On Designing Distribution-Free Homogeneously Weighted Moving Average Control Charts

Abstract

There are many practical situations in which the underlying process distribution is either completely unknown or partially known but deviates from normality. In such cases, the performance of the traditional parametric control charts deteriorates, and nonparametric control charts are considered as a robust alternative for monitoring the process. In this article, two new nonparametric homogeneously weighted moving average (NPHWMA) control charts are proposed for monitoring the deviations in process location from the target value. The proposed charts assign a specific weight to the current sample information, and the remaining weight is equally distributed among the previous samples. The proposed NPHWMA charts are based on sign test and Wilcoxon signed-rank test for process monitoring under the skewed and symmetric distributions, respectively. The Monte Carlo simulations are used to study the run length properties and compare the performance of the proposed charts with some existing control charts. It is found that the proposed charts outperform their existing counterparts. Empirical illustrations are provided for practical implementation of the proposed charts.

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.…”

“…Dawod et al (2020) proposed a bivariate HWMA scheme based on linear profiles to monitor the intercept, slope and variance parameters using the Bayesian estimation model and showed that it outperforms its competitors. Finally, Raza et al (2020) proposed a distribution-free HWMA scheme based on the sign and signed-rank statistics to monitor skewed and symmetric distributions observations. The key difference between the HWMA scheme proposed in this paper and the abovementioned HWMA schemes is that it is not assumed that the observations have perfect or exact measurements.…”

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

“…For the multivariate scenario, [40] and [41] studied the performance of the HWMA scheme in detecting shifts in the process mean vector in Cases K and U, respectively. For nonparametric schemes, [42] studied the performance of the HWMA scheme based on the sign and signed-rank statistics to monitor symmetric and skewed distributions which are applicable in the Case K scenario.…”

A New Nonparametric Composite Exponentially Weighted Moving Average Sign Control Chart

“…The synthetic version of the EWMA sign control chart was proposed by Haq [18] by integrating the existing EWMA sign control chart with the conforming run length. Recently, Raza et al [19] proposed the nonparametric homogeneously weighted moving average control charts based on sign and signed-rank statistics.…”