$3.$ The stress$-$time pattern shown in Fig. $1$ is to be repeated in blocks until failure of a test component occurs. The $\backslash ($ S$-$N $\backslash )$ curve for the material is also shown. The repeating block is decomposed into simple cycles as shown in Table $1.$ Estimate the hours of life until failure of this test component. $(10$ pts$.)$

Figure $1$: $($a$)$ Stress$-$time spectrum. $($b$)\backslash ($ S$-$N $\backslash )$ curve.

Table $1$: Decomposition of the repeating block into simple cycles