In this paper we develop a mathematical model for a harvested marine bio-resource stock. The stoc... more In this paper we develop a mathematical model for a harvested marine bio-resource stock. The stock consists of two discretely separated sub-stocks which connected by the dispersal of individuals. The model assumes that the production function of each stock follows a logistic equation, hence the full system of the stocks governed by a coupled logistic equation. We discuss a new proportional formula of the maximum sustainable yield (MSY) for each sub-stock and give a numerical simulation to illustrate the application of the formula. The simulation shows that ignoring the existence of the coupling of the system resulting in a lower total harvest from the population.
This paper deals with a stochastic system and maintenance service contract. We consider a situati... more This paper deals with a stochastic system and maintenance service contract. We consider a situation where an agent offers more then one service contract option and a company as the owner has to select the optimal option. This case is typically found in a mining industry where the original equipment manufacturer (OEM) is the only maintenance service provider. As repair time is related to the revenue of the company, service contract options need to consider the repair time target. We consider the repair time target from both the owner and OEM point of views. As an illustration, we give a numerical example with weibull failure distribution
This paper deals with a maintenance service contract for equipment (such as dump-trucks, excavato... more This paper deals with a maintenance service contract for equipment (such as dump-trucks, excavators) sold with two dimensional warranty. We consider a situation where an agent offers more then one service contract options and the owner of equipment (a company) has to select the optimal option. As high availability of the equipment is needed for achieving the revenue of the company, service contract options need to consider target availability. We study the maintenance service contract considering the target availability from both the owner and OEM point of views and use a non-cooperative game formulation to determine the optimal strategy (pricing structure) for the OEM and the optimal option for the owner.
In this paper, we investigate a maintenance service contract for a warranted product carried out ... more In this paper, we investigate a maintenance service contract for a warranted product carried out by the Original Equipment Manufacturer (OEM). The model was developed under the assumption that there are one consumer and one service provider who is the OEM. This is typically applied to the situation where the OEM is the only service provider such as in the mining industry. From the OEM point of view, two contract options were considered, they are: the OEM carried out all repairs and preventive maintenance activities; the OEM carries out failure and the customer undertakes in house preventive maintenance actions. The model uses a non-cooperative game formulation by maximizing expected profits. We use a linear function of failure intensity to consider a product with increasing failure intensity. We obtain the pricing structure in the contract. And for the customer, they can choose the optimal option under the term of contract.
One alternative to prolong a life time of a product is doing a preventive maintenance. The number... more One alternative to prolong a life time of a product is doing a preventive maintenance. The number of failures from the product can be reduced by optimal maintenance policy. This research investigates a periodic maintenance policy for a product sold with a two-dimensional warranty. Actually, this idea is a development of that in Murthy and Wilson (1991). The product failures is modeled using a one-dimensional approach in which usage is a function of age. Furthermore, it is assumed that the relation between these variables is linear. The slope of the line is the usage rate. The optimal periodic maintenance time can be derived by minimizing the expected cost per unit time.We also proved that the expected cost per unit time is a concave function, and gave the global optimal solution. As a numerical example, we choose Weibull distribution with different levels of usage rates. The numerical results show that the increase of usage rate will decrease the length of periodic maintenance time.
In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable... more In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable product sold with a two-dimensional non-renewing failure replacement warranty (NFRW). Modeling failure incorporates usage pattern of the product. For a given usage rate y, the hybrid policy is divided into two periods i.e. (0, S y ] and (S y , τ y ]. Under this policy, for a given usage rate y, the product is repaired minimally when it fails in (0, S y ] and it is replaced with a new one on first failure in (S y , τ y ] or when its age reaches y , whichever occurs first. We obtain the global optimal value S y , for a given τ y which minimizes the expected cost per unit time to the buyer. We present numerical examples to illustrate the properties of the optimal solution.
"This paper deals with a mathematical model for periodic replacement policy based on the number o... more "This paper deals with a mathematical model for periodic replacement policy based on the number of failures. The product is sold with a two-dimensional non-renewing failure replacement warranty. We model product failures using the one-dimensional approach which allows to modeling the effect of age and usage to the product's degradation. Under the periodic replacement policy, for a given usage rate y, the product is repaired with minimal repair when it fails at the first n-1 failures and it is replaced with a new one at n-th failure. We obtain the global optimal values of failures which minimizes the expected cost per unit time to the buyer and give a numerical example to illustrate the optimal solution.
Keywords: periodic replacement, two-dimensional warranty, global solution"
In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable... more In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable product sold with a two-dimensional non-renewing failure replacement warranty. We first model product failures using the one-dimensional approach and then use a more appropriate formulation to model the effect of age and usage to the product degradation. Under this policy, for a given usage rate y, the product is directly repaired minimally when it fails in (0,Sy] and replaced with the new one on the first failure in (Sy, τy] or when its age reaches , whichever occurs first. We obtain the global optimal solution of Sy, for a given τy which minimizes the expected cost per unit time to the buyer. We present numerical examples to illustrate the properties of the optimal solution.
