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Reliability analysis is the key to evaluate software's quality. Since the early 1970s, the Power Law Process, among others, has been used to assess the rate of change of software reliability as time-varying function by using its intensity function. The Bayesian analysis applicability to the Power Law Process is justified using real software failure times. The choice of a loss function is an important entity of the Bayesian settings. The analytical estimate of likelihood-based Bayesian reliability estimates of the Power Law Process under the squared error and Higgins-Tsokos loss functions were obtained for different prior knowledge of its key parameter. As a result of a simulation analysis and using real data, the Bayesian reliability estimate under the Higgins-Tsokos loss function not only is robust as the Bayesian reliability estimate under the squared error loss function but also performed better, where both are superior to the maximum likelihood reliability estimate. A sensitivity analysis resulted in the Bayesian estimate of the reliability function being sensitive to the prior, whether parametric or non-parametric, and to the loss function. An interactive user interface application was additionally developed using Wolfram language to compute and visualize the Bayesian and maximum likelihood estimates of the intensity and reliability functions of the Power Law Process for a given data.

Variable selection is crucial issue for high dimensional data modeling, where sample size is smaller compared to number of variables. Recently, majority scoring of filter measures in PLS (MS-PLS) is introduced for variable selection in high dimensional data. Filter measures are not greedy for optimal performance, hence we have proposed majority scoring with backward elimination in PLS (MSBE-PLS). In MSBE-PLS we have considered variable importance on projection (VIP) and selectivity ratio (SR). In each iteration of backward elimination in PLS variables are considered influential if they were selected by both filter indicator. The proposed method is implemented for corn’s and diesel’s content prediction. The corn contents include protein, oil, starch and moisture while diesel contents include boiling point at 50% recovery, cetane number, density, freezing temperature of the fuel, total aromatics, and viscosity. The proposed method outperforms in terms of RMSE when compared with reference methods. In addition to validating the spectrum models, data properties are also examined for explaining prediction behaviors. Moreover, MSBE-PLS select the moderate number of influential variables, hence it presents the parsimonious model for predicting contents based on spectrum data.

The Power Law Process, also known as Non-Homogeneous Poisson Process, has been used in various aspects, one of which is the software reliability assessment. Specifically, by using its intensity function to compute the rate of change of a software reliability as time-varying function. Justification of Bayesian analysis applicability to the Power Law Process was shown using real data. The probability distribution that best characterizes the behavior of the key parameter of the intensity function was first identified, then the likelihood-based Bayesian reliability estimate of the Power Law Process under the Higgins-Tsokos loss function was obtained. As a result of a simulation study and using real data, the Bayesian estimate shows an outstanding performance compared to the maximum likelihood estimate using different sample sizes. In addition, a sensitivity analysis was performed, resulting in the Bayesian estimate being sensitive to the prior selection; whether parametric or non-parametric.

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