Multivariate cumulative sum control chart for compositional data with known and estimated process parameters

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AbstractThis article uses the classic multivariate cumulative sum () chart scheme proposed by Crossier (1988) to present a new modified chart for compositional data (). For this purpose, the data are first transformed using isometric log‐ratio () coordinates representation to eliminate the constant sum constraint of . The ‐ control chart has been defined along with the performance measures of the proposed chart using the average run length (). Besides, the Markov chain method has been used to study the performance of the proposed chart. Assuming that the transformed data are normally distributed, the proposed ‐ charts have been compared with existing competitors such as ‐ and ‐ charts. The comparison shows that the proposed chart has better performance than the ‐ control charts, while the performance of the proposed chart is comparable with the ‐ chart. The effect of the estimated mean vector and variance‐co‐variance matrix on run‐length characteristics of the proposed ‐ control chart has also been studied in this paper. For the performance of ‐ with estimated parameters Monte Carlo simulation has been adopted. The effect of the number of variables , sample size , and subgroup size has also been studied on the data's upper control limit () and . In the end, two illustrative examples of the particle size distribution of plants and production of muesli are provided to represent the practical implementation of the ‐ chart.