Due to advances in technology, sampling procedures and short lag times between successive sampling, autocorrelation among the measured data has become common in most applications. Neglecting ...autocorrelation leads to a poor false alarm performance. In the current paper, the effect of the autocorrelation on the performance of a variable-parameters multivariate single control chart is investigated in the case of the simultaneous monitoring of the mean and variability. At first, formulas for the sample mean and variability of a multivariate autoregressive-moving average process are derived. Then, a variable-parameters single control chart is developed for the simultaneous monitoring of the mean vector and the covariance matrix of an autocorrelated multivariate normal process. Next, the performance of the proposed control chart is evaluated by using eight performance measures based on a dedicated Markov chain model. Finally, by presenting an illustrative example, the application of the proposed scheme is demonstrated in practice.
This paper on replenishment planning for multi-level assembly systems with several components at each level deals with the problem of calculating planned lead-times when the real lead-times for all ...components are assumed to be stochastic. This problem is already treated in the literature by using a recursive procedure and a Branch and Bound algorithm. Here, in order to decrease the computation time, a novel generalized probabilistic model based on an iterative approach is developed. The proposed model calculates the expected total cost, which is composed of the inventory holding cost for components and the backlogging and inventory holding costs for the finished product. An iterative approach and a hybrid genetic algorithm are introduced to determine the planned order release dates for components at the last level of the bill of materials that minimizes the expected total cost. Experimental results show that the proposed optimization algorithm efficiently finds good-quality approximate solutions regardless of the type of assembly system, the number of components at the last level and the variability of the finished product-related costs.
•Studies multi-level assembly systems with a fixed finished product demand and stochastic component lead times.•Develops a generalization of the models introduced in several studies.•Proposes a new efficient mathematical model.•Develops an efficient algorithm to resolve large problems.
•Finite production horizon (FPH) processes allow companies to achieve a high flexibility.•In FPH processes, SPC starts without estimates of the distribution parameters.•We investigate joint control ...charts for monitoring a FPH process.•Non parametric and robust statistics are considered to monitor position and scale.
Small production runs are becoming increasingly important in the manufacturing environment thanks to the technology advancements allowing products to be customized at competitive costs. Similarly, increasing flexibility in high volume production can allow for frequent and rapid changeovers from one part code to another to meet the lean principles. These manufacturing processes are characterized by finite production horizons. To assure high quality standards of products during a finite horizon production, implementing an efficient on-line process monitoring is a critical issue. In this paper we compare the performance of several control charts jointly monitoring location and scale for observations with a location-scale distribution in a finite horizon process where a limited number of inspections is scheduled. For an investigated set of symmetric distributions, our results show that the joint control charts implementing a signed-rank SR statistic and either the Downton’s D estimator or the average absolute deviation MD from median generally perform the best. An example illustrates the implementation of the control charts on a simulated dataset.
The effect of measurement errors on the performance of adaptive control charts has rarely been investigated in the univariate case and, as far as we know, it has not been investigated at all in the ...multivariate case. In this paper, we evaluate the effect of measurement errors on the VSS (Variable Sample Sizes) Hotelling’s T2 control chart. To do so, we suggest using six different performance measures: (i) the average and (ii) the standard deviation of the run length, (iii) the average and (iv) the standard deviation of the number of observations to signal, (v) the average and (vi) the standard deviation of the number of switches to signal. These performance measures should be as small as possible when the process is out-of-control to ensure an optimal chart efficiency. We use two models for defining the objective function which includes at least one of these performance measures. We find the optimal values of the sample sizes and the overall performance measures for each model and for different values of the measurement errors variance, the numbers of measurements and the values of the error model’s constants. Finally, we present an illustrative example to show the application of the proposed method.
A common assumption for most control charts is the fact that the process parameters are supposed to be known or accurately estimated from Phase I samples. But, in practice, this is not a realistic ...assumption and the process parameters are usually estimated from a very limited number of samples that, in addition, may contain some outliers. Recently, a median chart with estimated parameters has been proposed to overcome these issues and it has been investigated in terms of the unconditional Average Run Length (ARL). As this median chart with estimated parameters does not take the “Phase I between‐practitioners” variability into account, in this paper, we suggest to revisit it using the Standard Deviation of the ARL as a measure of performance. The results show that this Standard Deviation of the ARL–based median chart actually requires a much larger amount of Phase I data than previously recommended to sufficiently reduce the variation in the chart performance. Due to the practical limitation of the number of the Phase I data, the bootstrap method is recommended as a good alternative approach to define new dedicated control chart parameters.
Recent literature about quality control has investigated the continuous surveillance of the ratio of two normal random variables under the assumption of no measurement error. However, in practice, ...measurement errors always exist in quality control applications and may considerably affect the performance of control charts. In this paper, the performance of the Shewhart-RZ control chart is investigated in the presence of a measurement error and modelled by a linear covariate error model. Several figures and tables are generated and commented to show the statistical performance of the Shewhart-RZ control chart for different sources of the measurement error. Two examples illustrate the use of this chart on a quality control problem simulated from the food industry and a real industrial case from a plant treating batteries for recyclement.
Abstract
The effect of measurement errors on the performance of multivariate adaptive control charts has not been considered yet. In this article, we investigate the effect of measurement errors on ...the performance of the variable sampling intervals (VSI) Hotelling's
T
2
control chart in the case of known parameters. A linearly covariate error model is used as the measurement error function. In order to measure the chart's performance, we use the average time to signal criterion, which is obtained by using a Markov Chain model. Through a numerical analysis, we evaluate the negative effect of measurement errors on the performance of the VSI Hotelling's
T
2
control chart, and we also investigate the effect of multiple measurements as well as the value of linearly covariate error model's parameters on the main properties of the VSI Hotelling's
T
2
control chart. At last, we present an illustrative example.
The Adaptive Exponentially Weighted Moving Average (AEWMA) chart, which combines the Shewhart and classical EWMA schemes, is usually designed using the Average Run Length (
) as the criterion to be ...optimized. The shape of the run length distribution is known to change according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control or nearly to approximately symmetric when the shift is large. Therefore, the Median Run Length (
) provides a more meaningful interpretation than the
. In this paper, the
is used as an alternative performance criterion, and the AEWMA
chart is optimized for a wide range of mean shifts using zero and steady state modes. Comparative results show that the suggested AEWMA
chart offers a more balanced protection for detecting both small and large shifts in the process mean than the classical EWMA
chart, in terms of the
performance. The construction of the
-based AEWMA
chart is also illustrated using an example, and it is compared with competing charts.
Monitoring the coefficient of variation (CV) is an effective approach to monitor a process when both the process mean and the standard deviation are not constant but, nevertheless, proportional. ...Until now, few contributions have investigated the monitoring of the CV for short production runs. This paper proposes an adaptive Shewhart control chart implementing a variable sample size (VSS) strategy in order to monitor the coefficient of variation in a short production run context. Formulas for the truncated average run length are derived. Moreover, a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV in order to evaluate the performance of each chart in a short run context. An example illustrates the use of this chart on real data.
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