performance of the and S 2 charts under repetitive sampling when the process parameters are estimated from a preliminary in-control (Phase I) sample. We also present the exact expressions of the average run-length (ARL), standard deviation of run-length (SDRL) and average sample number (ASN) measures. A numerical analysis demonstrates that the effect of parameters estimation is significant when the Phase I sample and the sample size are small.

Designing of control chart of extended EWMA statistic using repetitive sampling scheme

In this paper, we propose extended exponential weighted moving average (EEWMA) control chart (CC) for the surveillance the process mean using repetitive sampling scheme under the assumption that quality characteristic of a product is a quantitative variable following the normal distribution. Two control limits named as inner and outer control limits of the proposed CC are derived using the in-control process mean and variance. The necessary measures are derived to obtain the process in-control and out-of-control average run length (ARL) and tabulated for different process shifts and smoothing constants. Comparisons are made to check the capability of intended CC with the EEWMA CC and repetitive EWMA CC in term of ARL. It has been observed that the presented CC shows better results in term of early detection of divergence in process mean. A simulation study is carried out to illustrate the performance of the proposed CC. An industrial example has been incorporated for its practical purpose.

Monitoring customer complaints using the repetitive sampling

A new control chart for a service performance index based upon the proportion of customer complaints using the repetitive sampling scheme is proposed. The control chart coefficients have been estimated for different parametric combinations using different levels of the performance index. The performance of the new control chart is evaluated on the basis of the average run length (ARL) for in-control and shifted processes. A simulation study for estimating three parameters of the proposed control chart is carried out in order to see the performance of the proposed methodology. The proposed control chart performs better than the existing chart in terms of the ARLs. A real-world example from industry has been included for the practical application of the proposed control chart.

Impact of Different Repetitive Sampling Schemes on the Performance of X-bar Control Chart

Repetitive sampling has been found very popular in improving the control chart techniques for last couple of years. In repetitive sampling based control charts, there are two additional control limits inside the usual upper control limit (UCL) and lower control limit (LCL). If any subgroup crosses these limits but remain inside outer limits, it is deferred and replaced with another selection. Process is said to be out of control if any subgroup falls outside UCL/LCL. In this article, the technique has been modified by introducing a relation between outer and inner control limits in terms of a ratio and need of this modification has also been justified by highlighting a gap in the existing technique. By using Monte Carlo simulation, several results have been generated relevant to different sample sizes and introduced ratios. The results have been described with the help of average run length (ARL) tables that how the efficiency of control chart is effected by using different ratios. The modification in the technique also provides variety of alternatives within the scope of repetitive based control charts. All the discussed options have summarized to one table to see that how the control limits under this technique behave and impact on detecting shifts in the process average. The schemes have been interpreted in the light of above ratio and their comparison has been described under different sample sizes that facilitate the user to select most appropriate scheme for a desired process control. An example has been included by choosing one of the proposed schemes to show the application and performance of the proposed control chart in a manufacturing process.

A control chart for monitoring the lognormal process variation using repetitive sampling

AbstractControl charts are developed to make the specific quality measures for a successful production process and follow normal distribution behaviors. But some real‐life practices do not match such practices and exhibit some positively skewed behavior like lognormal distribution. The present study has considered this situation and proposed a monitoring control chart based on lognormal process variation using a repetitive sampling scheme. This concept proved better for detecting shifts as quickly as possible, and compared with the existing concept, results are elaborated through extensive tables. The average run lengths and standard deviations of the run lengths are being used as a performance evaluation measures and computed by using Monte Carlo simulations performed in R language. A real‐life situation has been discussed in the example section to strengthen the proposed control chart concept in a real‐life situation.

A Nonparametric Repetitive Sampling DEWMA Control Chart Based on Linear Prediction

Distribution-free control charts can be useful in statistical process control (SPC) when only limited or no information about the distribution of the data of the process is available. In this paper, a linear prediction related double exponentially weighted moving average (DEWMA) sign control chart using a repetitive sampling scheme (RSNPDEBLP) has been considered for a binomially distributed process variable to improve the efficiency of detecting small drifts in its place of small changes. The proposed RSNPDEBLP control chart is assessed in average run length (ARL) for the various values of sample sizes. The efficiency of the proposed RSNPDEBLP control chart is compared with the existing EWMA and DEWMA sign control charts using single sampling and repetitive sampling schemes in terms of ARLs. When there are small changes in the process after the stabilization period, the proposed control chart is used to control small trends rather than small shifts.

Optimal truncated repetitive lot inspection with defect rates

• Truncated repetitive test plans based on defect count data are introduced. • Optimal truncated plans outperform the best standard repetitive plans. • Three optimization criteria are adopted and compared in detail. • The corresponding integer nonlinear programming problems are stated and solved. • Step-by-step computational procedures are proposed to solve the optimization problems. Single and repetitive sampling schemes are conventional methods for evaluating the quality of lots or batches of products. Truncation repetitive sampling plans are introduced in this paper in order to significantly reduce the size of samples drawn from the lot. Under this scheme type, if a decision about the acceptance or rejection of the lots cannot be made in the original inspection, they can be reinspected, at most, a prefixed number of times. The Poisson distribution is assumed for the number of defects found in the samples drawn from the lot. Best truncated repetitive sampling plans are determined by solving integer nonlinear programming problems. A simplified methodology is suggested to obtain the plans with optimal inspection effort and controlled risks by using an iterative procedure. According to the results obtained, optimal truncated plans are shown to be better than the optimal single and repetitive schemes in reducing the average sample number of the inspection. An application to the manufacturing of glass is presented for illustrative purposes.

