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This article thoroughly reviews the state-ofthe-art methods for setting ALARP upper border as a straight line in logarithmic graph, which is the common practice in the risk assessments of nuclear, chemical plants and maritime facilities. It also reviews methods for setting ALARP upper border based on economic importance of a considered ship type. As a result, inconsistency related to ALARP upper border has been identified and new methods to resolve such inconsistency are developed. Here, firstly a method for approximating FN diagrams of existing major ship types is proposed and it is applied to ship types which consist of ships above 100 gross tonnage. After that the approximated FN diagrams were checked by goodness-of-fit test by 5 % significance level, and it was validated that those approximated FN diagrams well express corresponding FN diagrams made from IHSF casualty and ship databases. This method can extrapolate FN diagrams made from those databases to the area of severer accidents with more fatalities, which have not been occurred yet, rationally. Secondly, problems that accompany with an existing method for setting ALARP upper border are discussed and methods for resolving the problems using the approximated FN diagrams are proposed. The methods can set ALARP upper border keeping consistency of ALARP upper border between individual risk and FN diagram. Lastly, the new method for safety analysis of ships using approximated FN diagrams of major ship types is introduced. The method is used in order to find ships' groups which should be considered preferentially. The method for approximating FN diagrams and the method for setting ALARP upper border proposed here is so general that they can be applied to risk analysis of the fields which have a lot of accident records like maritime field, such as aviation or automotive fields.