TTT Transforms

The concept of total time on test (TTT) plots was proved to be a very useful tool in many reliability applications such as model identification, aging properties, age replacement policies, etc. Plotting data is the first step to understand the information contained in the data. In case of failure data of repairable equipment, these plots indicate increasing or decreasing or constant failure rates. The health monitoring of any equipment can be found by using these plots, whether the failure data satisfies i.i.d assumption or not. If the data confirms i.i.d assumption and increasing failure rate, then, optimal age replacement interval is obtained by plotting the scaled TTT with Cumulative Distribution Function (CDF). If the data shows any trend in the form of deterioration, optimum replacement interval is obtained from the TTT plot by considering age of the equipment as discussed by Barlow. The ratio of cost of failure maintenance to cost of repair maintenance (cost ratio) is the deciding factor.

TTT plots can be constructed using different methods like Kaplan Meier Estimate, Rank Adjustment Method, Nelson, Piecewise Exponential Estimate and Maximum Likelihood Estimate methods. While first four methods are non-parametric, the last method is parametric. It is observed that whether the data is censored or not and follow i.i.d assumption, TTT plots are more suitable when maintenance policies are evaluated. Sometimes it is necessary to clean the data when it contains inappropriate and misleading events, before synthesizing it into a model to be used for future decisions and policy.

The applications of TTT transforms were advocated by Kelfsjo (1982, 1986) Kelfsjo and Westberg (1990). From the shape of the plot, one can easily know about failure rate of the equipment. If the plot shows convex upwards, then the machine is deteriorating (increase in failure rate) and if it is concave downwards, the machine is improving (decrease in failure rate) with time. If the plot crosses the diagonal several times, then the machine experiences a constant failure rate. TTT plots can be drawn using several methods namely Maximum Likelihood Estimates (MLE), Piecewise Exponential Estimates (PEXE) and Kaplan Meier Estimates (KME).