Design Of Charts Research Articles

Adaptive data collection for intraindividual studies affected by adherence.

Recently, the use of mobile technologies in ecological momentary assessments (EMAs) and interventions has made it easier to collect data suitable for intraindividual variability studies in the medical field. Nevertheless, especially when self-reports are used during the data collection process, there are difficulties in balancing data quality and the burden placed on the subject. In this paper, we address this problem for a specific EMA setting that aims to submit a demanding task to subjects at high/low values of a self-reported variable. We adopt a dynamic approach inspired by control chart methods and design optimization techniques to obtain an EMA triggering mechanism for data collection that considers both the individual variability of the self-reported variable and of the adherence. We test the algorithm in both a simulation setting and with real, large-scale data from a tinnitus longitudinal study. A Wilcoxon signed rank test shows that the algorithm tends to have both a higher F1 score and utility than a random schedule and a rule-based algorithm with static thresholds, which are the current state-of-the-art approaches. In conclusion, the algorithm is proven effective in balancing data quality and the burden placed on the participants, especially in studies where data collection is impacted byadherence.

Agreement between Lea Symbols and Patti Pics visual acuity in children and adults

BackgroundPatti Pics (PP) and Lea Symbols (LS) are commonly used by eye care practitioners worldwide. Although the relationship between the two tests is fairly well understood, the availability of different chart designs (single optotypes, multiple optotypes, multiple optotypes with crowding box) merits futher understanding. The purpose of this study is to explore the agreement between the acuity measures obtained with Patti Pics and Lea Symbols in children and adults and compare their performance with the Sloan Letter (SL) chart in adults. MethodsMonocular visual acuity was obtained from ninety-three 3 to 5-year-old children using Patti Pics and Lea Symbols. Acuities were also obtained from 113 adults using the same tests under identical conditions. Acuity results obtained with the pediatric tests were compared with the gold-standard Sloan Letter chart in adults. The Bland-Altman method was implemented to compare the level of agreement between tests. ResultsPatti Pics yielded worse visual acuity than the Lea Symbols by approximately half a logMAR line in both children (mean difference: -0.07 ± 0.07 logMAR, p <0.01) and adults (Mean difference: -0.05 ± 0.06 logMAR, p <0.01). The 95% limits of agreement between Lea Symbol acuity and Patti pics acuity in children was ± 0.14 logMAR. Mean difference between the Sloan Letter chart and Lea Symbols acuity was not statistically significant (p = 0.08) in adults but the difference was statistically significant between PP and SL (p<0.001). The 95% limits of agreement between LS and SL and between PP and SL was ± 0.19 logMAR and ± 0.22 logMAR, respectively. ConclusionPatti Pics consistently underestimated visual acuity as compared to Lea Symbols both in children and adults although the differences were not clinically significant. The LS and PP did not yield clinically significant differences in acuities when compared with Sloan letters in adults.

Double-objective economic statistical design of () control chart using Linex loss function

PurposeThe purpose of this paper is to develop a double-objective economic statistical design (ESD) of () control chart under Weibull failure properties with the Linex asymmetric loss function. The authors have expressed the probability of type II error (β) as the statistical objective and the expected cost as the economic objective.Design/methodology/approachThe design used in this study is based on a double-objective economic statistical design of () control chart with Weibull shock model via applying Banerjee and Rahim's model for non-uniform and uniform schemes with Linex asymmetric loss function. The results in the least average cost and β in uniform and non-uniform schemes by Linex loss function, compared with the same schemes without loss function.FindingsNumerical results indicate that it is not possible to reduce the second type of error and costs at the same time, which means that by reducing the second type of error, the cost increases, and by reducing the cost, the second type of error increases, both of which are very important. Obtained based on the needs of the industry and which one has more priority has the right to choose. These designs define a Pareto optimal front of solutions that increase the flexibility and adaptability of the control chart in practice. When the authors use non-uniform schemes instead of uniform schemes, the average cost per unit time decreases by an average and when the authors apply loss function, the average cost per unit time increases by an average. Also, this quantity for double-objective schemes with loss function compared to without loss function schemes in cases uniform and non-uniform increases. The reason for this result is that the model underestimated the costs before using the loss function.Practical implicationsThis research adds to the body of knowledge related to flexibility in process quality control. This article may be of interest to quality systems experts in factories where the choice between cost reduction and statistical factor reduction can affect the production process.Originality/valueThe cost functions for double-objective uniform and non-uniform sampling schemes with the Weibull shock model based on the Linex loss function are presented for the first time.

