Abstract
In quantitative forecasting models and tracking signal methods, input noise is often assumed to be normally and independently distributed. The goal of this research was to study the distribution of tracking signal and build new monitoring schemes for when the input noise distribution is not necessarily normal. A demand process in the Wilson inventory model was simulated using several input noise distributions. The effectiveness of a proposed tracking signal model was evaluated and compared to existing methods using an inventory cost model. It was found that it is not realistic to assume a normal distribution for the tracking signal even when the noise is normal. Because of the dependency of tracking signal elements, and since there is no specific distribution for it, we used simulation to estimate the best value for the standard deviation and suggest ±3 i ii as the control limits. We compared this value with those suggested by other papers, and showed that the proposed limits work better when the process is under control and also when there are different amounts of shifts in mean demand. We also studied different values for the tracking signal smoothing parameter and analyzed the inventory costs for each.
Highlights
The aim of a forecast monitoring system is to monitor how well a system is functioning, to detect “out of control” signals expeditiously, and to provide an unbiased estimate of the forecast error
In this paper we considered different distributions for the input noise and studied the distribution of a tracking signal
We showed that assuming a normal distribution for the tracking signal is not realistic even when the noise is normal
Summary
The aim of a forecast monitoring system is to monitor how well a system is functioning, to detect “out of control” signals expeditiously, and to provide an unbiased estimate of the forecast error. Tracking signal methods have been used as alarm mechanisms to ensure that forecasting systems remain in control, and to detect any abnormalities in a timely manner in order to provide information to decision makers. This allows for appropriate corrective action to be taken so that the forecasting system can be brought back to an “under control” status. Brown [1] was the first to suggest the use of tracking signals, and subsequent researchers such as Trigg continued and expanded upon Brown’s tracking signal method [2]. Deng et al used fuzzy-neural to suggest a new tracking signal [3]
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