Witten 1985 MAD, critical elements in a graph and Gompertz model

Witten 1985, Mech Ageing and Dev. 1985.

Witten85 used $R(t)$ as the survival function. $h_0$ as the initial mortality rate, $\gamma$ as the Gompertz coefficient.  Witten85 seems to treat probability = reliability (page 142), which is different from Leemis's approach.

Witten85 assumed $m$ critical components in a graph model of a cell. There existed a critical number $m_c$ that is the threshold for the system (cell) to fail. This is equivalent to the parallel block configuration used by GG01.

Witten85 used Markov transitional states to model the failure of each critical component $M*$.  I did not see how  these transitional states are used for his derivation of the Gompertz model.

Witten85 used 'deviation' concept from Witten83. Witten85 assumes exponential failure function for each critical component (page 148), similar to GG01. It seems that although 'deviation' argument was used, it was not incorporated into the building toward Gompertz model.

In Eq 21, Witten85 shows that system viability (reliability) $R_SYS$ is basically the viability function of a serial system. Witten85 assumed a 'critical time' $t*$ (page 148), and approximate the binomial form in Eq 21 to obtain the Gompertz form using the exactly approximation used by GG91. 

It is perplexing to me that Eq21 shows a serial configuration (based on Eq 14), but Witten85 argues for parallel configuration in Eq 13.  For serial system, the product form also means that any single failure of the critical components will lead to system failure.  If 'all of the critical elements must fail' for a system to fail, it should be a parallel configuration.

Witten85 introduced 'cost' in Eq 30 on page 152: Cost ~ m^beta, where $m$ is the number of critical elements.