Economic–statistical design of Bayesian control chart based on the predictive distribution

PurposeThe purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian control chart based on predictive distribution with two types of informative and noninformative prior distributions.Design/methodology/approachThe design used in this study is based on determining the control chart of the predictive distribution and then its ESD. The new proposed cost model is presented by considering the conjugate and Jeffrey's prior distribution in calculating the expected total cycle time and expected cost per cycle, and finally, the optimal design parameters and related costs are compared with the fixed ratio sampling (FRS) mode.FindingsNumerical results show decreases in costs in this Bayesian approach with both Jeffrey's and conjugate prior distribution compared to the FRS mode. This result shows that the Bayesian approach which is based on predictive density works better than the classical approach. Also, for the Bayesian approach, however, there is no significant difference between the results of using Jeffrey's and conjugate prior distributions. Using sensitivity analysis, the effect of cost parameters and shock model parameters and deviation from the mean on the optimal values of design parameters and related costs have been investigated and discussed.Practical implicationsThis research adds to the body of knowledge related to quality control of process monitoring systems. This paper may be of particular interest to quality system practitioners for whom the effect of the prior distribution of parameters on the quality characteristic distribution is important.Originality/valueeconomic statistical design (ESD) of Bayesian control charts based on predictive distribution is presented for the first time.

Nonparametric Control Charts for Monitoring Serial Dependence based on Ordinal Patterns

We consider the problem of monitoring for the existence of serial dependence in real-valued and continuously distributed processes. These can exist when a process goes out-of-control. Besides, as many control charts are designed under the assumption of independent and identically distributed observations, the validity of this assumption needs to be checked. In the literature, the majority of studies handled this problem by using a specific case of autoregressive moving-average time series models. Also a moving-window approach is often considered, which leads to the drawback that at least a window length of observations need to be collected before an out-of-control situation can be detected. Here, we use ordinal patterns and propose charts that are fully nonparametric and distribution-free, have a unique chart design, and can be used almost instantaneously at the start of process monitoring. The proposed control charts do not require any model fitting, thus, eliminating the problems associated with estimation errors, but might be used as part of a Phase-I study. Through a comprehensive performance comparison study under various out-of-control scenarios, the effectiveness of the charts in uncovering serial dependence is shown and recommendations for selection are given. Implementations of the proposed charts are illustrated by using batch yield data from a chemical process.

An integrated Markov chain model for the economic-statistical design of adaptive multivariate control charts and maintenance planning

An integrated Markov chain model for the economic-statistical design of adaptive multivariate control charts and maintenance planning

EWMA Control Chart for Rayleigh Process With Engineering Applications

Process monitoring is typically performed with quality control charts. The normality assumption is often taken into consideration for the development of control charts. However, this assumption may not hold in many real-life situations. One such circumstance is utilizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {V}_{\mathrm {SQR}}$ </tex-math></inline-formula> chart to track the process variability of Rayleigh distributed processes. The structure of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {V}_{\mathrm {SQR}}$ </tex-math></inline-formula> chart follows the basic design of the Shewhart-type chart, which is not sensitive mainly for smaller to moderate shifts in monitoring parameter. In this paper, an enhanced approach, namely Rayleigh exponential weighted moving average (REWMA) is introduced. The suggested REWMA scheme aims to significantly improve the detection capabilities of the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {V}_{\mathrm {SQR}}$ </tex-math></inline-formula> chart. Designated limits, along with charting parameters, are evaluated for different sample sizes. The effectiveness of the suggested REWMA control chart is assessed in terms of run length distributional parameters. Moreover, the Monte Carlo simulations are made to compare the run length properties of the proposed REWMA chart with the existing competitor design. The comparative assessment demonstrates that the suggested offers a considerable enhancement relative to the competing design. An application of the REWMA chart on simulated data also reveals that the proposed chart is highly sensitive to smaller and persistent shifts in the scaling parameter of Rayleigh distribution. Finally, an example from real-life has been presented to illustrate the importance of the suggested chart.

Design of Risk-Based Univariate Control Charts With Measurement Uncertainty

Design of Risk-Based Univariate Control Charts With Measurement Uncertainty

An integrated Markov chain model for the economic-statistical design of adaptive multivariate control charts and maintenance planning

An integrated Markov chain model for the economic-statistical design of adaptive multivariate control charts and maintenance planning

EWMA control chart using Bayesian approach under paired ranked set sampling schemes: An application to reliability engineering

&lt;abstract&gt; &lt;p&gt;Control charts are widely used to efficiently detect small to moderate shifts and they include exponentially moving average control charts, named memory type control charts. Today, memory type control charts are a significant tool to assure quality standards and monitor manufacturing goods. The proposed study suggests a novel Bayesian exponentially weighted moving average (EWMA) control chart design utilizing various pair ranked set sampling schemes for posterior and posterior predictive distributions given an informative prior. The proposed chart strategy is evaluated in terms of the small run length characteristic by using Monte Carlo simulation methods. The comparative analysis is also carried out by using a Bayesian EWMA control chart to apply simple random sampling for the respective average and standard deviation of the run length values in the both control chart designs. The results revealed efficient and rapid detection of shifts in process means which proves the success and superiority of the suggested design. A real-life data sets is used to elaborate the efficient application of the suggested Bay-EWMA-PRSS control chart design. The overall research findings support the theoretical and simulation results, which are provided in the form of extensive tables.&lt;/p&gt; &lt;/abstract&gt;

