A Multivariate Homogeneously Weighted Moving Average Control Chart

Abstract

This paper presents a multivariate homogeneously weighted moving average (MHWMA) control chart for monitoring a process mean vector. The MHWMA control chart statistic gives a specific weight to the current observation, and the remaining weight is evenly distributed among the previous observations. We present the design procedure and compare the average run length (ARL) performance of the proposed chart with multivariate Chi-square, multivariate EWMA, and multivariate cumulative sum control charts. The ARL comparison indicates superior performance of the MHWMA chart over its competitors, particularly for the detection of small shifts in the process mean vector. Examples are also provided to show the application of the proposed chart. INDEX TERMS Average run length, control chart, manufacturing process, quality control, statistical process control.

Auxiliary‐information‐based efficient variability control charts for Phase I of SPC

“…The two well-known measures for evaluating control charts' performance are average run length (ARL) and probability to signal (PTS). ARL is well suited for Phase II control charts, [41][42][43][44][45] while for Phase I charts, one is mostly interested in the probability of detecting inconsistent/contaminated samples (or observations). 29,46 Hence, in this study, PTS is used to compare the performance of the charts in Phase I.…”

Adaptive CUSUM and EWMA charts with auxiliary information and variable sampling intervals for monitoring the process mean

“…They have shown that these adaptive control charts perform uniformly better than their existing counterparts when detecting a range of mean shift sizes. Some related research works may be seen in Reynolds Jr, 9 Capizzi and Masarotto, 10 Scariano and Calzada, 11 Abbasi and Miller, 12 Abbas et al, 13 Haq, 14 Ajadi and Riaz, 15 Adegoke et al, 16 Adeoti and Malela‐Majika, 17 and in the references cited therein.…”

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

“…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. 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.…”