A new CUSUM control chart under uncertainty with applications in petroleum and meteorology

Abstract

In these last few decades, control charts have received a growing interest because of the important role they play by improving the quality of the products and services in industrial and non-industrial environments. Most of the existing control charts are based on the assumption of certainty and accuracy. However, in real-life applications, such as weather forecasting and stock prices, operators are not always certain about the accuracy of an observed data. To efficiently monitor such processes, this paper proposes a new cumulative sum (CUSUM) X¯ chart under the assumption of uncertainty using the neutrosophic statistic (NS). The performance of the new chart is investigated in terms of the neutrosophic run length properties using the Monte Carlo simulations approach. The efficiency of the proposed neutrosophic CUSUM (NCUSUM) X¯ chart is also compared to the one of the classical CUSUM X¯ chart. It is observed that the NCUSUM X¯ chart has very interesting properties compared to the classical CUSUM X¯ chart. The application and implementation of the NCUSUM X¯ chart are provided using simulated, petroleum and meteorological data.

Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length

“…Since τ cannot be specified in certain practical scenarios, this section also analyses the expected percentiles. In this paper, (τ min ,τ max ) is set as (1,2]. Table 4 shows the optimal charting parameters (L, LCL and UCL) and the EARL of the EARL-based design of the side sensitive synthetic-γ chart for γ 0 = 0.05 and n2{5,7,10,15}.…”

“…Similar to the EARL-based design, (τ min ,τ max ) is set as (1,2]. To ensure a fair comparison between the EARL-based and EMRL-based design, ξ is set to be equivalent to the MRL 0 in Table 5.…”

“…The MRL-based design in Section 4 is adopted to obtain the optimal charting parameters, where ξ = 250. The optimal charting parameters are (L,LCL, UCL) = (7,0,0.8418), which results in (Q05,MRL 1 ,Q95) = (1,7,76). By comparison, the ARLbased design by Yeong et al [24] results in (Q05,MRL 1 ,Q95) = (1,10,68) The MRL-based design can only be adopted if τ can be specified.…”

“…The optimal charting parameters are (L,LCL, UCL) = (7,0,0.8418), which results in (Q05,MRL 1 ,Q95) = (1,7,76). By comparison, the ARLbased design by Yeong et al [24] results in (Q05,MRL 1 ,Q95) = (1,10,68) The MRL-based design can only be adopted if τ can be specified. As the exact size of shift caused by the special cause may not be known, this section also considers the EMRL-based design with (τ min ,τ max ) = (1,2].…”

“…By convention, control charts monitor the process mean (μ) and/or standard deviation (σ), where shifts in μ and/or σ shows the presence of assignable cause(s). For example, readers can refer to the studies by Aslam et al [1], Riaz et al [2], Abujiya et al [3], and many others.…”