In manufacturing environments where the production horizon for a specific product can be limited to a few hours or shifts, statistical process monitoring based on control charts is strategic to cut ...scrap, rework costs, and meet due dates. In this article, a Markov chain model is proposed to design a fully adaptive Shewhart control chart in a process with finite production horizon. The proposed Markov chain model allows the exact computation of several statistical performance metrics, as well as the expected cost of the monitoring and operation process for any adaptive Shewhart control chart with an unknown but finite number of inspections. Illustrative examples show the implementation of the Vp
chart in short runs producing a finite batch of products.
Distribution-free control charts are an efficient quality monitoring tool to inspect lots of parts manufactured within a finite production horizon. In this work, the performance of the Exponentially ...Weighted Moving Average chart based on the Wilcoxon signed rank statistic is investigated for on-line monitoring of finite production runs. The chart's on-target performance is evaluated through a specific non-homogeneous Markov chain model under different process scenarios. A numerical analysis is conducted for determining its optimal design and a performance comparison with other available schemes is presented for different symmetric distributions of observations. Finally, an illustrative example is presented to show a practical implementation of the investigated chart.
In this paper, we present a number‐between‐events (NBE) control chart for monitoring the fraction nonconforming in finite horizon production (FHP) processes and related specific performance measures. ...When monitoring fractions nonconforming in FHP processes, the common binomial p$p$‐chart has two crucial limitations: the underlying distributional assumptions are violated when dealing with low‐volume production and a scarce efficiency in the case of processes characterized by a low fraction nonconforming. Thus, an efficient monitoring of FHP processes requires the selection of the correct underlying statistical model: in this case, a distribution from the hypergeometric family of discrete statistical distributions. An efficient statistical monitoring of processes with low fractions nonconforming can be achieved by means of discrete time‐between‐events (TBE) control charts, which count the number of units up to the appearance of a fixed number of nonconforming units in the sample. Here, we present a discrete TBE‐chart, denoted as NBE‐chart, based on the negative hypergeometric distribution that meets numerous requirements of efficient monitoring of FHP processes. The proposed control chart can be conveniently used for both low‐volume and mass production in processes with frequent changeovers.
This paper proposes an adaptive Shewhart control chart implementing a variable sample size strategy in order to monitor the coefficient of variation. The goals of this paper are as follows: (a) to ...propose an easy-to-use 3-parameter logarithmic transformation for the coefficient of variation in order to handle the variable sample size aspect; (b) to derive the formulas for computing the average run length, the standard deviation run length, and the average sample size and to evaluate the performance of the proposed chart based on these criteria; (c) to present ready-to-use tables with optimal chart parameters minimizing the out-of-control average run length as well as the out-of-control average sample size; and (d) to compare this chart with the fixed sampling rate, variable sampling interval, and synthetic control charts. An example illustrates the use of the variable sample size control chart on real data gathered from a casting process.
► Designing control charts for a short production run is a challenging issue. ► In a short run it is impossible to know a priori the entity of the next shift size for the process mean. ► t Control ...charts are an efficient means to perform SPC during a short run. ► We introduce for the first time the CUSUM t chart. ► We investigate the performance of the Shewhart, EWMA and CUSUM t charts in presence of unknown shift sizes.
Recently, control charts plotting a statistic having a Student’s t distribution have been proposed as an efficient solution to perform Statistical Process Control (SPC) in short production runs where the shift size of the in-control process mean from μ0 to μ1 is known a priori. The shift size is usually measured as a multiple δ of the in-control process standard deviation σ0: but in practice, at the beginning of the production run, both the value of next shift δ and σ0 are unknown. As a consequence, when the actual shift size differs from the value assumed at the chart design stage, the performance of the control chart can be seriously affected. To overcome this problem, this paper investigates the statistical performance of the Shewhart, EWMA and CUSUM t charts for short production runs when the shift size is unknown and modeled by means of a statistical distribution. An extensive numerical analysis allows the properties of the three charts to be compared and discussed when uniform and triangular distributions are used by quality practitioners to fit the unknown shift size. An illustrative example is utilized to demonstrate a practical implementation of the best performing among the three investigated charts.
Continuous surveillance of the ratio of population means of bivariate normal distributions is a quality control issue worth of consideration in several manufacturing and service-oriented companies. ...For this reason, some recent studies have investigated traditional and advanced Shewhart control charts to perform on-line monitoring of this kind of ratio. Anyway, Shewhart control charts are known to be insensitive to small and moderate shift sizes. Up to now, CUSUM control charts have not yet been considered for this quality control problem. In this paper, we propose and investigate the statistical properties of two Phase II one-sided CUSUM control charts for monitoring the ratio of population means of a bivariate normal distribution. Several figures and tables are provided to show the sensitivity of the two CUSUM charts to different deterministic shift sizes and their performance for the random shift size condition. In most cases, the numerical results demonstrate that the proposed CUSUM control charts are very sensitive to shifts in the ratio. An illustrative example comments the use of these charts in a simulated quality control problem from the food industry.
In quality control applications, the control chart is a powerful tool but its performance is adversely affected by the contamination from either the inspector or the measuring device leading to ...measurement errors. In this paper, we investigate the performance of the AEWMA median chart with measurement errors, and a methodology is proposed to obtain the optimal parameters by considering a linearly covariate error model. Several figures and tables show that, with the existence of measurement errors, the efficiency of the AEWMA median chart can be strongly affected, but this negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the Shewhart and the classical EWMA schemes confirm the superiority of the AEWMA scheme for detecting a wide range of shifts in the case of precise and imprecise data. An example is provided to illustrate the use of the AEWMA median chart with measurement errors.
The usual practice in Statistical Process Monitoring (SPM) techniques assumes that the data distribution is known and the related parameters are accurately estimated. In practice, the underlying ...distribution and its parameters are rarely known, and control charts need to be constructed with parameters being estimated. Such issues have recently received an increasing attention in evaluating the properties of both parametric and nonparametric charts. However, the same study is seldom conducted for the control charts based on the data‐driven tools. In this paper, we investigated the in‐control performance of a nonparametric control chart based on the Support Vector Data Description (SVDD) theory. More specifically, we discuss the conditional effect of the training Phase‐I samples on the Phase‐II efficiency when different distributions are considered. Simulation results show that the conditional performance of the SVDD‐based chart can be strongly affected by the Phase‐I samples. It this situation, adjusted control limits with a specific number of available training sample is suggested.
