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The most suitable tool for developing contingency plans in emergencies is the process decision program chart. This tool is specifically designed to assist in identifying potential problems and their corresponding solutions before they occur. The primary focus of a process decision program chart is to provide a structured way of assessing risk and formulating plans to address those risks should they arise. By breaking down the decision-making process and outlining possible scenarios and their outcomes, it allows teams to prepare for various emergency situations effectively.

In comparison, the fault tree diagram is typically used for analyzing the causes of system-level failures rather than planning for emergency responses. While it can provide insights into potential failures, it's more of a diagnostic tool than a proactive planning tool. The matrix diagram is better suited for showing relationships between different components or elements in a process, rather than specifically preparing for emergencies. Lastly, process value chain maps help visualize the steps involved in creating a product or service but do not directly relate to contingency planning as they focus more on operational efficiency.

Therefore, the process decision program chart is the most appropriate choice for developing contingency plans in emergencies, as it emphasizes preparedness and risk management.