Common control charts assume normality and known parameters. Quite often these assumptions are not valid and large relative errors result in the usual performance characteristics, such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than are usually available. Sufficiently large parametric families then provide realistic intermediate models. In this paper the performance of charts based on such families is considered. Exceedance probabilities of the resulting stochastic performance characteristics during incontrol are studied. Corrections are derived to ensure that such probabilities stay within prescribed bounds. Attention is also devoted to the impact of the corrections for an outof-control process. Simulations are presented both for illustration and to demonstrate that the approximations obtained are sufficiently accurate for use in practice.

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Standard control charts are based on the assumption that the observations are normally distributed. In practice, normality often fails and consequently the false alarm rate is seriously in error. Application of a nonparametric approach is only possible with many Phase I observations. Since nowadays such very large sample sizes are usually not available, there is need for an intermediate approach by considering a larger parametric model containing the normal family as a submodel. In this paper control limits are presented in such larger parametric models, with emphasis on the so called normal power family. Correction terms are derived, taking into account that the parameters are estimated. Simulation results show that the control limits are accurate, not only in the considered parametric family, but also for common distributions outside the parametric family, thus covering a broad class of distributions.

Land and forest fires in Kalimantan and Sumatra, Indonesia occurred annually at different magnitude and duration. Climate and sea interaction, like El Niño, influences the severity of dry seasons preceding the fires. However, research on the influence of El Niño intensity to fire regime in Kalimantan and Sumatra is limited. Therefore, this study aims to analyze the spatial and temporal patterns of the effects of El Niño intensity on land and forest fires in fire-prone provinces in Indonesia. Here, we applied the empirical orthogonal function analysis based on singular value decomposition to determine the dominant patterns of hotspots and rainfall data that evolve spatially and temporally. For analysis, the study required the following data: fire hotspots, dry-spell, and rainfall for period 2001-2019. This study revealed that El Niño intensity had a different impacts for each province. Generally, El Niño will influence the severity of forest fire events in Indonesia. However, we found that the impact of El Niño intensity varied for Kalimantan, South Sumatra, and Riau Province. Kalimantan was the most sensitive province to the El Niño event. The duration and number of hotspots in Kalimantan increased significantly even in moderate El Niño event. This was different for South Sumatra, where the duration and number of hotspots only increased significantly when a strong El Niño event occurred.

Land and forest fire have been identified as one of the main problems contributing to forest biodiversity and Global Warming and well known as the phenomenon affected by El Niño Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD). The total burned area becomes higher when either El Niño or positive IOD occur. This research aims to analyze and quantify the direct correlation of the Niño 3.4 and difference between west and east pole of IOD sea surface temperature anomaly (SSTA) to the burned area in Indonesia and the impact of ENSO and IOD of each category on the burned area. The correlation between spatial location with Niño 3.4 and difference IOD SST's will be analyzed using a heterogeneous correlation map. Meanwhile, the quantitative impact will be calculated based on the singular value decomposition analysis result to each year categories. The most significant impact of El Niño has occurred on Merauke following Kalimantan shows the strongest correlation between burned area and Niño 3.4 SST. However, the significant increase of burned area only occurred during very strong El Niño. Both areas can have double amount of burned area during peak fire in very strong El Niño. Moderate El Niño have the most diverse impact with the stronger one occurs on Kalimantan and Merauke. Weak El Niño can have a significant impact if occurred simultaneously with positive IOD. Even more, it can surpass the effect of a single Moderate El Niño. Meanwhile, the strongest IOD impact happened in the southern part of Sumatra.