Abstract The present study develops a stochastic process model for a series-configured manufacturing system incorporating functionally interconnected subsystems, wherein the performance of each unit directly influences the operational continuity of the entire plant. Since the functioning of each subsystem is dependent on the operational condition of the others, the reliability of the entire production process is strongly influenced by subsystem performance and maintenance effectiveness. The study incorporates seasonal environmental variations and maintenance policies to evaluate both technical and economic measures of the system. To strengthen operational continuity and enhance production efficiency, a cold standby unit is provided for the spinning subsystem. The system includes cutting, pressing, spinning, and polishing & packing subsystems operating sequentially to convert raw materials into finished products. Seasonal temperature variations are considered due to their direct influence on equipment degradation, lubrication effectiveness, machine efficiency, and maintenance requirements. The stochastic behavior of the system is analyzed through a Markov process combined with a regenerative point methodology to derive important performance indices.
Abstract The study examines the relationship between the Lévy measure of the immigration flux of particles, the branching mechanism, and the limit conditional law (LCL) of Markov branching processes (MBP). The aim is to obtain a given stationary distribution for a subcritical branching process with immigration. To achieve this, the work focuses on the particular cases in which the LCL is defined by the Borel, logarithmic, and geometric distributions. The convergence of the extended Sibuya law to the logarithmic series is also discussed. In particular, when the Lévy measure of the immigration coincides with the LCL, the stationary distribution is a compound Poisson law with the same Lévy measure. The Neyman–Scott (NS) immigration process provides a counterexample to this case, because its Lévy measure given by the zero-truncated Poisson distribution is log-concave. The stationary distribution of the NS immigration process with linear death branching is characterized by the special function known as the modified exponential integral, namely Ein ( z ) \operatorname{Ein}(z) . Some counterexamples are more interesting than examples.
Abstract Exit of employees is a common phenomenon in any manpower system. It is not wise to make recruitment frequently due to cost factor. In this paper, a single grade manpower system is considered in which clusters of voluntary and involuntary exits of employees are triggered by each policy decision taken at random epochs in ( 0 , ∞ ) (0,\infty) . A class of times to recruitment is defined for two stochastic models by considering two thresholds for different specific choices of loss of manhours due to these decisions. Analytical results for some performance measures related to the class of times to recruitment are determined under the conditions (i) number of clusters of exits for each policy decision form a sequence of independent and identically distributed random variables (ii) loss of manhours due to the classified exits in any cluster are independent and identically distributed random variables and (iii) the system has two thresholds which are non-identically distributed random variables following Lindley distribution in Model-1 and constants thresholds in Model-2. Assuming specific distributions, the analytical results are numerically illustrated to show how the monotonicity of expected time to recruitment changes when the nodal parameters increase, one at a time.
Abstract The overlap coefficient (OVL) is widely used to quantify the similarity between two probability distributions, with applications in agriculture, quality control, and related fields. This study evaluates four OVL estimators: two nonparametric methods, the histogram-based estimator and the kernel density estimator (KDE), and two parametric estimators under the binormal model, with and without Box–Cox transformation, in terms of bias and root mean squared error (RMSE). A simulation study examined estimator behavior under normal, approximately normalizable, and strongly non-normal distributions. Results indicate that the KDE provides more stable and accurate nonparametric estimates than the histogram method, while parametric estimators perform best when normality assumptions hold. The Box–Cox transformation provides a robust approach to transform to normality allowing for the use of the binormal model even when normality assumptions fail. The methods were also applied to a dataset on apple quality attributes to illustrate their performance in a real agricultural quality-control context. The empirical findings support the simulation results: KDE yields stable nonparametric estimates, and parametric estimators produce larger OVL values when normality is satisfied. These results offer practical guidance for selecting appropriate OVL estimators in agricultural and quality-control applications.
Abstract A Markov approach has been used to perform RAM (Reliability, Availability and Maintainability) analysis for a parallel system consisting of two non-identical units. Preventive maintenance is incorporated to reduce the risk of unexpected failures. One unit does not fail during maintenance and is fully restored. The analysis is based on the Chapman–Kolmogorov equations, which are solved using the Laplace transform method with Mathematica version 12.30. The failure and repair rates of the units are assumed to be constant, implying that the times follow a negative exponential distribution. A cost-benefit analysis has also been carried out using specific values for the failure and repair rates. Sensitivity analysis is conducted to examine the influence of system parameters on performance measures, with results presented through tables and graphical illustrations. Furthermore, a cost-benefit analysis is performed to evaluate the economic viability of the system under different operational scenarios. To highlight the practical relevance of the study, real-world applications have been discussed, particularly focusing on the functioning of Automated Teller Machines (ATMs) and Green Channel counters in banks.