Keywords: hybrid; minimal repair; age replacement; usage rate, repairable, product degradation, non-renewing failure replacement warranty, two-dimensional warranty, expected cost per unit time, renewal reward theorem, optimization.
Many researchers have shown renewal reward theorem for one dimensional warranty (age). However, n... more Many researchers have shown renewal reward theorem for one dimensional warranty (age). However, nowadays many manufacturers consider the age and usage (distance) as warranty coverage. Here, we show how the renewal reward theorem applied in two dimensional warranty. To simplify the model, we use conditional probability for given usage pattern. This work is initially carried out by Husniah et al. in the APIEMS 2010 proceeding.
This paper deals with a periodic replacement policy based on the number of failures after the exp... more This paper deals with a periodic replacement policy based on the number of failures after the expiry of warranty. The product is sold with a two-dimensional non-renewing failure replacement warranty. We model product failures using the one-dimensional approach which allows to modelling the effect of age and usage to the product's degradation. Under the periodic replacement theory, for a given usage rate y, the product is repaired with minimal repair when it fails at the firts n-1 failures and it is replaced with a new one at n-th failure. We obtain the optimal values of n which minimizes the expected cost per unit time to the buyer and give a numerical example to illustrate the optimal solution.
This paper deals with a hybrid minimal repair and age replacement policy after the expiry of warr... more This paper deals with a hybrid minimal repair and age replacement policy after the expiry of warranty for a repairable product sold with a non-renewing failure replacement warranty. Parameters of such policy are defined as 0 T and T which indicate as minimally repair time and planned replacement time respectively. Under the hybrid policy, the product with one dimensional warranty W is repaired minimally when it fails during [0,T0 ] and with a failure replacement on first failure after 0 T or a planned
replacement at time T , whichever occurs first. For a givenT , we obtain the optimal value 0 T which minimizes the expected cost per unit time to the buyer. A numerical example is given to illustrate the properties of the optimal solution.
Keywords: Hybrid maintenance policy, One-dimensional warranty, the expected cost per unit time.
This paper deals with a periodic replacement policy after the expiry of a warranty for a product ... more This paper deals with a periodic replacement policy after the expiry of a warranty for a product sold with a two-dimensional non-renewing failure replacement warranty. We model product failures using the one-dimensional approach and use a more appropriate formulation to model the effect of age and usage to the product’s degradation. Under the periodic replacement policy, for a given usage rate y, the product is repaired with minimal repair when it fails at age x, x<τy and it is replaced with a new one if its age reaches τy. We obtain the optimal value of τy which minimizes the long-run average cost to the buyer and give a numerical example to illustrate the optimal solution.
Keywords: Periodic replacement policy, Two-dimensional warranty, Long-run average cost, Accelerated failure time (AFT) model.
The thesis is concerned with the investigation of the economic life of a specific public transpor... more The thesis is concerned with the investigation of the economic life of a specific public transport (angkutan kota or angkot), both theoretically and practically.
Theoretically, the economic life of the public transport is studied using mathematical models within various categories, namely, discrete model, continuous model, deterministic model and stochastic model. A new approach of a continuous stochastic model is explored as a modification of a continuous deterministic model previously developed by Bethuyne.
Practically, the computation of the economic life of the public transport for certain trajectory in Bandung, that is the angkot serving the route of Margahayu Raya -- Ledeng, is discussed in this thesis. Several conclusions are found, among them is that the economic life of the angkot is affected by the level of the interest rate and the utility rate used in the computation. Further, it can also be concluded that the increase of the level of the interest rate increases the computed economic life of the angkot while the increase of the utility rate decreases the computed economic life of the angkot.
The existence and uniqueness of solution is among the paramount of many mathematical problems, wi... more The existence and uniqueness of solution is among the paramount of many mathematical problems, without which quantitative and qualitative properties of the solution may not be meaningful. In this paper we discuss the existence and uniqueness of solution of an optimization problem arising in replacement theory. We search sufficient conditions for a total cost function to have a unique optimal replacement time and found that if it is positive and concave up then it always has a unique optimal replacement time.
Dalam paper ini dibahas penentuan umur ekonomis suatu kendaraan. Untuk memperoleh umur ekonomis t... more Dalam paper ini dibahas penentuan umur ekonomis suatu kendaraan. Untuk memperoleh umur ekonomis tersebut dibuat sebuah model matematika dan umur ekonomis dapat diperoleh dalam bentuk persamaan implisit. Sebuah contoh aplikasi juga diberikan.
