PurposeThis study aims to focus on proposing a new memory-type chart called progressive mean exponentially weighted moving average (PMEWMA) control chart. This memory-type chart is an improvement on the existing progressive mean control chart, to detect small and moderate shifts in a process.Design/methodology/approachThe PMEWMA control chart is developed by using a cumulative average of the exponentially weighted moving average scheme known as the progressive approach. This scheme is designed based on the assumption that data follow a normal distribution. In addition, the authors investigate the robustness of the proposed chart to the normality assumption.FindingsThe variance and the mean of the scheme are computed, and the mean is found to be an unbiased estimator of the population mean. The proposed chart's performance is compared with the existing charts in the literature by using the average run-length as the performance measure. Application examples from the petroleum and bottling industry are also presented for practical considerations. The comparison shows that the PMEWMA chart is quicker in detecting small shifts in the process than the other memory-type charts covered in this study. The authors also notice that the PMEWMA chart is affected by higher kurtosis and skewness.Originality/valueA new memory-type scheme is developed in this research, which is efficient in detecting small and medium shifts of a process mean.
With the development of modern acquisition techniques, data with several correlated quality characteristics are increasingly accessible. Thus, multivariate control charts can be employed to detect changes in the process. This study proposes two multivariate control charts for monitoring process variability (MPVC) using a progressive approach. First, when the process parameters are known, the performance of the MPVC charts is compared with some multivariate dispersion schemes. The results showed that the proposed MPVC charts outperform their counterparts irrespective of the shifts in the process dispersion. The effects of the Phase I estimated covariance matrix on the efficiency of the MPVC charts were also evaluated. The performances of the proposed methods and their counterparts are evaluated by calculating some useful run length properties. An application of the proposed chart is also considered for the monitoring of a carbon fiber tubing process. K E Y W O R D Sdispersion monitoring, estimation effects, multivariate control chart, phase I, progressive setup INTRODUCTIONMany manufacturing processes have multiple correlated quality characteristics; multivariate control chart is very effective in monitoring such processes. 1 For example, monitoring multivariate quality variables like the diameter and length of the manufacturing process of a dowel pin. Hotelling 2 introduced a 2 -control chart; this chart is very efficient at detecting large shifts in the process mean vector, which is also mentioned by Mahmood et al. 3 Two multivariate cumulative sum (MCUSUM) charts were proposed by Healy, 4 where the first chart monitors the process mean vector, and the other monitors the covariance matrix. Crosier 5 also proposed a multivariate CUSUM chart. Pignatiello Jr and Runger 6 introduced another multivariate CUSUM control charts for detecting shifts in the process mean vector. Lowry et al 7 provided a Multivariate exponentially weighted moving average (EWMA) chart for detecting small and intermediate shifts in the process parameter. This chart is a direct extension of the univariate EWMA control chart by Roberts. 8 The multivariate CUSUM and EWMA control charts are very efficient in detecting small and moderate shifts in the process parameters. Ajadi and Riaz 9 proposed two multivariate charts which combine the effects of MEWMA and MCUSUM charts. Their proposed charts are more effective in detecting only small shifts in the proposed than the MEWMA and MCUSUM charts. Next, multivariate dispersion charts are employed to detecting changes in the covariance matrices. For example, Alt 10 proposed generalized variance chart (GVC), |S|. The determinant of the sample covariance matrix was employed as the summary statistics. Chen et al 11 worked on a Max-MEWMA chart in monitoring the mean vector and covariance matrix 2724
The corona virus disease 2019 (COVID-19) is a novel pandemic disease that spreads very fast and causes severe respiratory problem to its carrier and thereby results to death in some cases. In this research, we studied the trend, model Nigeria daily COVID-19 cases and forecast for the future occurrences in the country at large. We adopt the Box and Jenkins approach. The time plot showed that the cases of COVID-19 rises rapidly in recent time. KPSS test confirms the non-stationarity of the process (p < 0.05) before differencing. The test also confirmed the stationarity of the process (p > 0.05) after differencing. Various ARIMA (p,d,q) were examined with their respective AICs and Log-likelihood. ARIMA (1, 2, 1) was selected as the best model due to its least AIC (559.74) and highest log likelihood (-276.87). Both Shapiro-Wilk test and Box test performed confirm the fitness of the model (p > 0.05) for the series. Forecast for 30 days was then made for COVID-19 cases in Nigeria. Conclusively, the model obtained in this research can be used to model, monitor and forecast the daily occurrence of COVID-19 cases in Nigeria.
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