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This chapter has been seminal work of Dr K.S.S. Iyer, which has taken time to develop, for over the last 56 years to be presented here. The method in advance predictive analytics has developed, from his several other applications, in predictive modeling by using the stochastic point process technique. In the chapter on advance predictive analytics, Dr Iyer is collecting his approaches and generalizing it in this chapter. In this chapter, two of the techniques of stochastic point process known as Product Density and Random point process used in modelling problems in High energy particles and cancer, are redefined to suit problems currently in demand in IoT and customer equity in marketing (Iyer, Patil, & Chetlapalli, 2014b). This formulation arises from these techniques being used in different fields like energy requirement in Internet of Things (IoT) devices, growth of cancer cells, cosmic rays’ study, to customer equity and many more approaches.

The purpose of this paper is to provide the maintenance personnel with a methodology for modeling and estimating the reliability of critical machine systems using the historical data of their inter‐failure times.

The failure patterns of five different machine systems were modeled with NHPP‐log linear process and HPP belonging to stochastic point process for predicting their reliability in future time frames. Besides the classical approach, Bayesian approach was also used involving Jeffreys's invariant non‐informative independent priors to derive the posterior densities of the model parameters of NHPP‐LLP and HPP with a view to estimating the reliability of the machine systems in future time intervals.

For at least three machine systems, Bayesian approach gave lower reliability estimates and a larger number of (expected) failures than those obtained by the classical approach. Again, Bayesian estimates of the probability that “ROCOF (rate of occurrence of failures) would exceed its upper threshold limit” in future time frames were uniformly higher for these machine systems than those obtained with the classical approach.

This study indicated that, the Bayesian approach would give more realistic estimates of reliability (in future time frames) of the machine systems, which had dependent inter‐failure times. Such information would be helpful to the maintenance team for deciding on appropriate maintenance strategy.

With the help of Bayesian approach, the posterior densities of the model parameters were found analytically by considering Jeffreys's invariant non‐informative independent prior. The case study would serve to motivate the maintenance teams to model the failure patterns of the repairable systems making use of the historical data on inter‐failure times and estimating their reliability in future time frames.

Reliability models are generally estimated from small samples. This paper seeks to calculate the uncertainty affecting reliability parameters in function of the sample size.

The confidence intervals are calculated on the basis of Monte Carlo simulations and using the variance‐covariance matrix; the two methods are compared.

Numerical results for the estimation of uncertainty have been obtained for standard reliability models, non‐homogeneous Poisson process and generalized renewal process.

For the generalized renewal process, the article points out the influence of the age correction factor on the number of repairs authorized and on uncertainty. The surface plot of the likelihood function with respect to parameters is a convenient tool to interpret the uncertainty.

Usually the renewal stochastic processes are used for description of repairable systems performance in the fixed environment. The main characteristic that arises in applications is the mean number of failures or repairs and this is very significant for the spares assessment. In this paper the situation is generalized for the case of changing environment (deterministic or random). The renewal equations for various types of repair, ranging from perfect to minimal via general, are analyzed from the maintenance point of view. Several simple examples are considered.

The software reliability models to describe the reliability growth phenomenon are formulated by any stochastic point process with state‐dependent or time‐dependent intensity function. On the other hand, to deal with the environmental data, which consists of covariates influencing times to software failure, it may be useful to apply the Cox’s proportional hazards model for assessing the software reliability. In this paper, we review the proportional hazards software reliability models and discuss the problem to determine the optimal software release time under the expected total software cost criterion. Numerical examples are devoted to examine the dependence of the covariate structure in both the software reliability prediction and the optimal software release decision.

Considers trend testing in the context of reliability/survival applications. Suggests that the very common tendency in reliability testing to fit lifetime distributions to reliability/maintenance data might occasionally be invalid. Details the appropriate methods to assess the validity, or otherwise, of such a procedure. More specifically, discusses ROCOF curves and the Laplace test for trend, and demonstrates their use by means of a practical, reliability example.

The purpose of this paper is to present a novel method to estimate the optimal software testing time which minimizes the relevant expected software cost via a refined neural network approach with the grouped data, where the multi-stage look ahead prediction is carried out with a simple three-layer perceptron neural network with multiple outputs.

To analyze the software fault count data which follows a Poisson process with unknown mean value function, the authors transform the underlying Poisson count data to the Gaussian data by means of one of three data transformation methods, and predict the cost-optimal software testing time via a neural network.

In numerical examples with two actual software fault count data, the authors compare the neural network approach with the common non-homogeneous Poisson process-based software reliability growth models. It is shown that the proposed method could provide a more accurate and more flexible decision making than the common stochastic modeling approach.

It is shown that the neural network approach can be used to predict the optimal software testing time more accurately.

The unpredictable failure of submersible pump (SP) in groundwater irrigation systems has considerable negative economic consequences. The purpose of this paper is to develop a total cost minimization model that aims to optimize maintenance actions for SP. It reports on simulation-based stochastic scenario analysis for evaluating total cost of maintenance.

Stochastic simulation modeling has been performed for failure of pump motor and corresponding maintenance. Five alternative scenarios were compared for total cost over 15 years starting with empirical data from a northern Ethiopian site. Downtime probabilities and spare part supply uncertainty have been considered in the mathematical model. The model is also validated using multiple ways.

The scenario comparisons indicate that despite the challenges of accessing SP doing one motor rewinding for each purchased pump system upon failure (preferably with shorter supply lead time and variability) seems to result in lowest overall costs for the time horizon considered.

The model should help to make informed practical decision regarding planning and management of SP failure systems in a developing economy context. This should, therefore, lead to better revenue for smallholder farmers and improved food security in similar context.

There are limited number of publications that consider the life cycle costs with stochastic analysis when it comes to maintenance of SPs. To the best of the authors’ knowledge, no paper has previously directly addressed maintenance cost optimization for SP in irrigation. The study could be used to develop more sophisticated stochastic models with more efficient algorithms and consideration of additional sources of stochasticity for such system.