In this paper we discuss a learning curve or manufacturing progress curve of an industrial proces... more In this paper we discuss a learning curve or manufacturing progress curve of an industrial process.
An equation describing this process will be derived by solving a modified logistic differential equation. This derivation is slightly different to that usually done in many industrial engineering literatures. It is shown that the solution to this modified equation satisfies all properties needed by a manufacturing learning curve.
In this paper we discus a method to find the values of parameters in a manufacturing progress cur... more In this paper we discus a method to find the values of parameters in a manufacturing progress curve based on three points of data. In general to find better parameter estimation we need a lot of data. However, in some circumstances, the numbers of data are limited or even scarce, especially in the beginning of a manufacturing process. For this reason, we develop a simple method to determine the values of parameters if only three data are available. The curve we are dealing with is an inverse-like sigmoid that can describe a learning process in the beginning phase and has a lower bound in the long-term phase, hence a reasonably realistic curve.
Inverted S-Curve plays important roles in industrial data analysis, e.g., the numbers of product... more Inverted S-Curve plays important roles in industrial data analysis, e.g., the numbers of production errors could be modeled using this kind of curve. In this paper we discuss how to obtain such curve and how to estimate the parameters of the resulting curve by modifying the method of the three points of data.
In this paper we develop a mathematical model for a harvested marine bio-resource stock. The stoc... more In this paper we develop a mathematical model for a harvested marine bio-resource stock. The stock consists of two discretely separated sub-stocks which connected by the dispersal of individuals. The model assumes that the production function of each stock follows a logistic equation, hence the full system of the stocks governed by a coupled logistic equation. We discuss a new proportional formula of the maximum sustainable yield (MSY) for each sub-stock and give a numerical simulation to illustrate the application of the formula. The simulation shows that ignoring the existence of the coupling of the system resulting in a lower total harvest from the population.
This paper deals with a stochastic system and maintenance service contract. We consider a situati... more This paper deals with a stochastic system and maintenance service contract. We consider a situation where an agent offers more then one service contract option and a company as the owner has to select the optimal option. This case is typically found in a mining industry where the original equipment manufacturer (OEM) is the only maintenance service provider. As repair time is related to the revenue of the company, service contract options need to consider the repair time target. We consider the repair time target from both the owner and OEM point of views. As an illustration, we give a numerical example with weibull failure distribution
This paper deals with a maintenance service contract for equipment (such as dump-trucks, excavato... more This paper deals with a maintenance service contract for equipment (such as dump-trucks, excavators) sold with two dimensional warranty. We consider a situation where an agent offers more then one service contract options and the owner of equipment (a company) has to select the optimal option. As high availability of the equipment is needed for achieving the revenue of the company, service contract options need to consider target availability. We study the maintenance service contract considering the target availability from both the owner and OEM point of views and use a non-cooperative game formulation to determine the optimal strategy (pricing structure) for the OEM and the optimal option for the owner.
In this paper, we investigate a maintenance service contract for a warranted product carried out ... more In this paper, we investigate a maintenance service contract for a warranted product carried out by the Original Equipment Manufacturer (OEM). The model was developed under the assumption that there are one consumer and one service provider who is the OEM. This is typically applied to the situation where the OEM is the only service provider such as in the mining industry. From the OEM point of view, two contract options were considered, they are: the OEM carried out all repairs and preventive maintenance activities; the OEM carries out failure and the customer undertakes in house preventive maintenance actions. The model uses a non-cooperative game formulation by maximizing expected profits. We use a linear function of failure intensity to consider a product with increasing failure intensity. We obtain the pricing structure in the contract. And for the customer, they can choose the optimal option under the term of contract.
One alternative to prolong a life time of a product is doing a preventive maintenance. The number... more One alternative to prolong a life time of a product is doing a preventive maintenance. The number of failures from the product can be reduced by optimal maintenance policy. This research investigates a periodic maintenance policy for a product sold with a two-dimensional warranty. Actually, this idea is a development of that in Murthy and Wilson (1991). The product failures is modeled using a one-dimensional approach in which usage is a function of age. Furthermore, it is assumed that the relation between these variables is linear. The slope of the line is the usage rate. The optimal periodic maintenance time can be derived by minimizing the expected cost per unit time.We also proved that the expected cost per unit time is a concave function, and gave the global optimal solution. As a numerical example, we choose Weibull distribution with different levels of usage rates. The numerical results show that the increase of usage rate will decrease the length of periodic maintenance time.
In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable... more In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable product sold with a two-dimensional non-renewing failure replacement warranty (NFRW). Modeling failure incorporates usage pattern of the product. For a given usage rate y, the hybrid policy is divided into two periods i.e. (0, S y ] and (S y , τ y ]. Under this policy, for a given usage rate y, the product is repaired minimally when it fails in (0, S y ] and it is replaced with a new one on first failure in (S y , τ y ] or when its age reaches y , whichever occurs first. We obtain the global optimal value S y , for a given τ y which minimizes the expected cost per unit time to the buyer. We present numerical examples to illustrate the properties of the optimal solution.
