An integrated distribution-free approach to monitor multiple process aspects with application in delivery time management

Amitava Mukherjee and Hidetoshi Murakami

Journal of Applied Statistics, 2026, vol. 53, issue 10, 1860-1888

Abstract: Monitoring time between events, operational delays or responding to a customer call is essential for maintaining and enhancing service quality. Several aspects of the processes, including location such as median time, variability and shape, are pivotal. This paper introduces a new and innovative distribution-free cumulative sum (CUSUM) procedure based on a combination of three orthogonal rank statistics, following from the Legendre polynomials, for simultaneously monitoring location, scale, and skewness aspects in the context of Phase-II applications. Implementation design and post-signal follow-up procedure for identifying which parameter is more responsible for the signal are discussed. The in-control robustness of the proposed scheme is studied via simulation. The run-length properties of the proposed scheme are compared with various CUSUM schemes. The proposed scheme displays outstanding out-of-control performance in identifying a broad class of shifts involving one or more of the three parameters in an underlying process distribution. An illustration of the proposed scheme for monitoring the time it takes to deliver food items by an e-commerce facility is presented to explain manufacturing quality monitoring applications. We finally offer some concluding remarks.

Date: 2026
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DOI: 10.1080/02664763.2025.2575041

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