Robust Tukey–CUSUM Control Chart for Process Monitoring

Abstract

In real world scenarios, we continuously inspect the performing behavior of different features of processes. A change in the process parameters may affect the product quality and therefore needs a timely identification. For this purpose we have designed new memory structure based on Tukey control chart (TCC) under cumulative sum (CUSUM) setup. The proposed chart, namely Tukey‐CUSUM, combines the feature of TCC with CUSUM design for improved detection of shifts for normal and non‐normal data. The performance of the study proposal is evaluated through different measures based on run length including ARL, EQL, PCI and RARL. We have observed that the proposed Tukey‐CUSUM design is quite robust and efficient, especially using asymmetrical decision intervals for different process models. An application example is also provided to illustrate the study proposal. Moreover, sample selection is always of great concern for practitioners so we have included a brief description of the steps for sample selection with reference to process monitoring. Copyright © 2015 John Wiley & Sons, Ltd.

A New Nonparametric Tukey MA-EWMA Control Charts for Detecting Mean Shifts

“…The data sets: The data generated the MA, MME, MEM, MA-TCC, MEM-TCC, and MME-TCC control charts from equations (5), (7), (9), (12), (13), (14) and (15) as shown in graphical results as Figures 5-6. For this case study, the set of data that had the normal distribution showed that the proposed chart was able to detect the change from the 5 th , the MME and MEM-TCC charts were able to detect at 6 th , the MEM chart can be detected at 7 th , the MA and MA-TCC charts were able to detect at 27 th .…”

“…However, it depended on set the parameter of each control chart. Besides, the researchers compared ARL performance of proposed MME-TCC chart vs. Tukey-EWMA [16], Tukey-CUSUM [15] and Tukey EWMA-CUSUM [17] charts under the Normal (0,1) distribution, ARL0 =370 and the numerical ARL1 where  is a shift sizes: 4.00 4.00  −   . The numerical results found the performance of the proposed chart performed better than the Tukey-EWMA, Tukey-CUSUM and Tukey EWMA-CUSUM charts for all magnitudes of change, except for at  = 0.25, the Tukey EWMA-CUSUM performed better than the proposed chart.…”

“…In 2012, Sukparungsee [14] studied the strength of TCC for the data with normal and non-normal distributions and found that TCC had better efficiency to detect the larger changes than Shewhart's chart and EWMA. Then, in 2014, Khaliq and Riaz [15] proposed the Tukey-Cumulative Control Chart (TCC-CUSUM) to detect the change of average when the process had the symmetric and asymmetric distribution. The proposed control chart had higher efficiency in detecting the change than TCC and CUSUM.…”

On the Performance of Median Based Tukey and Tukey-EWMA Charts Under Rational Subgrouping

“…This design is a good alternate to classical EWMA, when data follows a skewed distribution. Khaliq and Riaz [16] designed the CUSUM structure of Tukey chart for small and sustained shifts. This design is best alternate to classical CUSUM chart, when data follow the skewed distribution.…”

A new dual CUSUM mean chart

“…Recently, Raji et al have considered different robust estimators of the process mean and then used them to construct DCUSUM charts for monitoring the process mean when the probability distribution of the underlying quality characteristic is not normal. For more related works on the CUSUM charts, the readers are referred to Waldmann, Jiang et al, Wu et al, Jiang et al, Shu et al, Riaz et al, Abbasi et al, Calzada and Scariano, Nazir et al, Zaman et al, Haq et al, Khaliq and Riaz, Riaz et al, Zaman et al, Abid et al, Faisal et al, and the references cited therein.…”