A hybrid homogeneously weighted moving average control chart for process monitoring

Abstract

Several modifications and enhancements to control charts in increasing the performance of small and moderate process shifts have been introduced in the quality control charting techniques. In this paper, a new hybrid control chart for monitoring process location is proposed by combining two homogeneously weighted moving average (HWMA) control charts. The hybrid homogeneously weighted moving average (HHWMA) statistic is derived using two smoothing constants λ 1 and λ 2. The average run length (ARL) and the standard deviation of the run length (SDRL) values of the HHWMA control chart are obtained and compared with some existing control charts for monitoring small and moderate shifts in the process location. The results of study show that the HHWMA control chart outperforms the existing control charts in many situations. The application of the HHWMA chart is demonstrated using a simulated data. K E Y W O R D S average run length (ARL), control chart, homogeneously weighted moving average (HWMA), hybrid homogeneously weighted moving average (HHWMA), process monitoring

Distribution‐free triple EWMA control chart for monitoring the process location using the Wilcoxon rank‐sum statistic with fast initial response feature

“…There are four different types of memory‐type control charts in the SPM literature and these are: (1) exponentially weighted moving average (EWMA) chart by Roberts, 2 (2) cumulative sum chart by Page, 3 (3) generally weighted moving average chart by Sheu and Lin, 4 and (4) homogeneously weighted moving average chart by Abbas 5 . For more detailed studies or literature reviews on the latter memory‐type schemes, see Hawkins and Olwell, 6 Ruggeri et al., 7 Mabude et al., 8 Nawaz and Han, 9 Abid et al., 10 Adegoke et al., 11 and Adeoti and Koleoso 12 . The focus of this paper is on improving the performance of the nonparametric EWMA‐type charts to monitor the process location, especially during start‐up period.…”

The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme

“…More recently, Abbas (2018) developed a new memory-type scheme that allocates a specific weight to the current sample and the remaining weight is distributed equally among the previous samples; this scheme is known as the homogeneously weighted moving average (HWMA) monitoring scheme. The HWMA scheme is by its nature a memory-type scheme used to effectively monitor small-to-moderate shifts (see for example the following articles on the HWMA-type monitoring schemes: Abbas (2018), Abbas et al (2020), Abid et al (2020a, b), Adegoke et al (2019a, b), Adeoti and Koleoso (2020), Dawod et al (2020), Nawaz and Han (2020), Raza et al (2020). Nawaz and Han (2020) studied the performance of the HWMA scheme using structured sampling techniques, that is, ranked set sampling (RSS), extreme RSS, median RSS and neoteric RSS.…”

“…More recently, Abid et al (2020a) proposed the double HWMA scheme for monitoring small shifts in the process mean and they also investigated the effect of non-normality and parameter estimation on the performance of the double HWMA scheme. Adeoti and Koleoso (2020) proposed a hybrid HWMA scheme for monitoring the process mean and they also investigated the effect of non-normality. Note that the double (hybrid) design of the HWMA scheme entails applying the same (different) smoothing parameter twice, respectively.…”

Parameter Estimation Effect of the Homogeneously Weighted Moving Average Chart to Monitor the Mean of Autocorrelated Observations With Measurement Errors

“…Thereafter, [36] investigated the use of an auxiliary variable in the form of a regression estimator as an unbiased estimate of the process mean in Cases K and U; and robustness to normality is illustrated. Next, [37] and [38] proposed the double and hybrid HWMA schemes as well as robustness to normality, respectively. The double (hybrid) model entails using the same (different) smoothing parameters to design a monitoring scheme.…”

“…The double (hybrid) model entails using the same (different) smoothing parameters to design a monitoring scheme. While [37] studied both Cases K and U, [38] investigated Case K only. More recently, [39] proposed a bivariate HWMA scheme based on linear profiles to monitor the intercept, slope and variance parameters using the Bayesian estimation framework and illustrated its efficiency over a number of competitors in Case U.…”