Process Yield Index and Variable Sampling Plans for Autocorrelation Between Nonlinear Profiles

In this paper, a process yield-index for autocorrelation between nonlinear profiles is proposed. Applying a one-dimensional Taylor series expansion, the mean and variance of the estimator of the yield index are derived. To evaluate the performance of the proposed yield index a simulation study is conducted. The new index is employed to design three acceptance sampling plans for quality characteristics described by auto-correlated nonlinear profiles. The first sampling plan is based on resubmission. The remaining two follow the repetitive group and multiple dependent repetitive sampling schemes respectively. For all sampling plans, the operating characteristic function is developed. A non-linear optimization approach with search algorithm is employed to determine the number of profiles required for inspection and to decide critical values for acceptance, rejection, and resubmission criteria. The performance of the new methods is investigated and compared with traditional single sampling plan. The comparison confirms all of the three proposed methods possess higher efficiency than a single sampling plan in terms of sample size. For practical applications tables are provided. Two numerical examples from the automobile engine testing and particleboard manufacturing process are used to demonstrate the applicability of the proposed methods.

New EWMA Control Charts for Monitoring Mean Under Non-normal Processes Using Repetitive Sampling

Control charts in statistical process control are powerful tools for assessing the process stability. The traditional charts perform well under the assumption of normality, but when data violate the assumption of normality, the robust approaches are needed. The aim of the research is to develop exponentially weighted moving average control charts for mean (EWMAM) based on M-scale estimators with in-control variance under non-normal processes using repetitive sampling scheme. Since M-scale estimators are considered as an alternative to standard deviation, the control charts are developed using these estimators. The performance of proposed charts is compared with the traditional EWMAM chart on the basis of out-of-control average run lengths. The application on practical data set is also provided.

Multiple dependent state repetitive sampling plans with or without auxiliary variable

ABSTRACTIn this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.

Magnetic Resonance Fingerprinting with short relaxation intervals

PurposeThe aim of this study was to investigate a technique for improving the performance of Magnetic Resonance Fingerprinting (MRF) in repetitive sampling schemes, in particular for 3D MRF acquisition, by shortening relaxation intervals between MRF pulse train repetitions. Material and methodsA calculation method for MRF dictionaries adapted to short relaxation intervals and non-relaxed initial spin states is presented, based on the concept of stationary fingerprints. The method is applicable to many different k-space sampling schemes in 2D and 3D. For accuracy analysis, T1 and T2 values of a phantom are determined by single-slice Cartesian MRF for different relaxation intervals and are compared with quantitative reference measurements. The relevance of slice profile effects is also investigated in this case. To further illustrate the capabilities of the method, an application to in-vivo spiral 3D MRF measurements is demonstrated. ResultsThe proposed computation method enables accurate parameter estimation even for the shortest relaxation intervals, as investigated for different sampling patterns in 2D and 3D. In 2D Cartesian measurements, we achieved a scan acceleration of more than a factor of two, while maintaining acceptable accuracy: The largest T1 values of a sample set deviated from their reference values by 0.3% (longest relaxation interval) and 2.4% (shortest relaxation interval). The largest T2 values showed systematic deviations of up to 10% for all relaxation intervals, which is discussed. The influence of slice profile effects for multislice acquisition is shown to become increasingly relevant for short relaxation intervals. In 3D spiral measurements, a scan time reduction of 36% was achieved, maintaining the quality of in-vivo T1 and T2 maps. ConclusionsReducing the relaxation interval between MRF sequence repetitions using stationary fingerprint dictionaries is a feasible method to improve the scan efficiency of MRF sequences. The method enables fast implementations of 3D spatially resolved MRF.

A new S2 control chart using repetitive sampling

A new S2 control chart is presented for monitoring the process variance by utilizing a repetitive sampling scheme. The double control limits called inner and outer control limits are proposed, whose coefficients are determined by considering the average run length (ARL) and the average sample number when the process is in control. The proposed control chart is compared with the existing Shewhart S2 control chart in terms of the ARLs. The result shows that the proposed control chart is more efficient than the existing control chart in detecting the process shift.

Designing of X-bar control charts based on process capability index using repetitive sampling

A control chart, being an important tool of statistical process control, has been used for process monitoring and detection of any out-of-control process situation. In this paper, the Shewhart [Formula: see text] chart, also known as the traditional control chart, in combination with the process capability index [Formula: see text] proposed by Subramani and Balamurali, is presented under the repetitive sampling scheme. The optimal design parameters of the proposed control chart are calculated. The performance of the proposed control chart is evaluated through the average run lengths (ARLs). Numerical tables have been constructed for the purpose of comparing the in-control ARL and the out-of-control ARL with the single sampling scheme. The findings of the study show that the newly suggested sampling scheme is better than the existing single sampling scheme in detection of mean shift of the process.

Profiling effects in industrial data mining by non-parametric DOE methods: An application on screening checkweighing systems in packaging operations

There is a growing interest in applying robust techniques for profiling complex processes in industry. In this work, we present an approach for analyzing fractional-factorial data by building distribution-free models suitable for dealing with replicated trials in search of non-linear effects. The technique outlined in this article is synthesized by implementing four key elements: (1) the data collection efficiency of non-linear fractional factorial designs, (2) the data compression capabilities of rank-sums for repetitive sampling schemes, (3) the rank-ordering as a means to transform data, and (4) the non-parametric screening for prominent effects where the normality and sparsity assumptions are waived. The technique is tested on four controlling factors for profiling the packaging weighing operations of a pharmaceutical enterprise. The robust data mining of repeated trials based on an L9(34) orthogonal array scheme with embedded uncontrolled noise is discussed extensively. The technique has been subjected to quality control as it is tested with well-defined artificial data. Concluding remarks involve contrasting this new technique with mainstream competing schemes.