A New Nonparametric EWMA Control Chart for Monitoring Process Variability

Abstract

The exponentially weighted moving average (EWMA) control chart is one of a potentially powerful process monitoring tool of the statistical process control. The EWMA chart has now been widely used because of its excellent ability to detect small to moderate shifts in the process parameter(s). In this study, we propose a new nonparametric/distribution-free EWMA chart for efficiently monitoring the changes in the process variability. We use extensive Monte Carlo simulations to compute the run length profiles of the proposed EWMA chart. For a better performance comparison, the proposed EWMA chart is compared with a recent existing EWMA chart that has already shown to have better performance than the existing control charts. It turns out that the proposed EWMA chart performs substantially and uniformly better than the existing powerful EWMA chart. The working and implementation of the proposed and existing EWMA charts with the help of an illustrative example are also included in this study. The basic concept of a control chart was first introduced by Walter A. Shewhart in the 1920s. Later, this concept laid the foundation of the modern SPC. Presently, the advanced statistical process monitoring techniques include the exponentially weighted moving average (EWMA) and the cumulative sum (CUSUM) control charts. These control charts are quite frequently used in practice because of their sensitive nature to react against the small to moderate persistent shifts in the process parameter(s). This is the main reason why they are frequently employed in the process and service industries where small disturbance may impose serious financial penalties. On the other hand, we have the Shewhart control charts. These control charts are able to detect large shifts more frequently than the EWMA and CUSUM charts. It is interesting to note that the classical Shewhart chart becomes a special case of both the EWMA and CUSUM charts. There are two phases for monitoring the process changes-phases I and II. In phase I, m historical samples, each of size n, are recorded to estimate the unknown process parameter(s) from an in-control process. Having estimated the unknown parameters, the control chart is then designed in phase II to monitor the process.In practice, the aforementioned control charts are implemented with the assumption that the underlying quality characteristic is normally distributed or follows a well-known probability distribution. But, in practice, this assumption does not stand. This necessitates the use of the nonparametric/distribution-free statistics-based control charts. Both the EWMA and the CUSUM control structures based on different nonparametric statistics have also gained the attention of several researchers that has resulted in the development of new nonparametric control charts. For some relevant works in this direction, we refer to Amin et al., 2 Bakir, 3 Khoo and Lim, 4 Yang et al., 5 Yang, 6 Aslam et al., 7 Zhou et al.,8 Riaz and Abbasi, 9 and the references cited therein.Recently, Yang and Arnold 10 suggested a di...

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“…27 EWMA kontrol çizelgelerinin uygulamada sıklıkla kullanılmasının asıl sebebi süreç parametrelerindeki küçük ve orta derecede değişimlere karşı tepki gösterecek hassas özelliklere sahip olmasıdır. 36 meydana gelen küçük ve kalıcı değişimleri tespit etmek için etkilidir. 37 EWMA'nın Gaussian gürültü anlamında bir değişimi belirlemede de diğer yöntemler kadar güçlü olabileceği gösterilmiştir.…”

“…27 EWMA kontrol çizelgelerinin uygulamada sıklıkla kullanılmasının asıl sebebi süreç parametrelerindeki küçük ve orta derecede değişimlere karşı tepki gösterecek hassas özelliklere sahip olmasıdır. 36 Shewhart çizelgesi süreçteki büyük değişimleri tespit etmek için etkilidir. CUSUM ve EWMA çizelgeleri ise süreç ortalaması ve/veya standart sapmasında meydana gelen küçük ve kalıcı değişimleri tespit etmek için etkilidir.…”

“…0 ile 1 arasında ında biriken değişimlerden yararlanarak olarak bu kontrol çizelgesi süreçte meydana EWMA kontrol çizelgelerinin uygulamada metrelerindeki küçük ve orta derecede lere sahip olmasıdır. 36 Shewhart çizelgesi ilidir. CUSUM ve EWMA çizelgeleri ise eydana gelen küçük ve kalıcı değişimleri gürültü anlamında bir değişimi belirlemede terilmiştir.…”

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