Distribution-free Shewhart-Lepage type premier control schemes for simultaneous monitoring of location and scale

- A distribution-free fuzzy Shewhart-Lepage (FSL) scheme is proposed.
- Fuzzy scheme is a computer intensive process.
- Optimization algorithm of the FSL scheme based on simulation is developed.
- The FSL scheme performs favourably compared to other schemes.
- Some applications in industrial engineering and manufacturing are shown.

Distribution-free or nonparametric process control schemes are often preferred over traditional schemes as these schemes do not require any assumption related to the underlying process distribution, such as normality. Consequently, distribution-free schemes are robust for various types of continuous process distributions and therefore, may be more useful in practice. We review the distribution-free Shewhart-Lepage (SL) type control scheme, introduce a competitor of such scheme and further propose a fuzzy control scheme for joint monitoring of the location and scale parameters of a process. We study the design, implementation procedures and early false alarm probabilities in detail. We also carry out detailed performance comparisons among various schemes, in terms of the mean, standard deviation and median together with some percentiles of the run length distribution. Our numerical findings, based on Monte-Carlo simulation, are extremely interesting and it shows that the fuzzy SL (FSL) control scheme performs favourably compared to its basic counterparts, i.e. the SL type distance (SL-D) and SL type max (Max-SL) schemes, as the FSL scheme combines the merits of both the SL-D and Max-SL schemes. We illustrate the implementation of the proposed FSL scheme using two real datasets.