Aplication Development and It’s Aplicated in Yasmin Store of Buton Sentral Distric

The increasingly rapid development of technology has a real impact on changes in various sectors, not least in the marketing sector, especially in the recording of business transactions. Based on the results of initial field observations, it was found that the Yasmin Store still uses manual recording, this is what underlies the implementation of abdimas activities in the form of developing a sales information system application and its application to the Yasmin Store so that this application can provide real benefits in terms of recording business transactions. Sales information system application designed in the form of a flow chart and user interface program design so as to form a complete system component that is incorporated in the sales application according to user needs. The program interface design is made user friendly so that user actors can easily operate the application. Methods of implementing activities include: 1) Needs analysis; 2) Application design; 3) Feasibility test; 4) Testing/Implementation; 5) Application of sales information system application; 6) Evaluation and 7) Reporting on the results of activities. The benefits of using this application include making it easier for users to check: 1) stock of goods on a regular basis; 2) customer data reports 3) supplier data reports and check sales and purchase recapitulation reports per day, month, or year. The final result expected in this activity is that the user is able to operate and use the sales information system application permanently.

Alternative Design of One-Sided Shewhart Control Charts for the Multivariate Coefficient of Variation

The control charting technique is an approach to quality control and was implemented in various industries. There are many control charts, where the coefficient of variation control chart was one of the common charts and greatly used in Statistical Process Control. Since most processes are multivariate, the multivariate coefficient of variation charts has received great attention in the past few years. However, the existing multivariate coefficient of variation control charts was evaluated in terms of the average run length criterion, which may misinterpret the actual performance of the charts. This paper designs an alternative for the Shewhart multivariate coefficient of variation chart by considering the median run length and expected median run-length criteria to circumvent this problem. The research on the multivariate coefficient of variation chart is very limited in the existing literature by considering the median run length criterion. This proposed chart in this paper can minimize this research gap. The formulas and algorithms of the proposed chart are presented. The outputs of the proposed charts are shown by examining the different upward and downward process shifts. Additionally, the sample sizes, the process shifts, and the variation of the run-length distribution are investigated for their effects on the proposed chart. The findings reveal that the run-length distribution’s variation is inversely proportional to the shift size. Furthermore, it shows that the variation decreases if the shift size increases.

A study on inspection schemes in optimal design of control charts for deteriorating processes

A study on inspection schemes in optimal design of control charts for deteriorating processes

On designing an optimal SPRT control chart with estimated process parameters under guaranteed in-control performance

Being one of the most sophisticated control charts, the sequential probability ratio test (SPRT) chart possesses fast detection ability across a broad range of process shifts. The SPRT chart has the advantage of sampling only a modest number of observations. Thus far, the SPRT chart has been developed under the assumption that the process parameters are known. As process parameters are often unknown in practice, this article reveals that parameter estimation from a limited amount of Phase-I data, leads to excessive false alarms and unstable chart’s performances. To counter these problems, this article advocates the use of adjusted control limits to ensure that a sufficiently high proportion of the in-control conditional average time to signal value, is greater than a pre-specified level. This increasingly prevalent design of control charts is known as Guaranteed In-Control Performance (GICP). In this article, we propose an optimization design for the SPRT chart with estimated process parameters, by minimizing the expected value of the average extra quadratic loss under the GICP framework. Theoretical derivations by means of the Markov chain approach are developed in this article to evaluate the run-length properties of the SPRT chart with estimated process parameters. Results show that the overall performance of the proposed optimal SPRT chart is almost twice as good as the optimal CUSUM chart over a given range of process mean shifts. Finally, an implementation of the proposed optimal SPRT chart is demonstrated with real industrial data obtained from an epitaxial process.

Design of Shewhart-type control charts with estimated parameter for the Rayleigh distribution using frequentist and Bayesian approaches

ABSTRACT Studies on control charts with estimated parameters have received much attention in the recent literature. In this paper, the effect of parameter estimation on the performance of the Shewhart-type chart for the Rayleigh distribution, namely the chart, is first studied under the conditional perspective. It is found that parameter estimation has a serious effect on the performance of the frequentist chart. In order to solve this problem, the frequentist chart is adjusted by using the exceedance probability criterion to guarantee the in-control performance. Since the frequentist chart uses the sample information from Phase I, but not the process information from past experience, an alternative chart, namely the Bayesian chart, is proposed based on the predictive distribution of the plotting statistic. The performances of the Bayesian and adjusted frequentist charts are evaluated and compared in terms of the percentiles, mean, and standard deviation of the conditional average run length distribution. The results suggest that the Bayesian chart outperforms the frequentist counterpart, especially when more prior information is available.

