On a New Point Process Approach to Reliability Improvement Modeling for Repairable SystemsFinkelstein, Maxim; Cha, Ji Hwan
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2906
In this paper, we are the first to consider the combination of the minimal repair with the defined better than minimal repair. With a given probability, each failure of a repairable system is minimally repaired and with complementary probability it is better than minimally repaired. The latter can be interpreted in terms of a reliability growth model when a defect of a system is eliminated on each failure. It turns out that the better than minimal repair can be even better than a perfect one if a perfect repair is understood as a replacement of the whole system or stochastically equivalent operation. We provide stochastic description of the failure/repair process by introducing and describing the corresponding bivariate point process via the concept of stochastic intensity. Distributions for the number of failures for the pooled and marginal processes are derived along with their expected values. The latter can describe the process of reliability growth in applications. Some meaningful special cases are discussed.
Is (Independent) Subordination Relevant in Equity Derivatives?Azzone, Michele; Baviera, Roberto
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2904
Monroe (1978) demonstrates that any local semimartingale can be represented as a time‐changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time‐change are independent? We prove that a local semimartingale is not equivalent to a BM with a time‐change that is independent from the BM. Our result is obtained utilizing a class of additive processes: the additive normal tempered stable (ATS). This class of processes exhibits an exceptional ability to calibrate the equity volatility surface accurately. We notice that the sub‐class of additive processes that can be obtained with an independent additive subordination is incompatible with market data and shows significantly worse calibration performances than the ATS, especially on short time maturities. These results have been observed every business day in a semester on a dataset of S&P 500 and EURO STOXX 50 options.
Comparison Between Hierarchical Time Series Forecasting Approaches for the Electricity Consumption in the Brazilian Industrial SectorMesquita Lopes Cabreira, Marlon; Leite Coelho da Silva, Felipe; da Silva Cordeiro, Josiane; Ureta Tolentino, Jeremias Macias; Carbo‐Bustinza, Natalí; Canas Rodrigues, Paulo; López‐Gonzales, Javier Linkolk
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2907
In Brazil, the industrial sector is the largest electricity consumer. Therefore, energy planning becomes important for industrial development. Electricity consumption data in the Brazilian industrial sector can be organized into a hierarchical structure composed of each geographic region (South, Southeast, Center‐West, Northeast, and North) and their respective states. This work aims to evaluate the predictive capacity of the bottom‐up, top‐down, and optimal combination approaches used to obtain electricity consumption forecasting in the Brazilian industrial sector. These approaches were integrated with the predictive models of exponential smoothing, Box and Jenkins, and neural networks. The results showed that the bottom‐up approach integrated with the Long Short‐Term Memory (LSTM) model provided the best predictions and outperformed the other hierarchical forecasting approaches with an average MAPE of less than 3%.
Start Over After Pre‐Empt (SOAP) ProtocolSethuraman, Jayaram
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2902
Consider a job that normally requires a$$ a $$ units of time to complete. A higher authority comes and interrupts the service. The inter‐arrival times of the interrupts are X1,X2,⋯$$ {X}_1,{X}_2,\cdots $$, which are the actual available service times to work on the job. Thus, if the first available service time X1$$ {X}_1 $$ is larger than a$$ a $$, the job gets completed, and the remaining service time X1−a$$ {X}_1-a $$ is the first available service time for the next job. If not, the previous service is lost and service on the job starts from scratch using X2$$ {X}_2 $$ the next available service time. As before, if X2≥a$$ {X}_2\ge a $$, the job gets completed and the remaining service time X2−a$$ {X}_2-a $$ is the first available service time for the next job. If not, the service is lost, and X3$$ {X}_3 $$ is the available service time for the job. And so on. Let Ta$$ {T}_a $$ be the time to complete the job. This is called the start over after pre‐empt (SOAP) protocol. An example of such interrupts is power outages. After a power outage interrupt the partial service on a job running on a computer is lost and service on the job has to start again. We study properties of Ta$$ {T}_a $$ and Ta,b$$ {T}_{a,b} $$, the time to complete two jobs normally requiring times a,b$$ a,b $$, and give some guidance whether E(Ta,b)≤E(Tb,a)$$ E\left({T}_{a,b}\right)\le E\left({T}_{b,a}\right) $$ when a<b$$ a<b $$. We obtain the asymptotic distribution of a stochastic process based on Ta$$ {T}_a $$ which has interesting independent increments of a new type. My frustrations standing in a queue in India, where a supervisor interrupts and the service on my job has to start again, were my inspiration for the protocol named here as SOAP. A careful referee pointed out that the SOAP protocol is not new in the queues literature. It goes by the name RESTART and has variants called RESUME and REPLACE.