Layth C. Alwan

Effects of autocorrelation on control chart performance

In this article, we study the capability of the standard control chart for individual observations with fixed control limits to identify special causes reflected as isolated extreme points in the presence of autocorrelation. We consider both the application of standard Shewhart limits and moving-range limits and derive the risks of false positive and false negative when the control chart observations follow a general ARMA(p,q) process.

The Problem of Misplaced Control Limits

The paper draws on simple data analysis and time series ideas to assess the limitations of standard control chart procedures in various practical applications in which the underlying assumptions of control charts may be materially violated and, in consequence, the control limits may be misplaced. To give an idea of the kinds and frequency of violations that occur in practice, we summarize an empirical study of a sample of 235 quality control applications. This collection includes two data sets reported by leading statisticians that are explicitly discussed here to illustrate difficulties in the proper placement of control limits. The results of the study of all 235 data sets suggest that violations of assumptions are the rule rather than the exception in practice.

TIME-SERIES INVESTIGATION OF SUBSAMPLE MEAN CHARTS

Abstract Autocorrelation of quality-control measurements violates one of the basic assumptions underlying the use of statistical control charts for process mean. Several investigators have studied the impact of autocorrelation on charting procedures based on single observations, however, little work has been directed to charts with subsampling. This paper examines different properties of the subsample means in the presence of autocorrelation. Specifically, using aggregation and systematic sampling theory, we show the time-series behavior of the subsample means. We also investigate the Type I error rate for the X¯ chart and present recommendations for statistical process control in the presence of autocorrelation. Our investigation of the Type I error provides additional insights of the impact of autocorrelation on the subsample range statistic.

Information theoretic framework for process control

Abstract This paper proposes a general framework for constructing control charts based on information theory. The potential applications include developing information charts , for monitoring moments and distributions of a process variable and process attributes. In information theoretic process control (ITPC), process moments are mapped to process distributions at in-control and monitoring states, and then to a control function via constrained maximization of entropy and minimization of Kullback–Leibler function (cross-entropy). Variants of information charts can be developed without using distributional assumptions and based on a single criterion function, the information discrepancy between two distributions . An example of an information chart, Information mean-variance chart, IMV-chart , for monitoring process mean and variance is developed. The IMV-chart combines the standard x -chart and s 2 -chart, and provides an information theoretic explication of the traditional procedures. Based on a run-length study, it is found that the IMV-chart singly possesses certain advantages over the standard two-chart implementation of x -chart and s 2 -chart. Multivariate extension, monitoring counts and proportions, and monitoring distributional changes are briefly discussed.

Forecast facilitated lot-for-lot ordering in the presence of autocorrelated demand

With consistent effort in setup reduction as encouraged by JIT principle, lot-for-lot ordering is gaining popularity in MRP applications. A lot-for-lot order is an immediate copy of the MPS (master production schedule) - direct reflection of demand forecasts. Since all levels of MRP plans are based on MPS, the accuracy of MRP is highly dependent of the accuracy of demand forecasting. In this paper, we are concerned about the impact of forecasting to the performance of a lot-for-lot MRP system when there is notable variability and autocorrelation in the underlying demand process (e.g., an AR(1) process). Specifically under a stationary AR(1) demand, we examine the performance of the MRP based on the most common EWMA forecast model, and then compare it with a minimum mean square error (MSE) forecast model. The notable findings of this study include: (1) MRP performance differs noticeably under the two different forecasting models. (2) The MSE-optimal forecasting performs no worse than the EWMA forecasting in all aspects of MRP applications.

The Dynamic Newsvendor Model with Correlated Demand

The classic newsvendor model was developed under the assumption that period-to-period demand is independent over time. In real-life applications, the notion of independent demand is often challenged. In this article, we examine the newsvendor model in the presence of correlated demands. Specifically under a stationary AR(1) demand, we study the performance of the traditional newsvendor implementation versus a dynamic forecast-based implementation. We demonstrate theoretically that implementing a minimum mean square error (MSE) forecast model will always have improved performance relative to the traditional implementation in terms of cost savings. In light of the widespread usage of all-purpose models like the moving-average method and exponential smoothing method, we compare the performance of these popular alternative forecasting methods against both the MSE-optimal implementation and the traditional newsvendor implementation. If only alternative forecasting methods are being considered, we find that under certain conditions it is best to ignore the correlation and opt out of forecasting and to simply implement the traditional newsvendor model.

Study of average run lengths for supplementary runs rules in the presence of autocorrelation

The basic assumption underlying statistical control chart criteria is that the process measurements are independent and identically distributed over time. However, autocorrelation and other time-series effects occur frequently in application. In this paper, the effects of autocorrelation are investigated for the frequently advocated supplementary runs rules. For both individual control charts based on the moving range and sample standard deviation, using simulation, the impact of autocorrelation for the AR(1) on in-control average run lengths is given.

Designing an effective exponential cusum chart without the use of nomographs

The development of control charts for monitoring processes associated with very low rates of nonconformities is increasingly becoming more important as manufacturing processes become more capable. Since the rate of nonconformities can typically be modeled by a simple homogeneous Poisson process, the perspective of monitoring the interarrival times using the exponential distribution becomes an alternative. Gan (1994) developed a CUSUM-based approach for monitoring the exponential mean. In this paper, we propose an alternative CUSUM-based approach based on its ease of implementation. We also provide a study of the relative performance of the two approaches.

Option Contracts: A Solution for Overloading Problems in the Delivery Service Supply Chain

Owing to the limited service capacity of express delivery providers, most online retailers have to reject many orders during hot selling seasons. In this paper, we consider an express delivery service supply chain consisting of an express delivery provider and an online retailer whereby the selling season includes both regular periods and online sales periods. Utilizing a modified newsvendor model, we derive the express delivery provider’s optimal capacity decision and find that the overloading problem cannot be avoided because delivery service cannot be inventoried. To solve such a problem, we introduce an option contract to coordinate the supply chain. By allowing the online retailer to book the capacity, the express delivery provider can rent capacity from a third party in advance. Results show this approach can mitigate the problem significantly. We also extend our model to a supply chain consisting of a delivery provider and two retailers.

Detecting Variance Reductions Using the Moving Range

For individual measurements, the standard chart for monitoring process variance is the moving-range chart. Although certain deficiencies of this chart have been mentioned, little research has been done to assess formally its capabilities or to resolve a..