Optimized np Attribute Control Chart Using Triple Sampling

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (ARL1). Tables of ARL1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of ARL1 detecting small and moderate shifts in the process nonconforming rate in-control (p0) compared with MDSRS and DS-np.

Monitoring count time series: Robustness to nonlinearity when linear models are utilized

AbstractLinear models are typically utilized for time series analysis as these are often simple to implement and interpret, as well as being useful in modeling many practical phenomena. Hence, most of the literature on control charts for monitoring time series also consider linearity of the data generating processes (DGP). In practice, however, a nonlinear DGP can be modeled as if it is linear, either due to overlook or illusion, when it is approximately linear. This study quantifies the effects of nonlinear DGPs, misspecified and modeled as linear, on the performance of Shewhart‐type and cumulative sum (CUSUM) control charts for count time series data. Time series models for bounded and unbounded counts with several parametrizations are considered for studying the sensitivity of linear approximations to nonlinear DGPs. The Markov chain (MC) approach and simulations are used to compute the average run length (ARL) performance of the control charts. Robustness of the performance is evaluated with respect to the extent that the DGP violates linearity, with and without errors in parameter estimation. It is shown that the chart designs are, in general, robust to model misspecification when the parameters are specified. However, the CUSUM performance can be affected significantly if both the model is misspecified and the parameters are estimated. Real‐world data implementations are provided to illustrate the sensitivity of the control charts' performances to the type of model and to the estimation approach.

Optimal statistical design of the double sampling np chart based on expected median run length

Double sampling (DS) control charts are widely regarded as an effective process monitoring tool owing to their remarkable properties, such as the ability to detect small and moderate process shifts efficiently with the reduced sample size. Since the shape of the run length distribution is highly right-skewed for the process small shift size and becomes almost symmetric when the process shift size is large, the use of median run length (MRL) as a performance measure is therefore more representative. Existing works on the DS np chart construction were performed by taking an approach that the shift size of the process fraction nonconforming is assumed to be known. However, the shift size of the fraction nonconforming is usually unknown by the quality practitioners in practice. Herein, to address this issue, the expected median run length (EMRL) has been suggested as a performance measure for the unknown shift size. This paper suggests an optimal design procedure for the DS np chart based on the EMRL criterion. An example is provided to illustrate the construction of the EMRL-based DS np chart. The DS np chart is compared with a competing chart based on the EMRL criterion. Findings obtained reveal that when the shift size is unknown, the EMRL is an alternative performance measure for the DS np chart, with greater sensitivity observed for the DS np chart in contrast to the standard np chart for detecting a wide range of shifts.

A production-inventory model under quality-maintenance policy with rework process in the presence of random failures and multiple assignable causes

ABSTRACT This research presents simultaneous design of production planning, maintenance strategy and control chart in which two issues are considered: (1) multiple assignable cause and (2) equipment failure. The first one means that various factors may shift the process to an out-of-control state; while the second one means that the equipment is not always available and may be suddenly failed. Also, to reduce the production costs, a rework process is performed on the nonconforming items right after the regular cycle. Furthermore, three types of maintenance activities are applied based on system conditions. The corrective maintenance is conducted when the equipment failure occurs. The preventive maintenance is accomplished when the process continues until the end of the cycle, and the predictive maintenance is performed whereas the chart issues a true alarm. To check the effectiveness of the model, three comparative studies are examined. The first one compares the suggested model with a similar model without the rework process; the second one demonstrates the importance of employing the statistical process monitoring; and the last one compares the model with a similar model without considering the equipment failure. The results show the superiority of the integrated model compared to the others in the cost-saving.

Joint design of control chart and maintenance policy under multiple assignable causes and random failures by considering the statistical constraints

ABSTRACT In modern industries, statistical process monitoring (SPM) and maintenance management are extensively employed to increase the production rate of conforming items. Aiming at minimizing the expected total cost per time unit subject to some statistical constraints, this study proposes a hybrid quality-maintenance model for imperfect short-run process. To bring the proposed model closer to real short-run systems, it is considered that the process mean may shift to an out-of-control condition due to occurrence of several types of assignable causes. Furthermore, it is supposed that the time-to-failure follows a non-homogenous Poisson process implying that the system may suddenly fail with an increasing failure rate function. Moreover, a non-uniform sampling scheme is developed in order to improve the system reliability. Finally, the main advantages of the proposed model are highlighted by conducting two comparative studies. The first one illustrates the efficiency of the non-uniform sampling scheme in increasing the in-control time interval and decreasing the expected total cost. The second one confirms the importance of considering the system failure on both the expected total cost and in-control time interval.