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Distribution-free phase-II exponentially weighted moving average schemes for joint monitoring of location and scale based on subgroup samples

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Abstract

In this article, we introduce some distribution-free exponentially weighted moving average (EWMA) schemes for phase-II monitoring. Our proposed schemes are based on the well-known Lepage statistic and are referred to as the EWMA-Lepage (EL) procedures. These schemes are designed for monitoring the location and the scale parameters of an unknown but continuous univariate process at phase II. A novelty of these schemes is that a single chart can monitor both the location and scale parameters. Moreover, their distribution-free characteristic ensures that the in-control (denoted IC) properties of the proposed procedure remain invariant and known for all univariate continuous distributions. We discuss both the exact and the steady-state control limits. We obtain control limits under different situations for practical implementation of these schemes and examine the IC and out-of-control (denoted OOC) properties of the monitoring schemes through simulation studies in terms of the average, the standard deviation, the median, and some percentiles of the run length distributions. We illustrate the proposed procedure with two sets of data arriving out of manufacturing sector. We also offer some remarks and future research directions.

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Authors and Affiliations

  1. Production, Operations and Decision Sciences, XLRI—Xavier School of Management, C.H.Area (East), XLRI Jamshedpur, Jharkhand, 831001, India

    Amitava Mukherjee

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  1. Amitava Mukherjee
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Correspondence to Amitava Mukherjee.

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Mukherjee, A. Distribution-free phase-II exponentially weighted moving average schemes for joint monitoring of location and scale based on subgroup samples. Int J Adv Manuf Technol 92, 101–116 (2017). https://doi.org/10.1007/s00170-016-9977-2

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  • DOI: https://doi.org/10.1007/s00170-016-9977-2

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