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Since the 1990s, governments growing interest in sustainability has promoted widespread adoption of life cycle costing (LCC) in investment appraisal. LCC relies on the estimates of financial variables that contain acknowledged uncertainty. Despite numerous probabilistic studies in the literature, the influence of uncertainty is still unclear because conventional approaches are data-intensive and/or computationally complex. In this light, the thesis aims to develop an improved approach with second order moment thinking, and explicitly identify the influence for the purpose of addressing the inherent uncertainty. First, the thesis respectively examines the single-variable uncertainty concerning the underlying variables (cash flows, interest rates, timing of cash flows, asset lifetime). For each variable being probabilistic, second order moment theory is employed to establish a formulation for obtaining the expected value and variance of present worth. Four formulations are presented/established; the moments of the variables, the squares of timing, and the logarithms of interest rates are involved in measuring uncertainty. The formulations are subsequently implemented on numerical studies, which utilise unit cash flows, and three case studies: a vertical greening system in Italy, an extensive green roof in Malaysia, and a green roof in the US. The numerical studies are proven to generate typical trends applicable to real cases. The thesis finds that i) the need to consider cash flow uncertainty primarily lies in the estimation of the present worth variance of an investment, and investors ignoring such uncertainty might underestimate the influence of interest rates on the variance; ii) the inclusion of interest rate uncertainty causes interest rates to positively impact present worth variance. A turning point rate exists and gives the largest variance; iii) timing uncertainty could be influential and potentially leads to the rejection of a viable investment option. This uncertainty also diminishes the influence of interest rate fluctuation on LCC; and iv) asset lifetime uncertainty slightly reduces expected present worth and could result in the largest variance of present worth at any stage of the project, depending on the COV of asset lifetime. Next, the thesis analyses multiple-variable uncertainty by simultaneously characterising all variables with expected value and variance. The thesis continues employing second order moment theory to establish an integrated formulation for this scenario. Numerical studies and case studies are conducted to uncover the combined influences of multiple variables. The results reveal that the uncertainty around interest rates, timing, and asset lifetime makes cash flows more influential in determining LCC results. There exists a positive influence of the interest rate on present worth variance, and this influence can be enhanced by lower cash flow uncertainty, higher asset lifetime uncertainty, and stronger cash flow correlation. Furthermore, the thesis resolves several substantial issues concerning the implementation of the proposed formulations: i) the primary concern regarding data availability is addressed through the fractile approach that requires professional judgements; ii) a declining rate following gamma distribution is incorporated into the formulation to achieve intergeneration fairness; and iii) equations converting expected value and variance to distribution parameters are summarised to interpret present worth. Ten distributions are eligible, providing high flexibility for the interpretation. The thesis relies on the assumption that cash flows, interest rates, timing, and asset lifetime are independent. However, the correlations among the four variables might exist and affect the conclusions drawn. It is worth considering the correlations in the proposed formulations, and examining potential influence on the results in a future study. Additionally, the proposed formulations are based on a Taylor series expansion and use only the first and second order moments for simplicity. Future research could include higher order moments for the sake of improved accuracy. The thesis demonstrates the importance of considering uncertainty in LCC, particularly the uncertainty around timing of cash flows and asset lifetime. Investors should not neglect the impacts of the uncertainty attached to these two variables, especially when the cash flows, of which the timing is probabilistic, are cost-related, and investment projects have long life spans. The thesis will be of interest to anyone conducting probabilistic investment appraisals, especially those with limited data availability and mathematical skills. The originality of the thesis lies in developing a readily understandable methodology that overcomes the existing barriers of obtaining sufficient data and the use of complex calculations in probabilistic LCC analysis, and providing an in-depth understanding of the influence of uncertainty on LCC results.