People interact with different critical applications in day-to-day life. Some examples of critical applications include computer programs, anonymous vehicles, digital healthcare, smart homes, etc. There are inherent risks in these critical applications if they fail to perform properly. In my dissertation, we mainly focus on developing methodologies for performance improvement for software security and healthcare prognosis. Cryptographic vulnerability tools are used to detect misuses of Java cryptographic APIs and thus classify secure and insecure parts of code. These detection tools are critical applications as misuse of cryptographic libraries and APIs causes devastating security and privacy implications. We develop two benchmarks that help developers to identify secure and insecure code usage as well as improve their tools. We also perform a comparative analysis of four static analysis tools. The developed benchmarks enable the first scientific comparison of the accuracy and scalability of cryptographic API misuse detection. Many published detection tools (CryptoGuard, CrySL, Oracle Parfait) have used our benchmarks to improve their performance in terms of the detection capability of insecure cases. We also examine the need for performance improvement for healthcare applications. Numerous prediction applications are developed to predict patients' health conditions. These are critical applications where misdiagnosis can cause serious harm to patients, even death. Due to the imbalanced nature of many clinical datasets, our work provides empirical evidence showing various prediction deficiencies in a typical machine learning model. We observe that missed death cases are 3.14 times higher than missed survival cases for mortality prediction. Also, existing sampling methods and other techniques are not well-equipped to achieve good performance. We design a double prioritized (DP) technique to mitigate representational bias or disparities across race and age groups. we show DP consistently boosts the minority class recall for underrepresented groups, by up to 38.0%. Our DP method also shows better performance than the existing methods in terms of reducing relative disparity by up to 88% in terms of minority class recall. Incorrect classification in these critical applications can have significant ramifications. Therefore, it is imperative to improve the performance of critical applications to alleviate risk and harm to people. / Doctor of Philosophy / We interact with many software using our devices in our everyday life. Examples of software usage include calling transport using Lyft or Uber, doing online shopping using eBay, using social media via Twitter, check payment status from credit card accounts or bank accounts. Many of these software use cryptography to secure our personal and financial information. However, the inappropriate or improper use of cryptography can let the malicious party gain sensitive information. To capture the inappropriate usage of cryptographic functions, there are several detection tools are developed. However, to compare the coverage of the tools, and the depth of detection of these tools, suitable benchmarks are needed. To bridge this gap, we aim to build two cryptographic benchmarks that are currently used by many tool developers to improve their performance and compare their tools with the existing tools. In another aspect, people see physicians and are admitted to hospitals if needed. Physicians also use different software that assists them in caring the patients. Among this software, many of them are built using machine learning algorithms to predict patients' conditions. The historical medical information or clinical dataset is taken as input to the prediction models. Clinical datasets contain information about patients of different races and ages. The number of samples in some groups of patients may be larger than in other groups. For example, many clinical datasets contain more white patients (i.e., majority group) than Black patients (i.e., minority group). Prediction models built on these imbalanced clinical data may provide inaccurate predictions for minority patients. Our work aims to improve the prediction accuracy for minority patients in important medical applications, such as estimating the likelihood of a patient dying in an emergency room visit or surviving cancer. We design a new technique that builds customized prediction models for different demographic groups. Our results reveal that subpopulation-specific models show better performance for minority groups. Our work contributes to improving the medical care of minority patients in the age of digital health. Overall, our aim is to improve the performance of critical applications to help people by decreasing risk. Our developed methods can be applicable to other critical application domains.