A New Nonparametric Control Chart for Monitoring Variability

Exponentially distributed data are commonly encountered in high‐quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero‐state and steady‐state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice.

“…Step 4: Generate out-of-control random vectors X t = (X 1,t , X 2,t ) ⊺ of the GBE ( 1 ′ , 2 ′ , ) model at time t = q+1, q+2, … , using (14), (15) and (16).…”

Section: Steady-state Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data

Xie

Sun

Castagliola

et al. 2020

“…Shirke et al have proposed a nonparametric control chart for process variability based on in‐control deciles. Zhou et al provided a nonparametric quality control chart based on Ansari‐Bradly test statistic for variability. Chowdhury et al constructed a nonparametric control chart for joint location and scale monitoring, which is based on the Lepage test.…”

Section: Introductionmentioning

confidence: 99%

A nonparametric CUSUM chart for process dispersion

Shirke

Barale

2018

In the present article, we propose a nonparametric cumulative sum control chart for process dispersion based on the sign statistic using in-control deciles. The chart can be viewed as modified control chart due to Amin et al, 6 which is based on in-control quartiles. An average run length performance of the proposed chart is studied using Markov chain approach. An effect of nonnormality on cumulative sum S 2 chart is studied. The study reveals that the proposed cumulative sum control chart is a better alternative to parametric cumulative sum S 2 chart, when the process distribution is non-normal. We provide an illustration of the proposed cumulative sum control chart.

“…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 ., Bakir, Khoo and Lim, Yang et al ., Yang, Aslam et al ., Zhou et al ., Riaz and Abbasi, and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

A New Nonparametric EWMA Control Chart for Monitoring Process Variability

Haq

2017

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...