Geometric and Geometric-Like Processes and Their Applications in Warranty Analysis

Nonzero repair times dependent on the failure hazard

“…The review by Arnold et al found that most of the attention on nonzero repair to date has focussed on geometric and geometric‐like processes. The model we present here represents an alternative means of approaching the problem, and we expect the modelling of nonzero repair times will attract increasing attention in the literature through a broader class of models.…”

“…A variety of extensions of the GP, which we refer to as geometric‐like processes (GLPs), have been proposed to address an even wider range of scenarios and trends . For a review of GLPs, the reader is referred to Arnold et al In the setting of alternating operating and (nonzero) repair times, Arnold et al have provided models where the operating times and repair times follow decreasing and increasing geometric processes, respectively.…”

Some Extended Geometric Processes and Their Estimation Methods

“…Mean squared error [26]- [29], [31]- [34], [36]- [38], [40], [41], [43] Coverage percentage [42] and predicting the number of warranty claims etc. Several existing research publications have reviewed [7], [47]. In this article, we would like to focus on other applications of the GP-like models.…”

“…This phenomenon can be described by the geometric process (GP), which was first introduced by [1]. Since then, the GP has been widely applied in different fields such as software reliability analysis [2], [3], reliability analysis [4], maintenance policy optimisation [5], [6], warranty analysis [7] and electricity pricing, etc. [8]- [11].…”

“…[8]- [11]. Besides, the multiple extensions of the GP has been introduced: the arithmetic geometric process (AGP) [12], the α-series process (α-series) [13], the threshold geometric process (TGP) [14], the extended poisson process (EPP) [15], the exponent extended geometric process (EEGP) [16], the extended geometric process (EGP) [17], the doubly geometric process (DGP) [18], the semi-geometric process (SGP) [19], the alternating geometric process (alternating GP) [7], and the double ratio geometric process (DRGP) [20].…”