This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a r...This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a recurrent process and admit recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving like t-v with 1 v as t → ∞. The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated exponential law with CDF H(y) = P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made between heavy tailed mean waiting time to break down and light tailed mean waiting time to break down values. The recruitment policy operating under the heavy tailed case is shown to be more economical in all types of manpower systems.展开更多
The recently experienced hype concerning the so-called “4<sup>th</sup> Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production S...The recently experienced hype concerning the so-called “4<sup>th</sup> Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.展开更多
文摘This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a recurrent process and admit recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving like t-v with 1 v as t → ∞. The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated exponential law with CDF H(y) = P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made between heavy tailed mean waiting time to break down and light tailed mean waiting time to break down values. The recruitment policy operating under the heavy tailed case is shown to be more economical in all types of manpower systems.
文摘The recently experienced hype concerning the so-called “4<sup>th</sup> Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.
