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This article introduces a four-parameter probability distribution function derived by introducing an additional parameter to the New Weighted Weibull distribution proposed by[1]. Using the quadratic rank transmutation map (QRTM) introduced by [2], the three-parameter New Weighted Weibull distribution was generalized to its four-parameter variant titled "Transmuted New Weighted Weibull distribution (TNWWD)". The probability density function (pdf), cumulative distribution function (CDF), hazard rate, and survival function of the TNWWD model were computed and validated. Consequently, some of the mathematical properties of the proposed model were extensively studied and articulated. The parameter(s) of the TNWWD model were estimated using the method of maximum likelihood estimate. The proposed TNWWD model generally outperforms the competing Weibull and New Weighted Weibull distributions in terms of the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan quin information criterion (HQIC), and related performance measures. By this, the proposed four-parameter probability distribution function is expected to perform better with a real dataset and at all times. A real dataset on survival time was used to demonstrate the practical application of the proposed TNWWD model. [ABSTRACT FROM AUTHOR]

In recent studies, auxiliary information technique in control charts have shown superior run length performances to control charts developed without using it. This paper proposes a side-sensitive group runs chart for detecting mean shifts using auxiliary information (SSGR-AI), where its charting characteristics require information from the study and auxiliary variables to efficiently monitor the process shifts. The control chart statistic, optimal design of parameters and implementation of the proposed SSGR-AI chart are explained. The performance of the SSGR-AI chart is evaluated using the average run length (ARL) and expected average run length (EARL) criteria. The ARL and EARL performances of the SSGR-AI chart are compared with that of the synthetic chart with auxiliary information (Syn-AI) and exponentially weighted moving average chart with auxiliary information (EWMA-AI). The results show that the SSGR-AI chart outperforms the (i) Syn-AI chart for all shift sizes and values of correlation coefficient, and (ii) EWMA-AI chart, except for small shifts and small values of correlation coefficient. [ABSTRACT FROM AUTHOR]