"This paper deals with a mathematical model for periodic replacement policy based on the number o... more "This paper deals with a mathematical model for periodic replacement policy based on the number of failures. The product is sold with a two-dimensional non-renewing failure replacement warranty. We model product failures using the one-dimensional approach which allows to modeling the effect of age and usage to the product's degradation. Under the periodic replacement policy, for a given usage rate y, the product is repaired with minimal repair when it fails at the first n-1 failures and it is replaced with a new one at n-th failure. We obtain the global optimal values of failures which minimizes the expected cost per unit time to the buyer and give a numerical example to illustrate the optimal solution.
Keywords: periodic replacement, two-dimensional warranty, global solution"
In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable... more In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable product sold with a two-dimensional non-renewing failure replacement warranty. We first model product failures using the one-dimensional approach and then use a more appropriate formulation to model the effect of age and usage to the product degradation. Under this policy, for a given usage rate y, the product is directly repaired minimally when it fails in (0,Sy] and replaced with the new one on the first failure in (Sy, τy] or when its age reaches , whichever occurs first. We obtain the global optimal solution of Sy, for a given τy which minimizes the expected cost per unit time to the buyer. We present numerical examples to illustrate the properties of the optimal solution.
Keywords: hybrid; minimal repair; age replacement; usage rate, repairable, product degradation, non-renewing failure replacement warranty, two-dimensional warranty, expected cost per unit time, renewal reward theorem, optimization.
Many researchers have shown renewal reward theorem for one dimensional warranty (age). However, n... more Many researchers have shown renewal reward theorem for one dimensional warranty (age). However, nowadays many manufacturers consider the age and usage (distance) as warranty coverage. Here, we show how the renewal reward theorem applied in two dimensional warranty. To simplify the model, we use conditional probability for given usage pattern. This work is initially carried out by Husniah et al. in the APIEMS 2010 proceeding.
This paper deals with a periodic replacement policy based on the number of failures after the exp... more This paper deals with a periodic replacement policy based on the number of failures after the expiry of warranty. The product is sold with a two-dimensional non-renewing failure replacement warranty. We model product failures using the one-dimensional approach which allows to modelling the effect of age and usage to the product's degradation. Under the periodic replacement theory, for a given usage rate y, the product is repaired with minimal repair when it fails at the firts n-1 failures and it is replaced with a new one at n-th failure. We obtain the optimal values of n which minimizes the expected cost per unit time to the buyer and give a numerical example to illustrate the optimal solution.
This paper deals with a hybrid minimal repair and age replacement policy after the expiry of warr... more This paper deals with a hybrid minimal repair and age replacement policy after the expiry of warranty for a repairable product sold with a non-renewing failure replacement warranty. Parameters of such policy are defined as 0 T and T which indicate as minimally repair time and planned replacement time respectively. Under the hybrid policy, the product with one dimensional warranty W is repaired minimally when it fails during [0,T0 ] and with a failure replacement on first failure after 0 T or a planned
replacement at time T , whichever occurs first. For a givenT , we obtain the optimal value 0 T which minimizes the expected cost per unit time to the buyer. A numerical example is given to illustrate the properties of the optimal solution.
Keywords: Hybrid maintenance policy, One-dimensional warranty, the expected cost per unit time.
This paper deals with a periodic replacement policy after the expiry of a warranty for a product ... more This paper deals with a periodic replacement policy after the expiry of a warranty for a product sold with a two-dimensional non-renewing failure replacement warranty. We model product failures using the one-dimensional approach and use a more appropriate formulation to model the effect of age and usage to the product’s degradation. Under the periodic replacement policy, for a given usage rate y, the product is repaired with minimal repair when it fails at age x, x<τy and it is replaced with a new one if its age reaches τy. We obtain the optimal value of τy which minimizes the long-run average cost to the buyer and give a numerical example to illustrate the optimal solution.
Keywords: Periodic replacement policy, Two-dimensional warranty, Long-run average cost, Accelerated failure time (AFT) model.
The thesis is concerned with the investigation of the economic life of a specific public transpor... more The thesis is concerned with the investigation of the economic life of a specific public transport (angkutan kota or angkot), both theoretically and practically.
Theoretically, the economic life of the public transport is studied using mathematical models within various categories, namely, discrete model, continuous model, deterministic model and stochastic model. A new approach of a continuous stochastic model is explored as a modification of a continuous deterministic model previously developed by Bethuyne.
Practically, the computation of the economic life of the public transport for certain trajectory in Bandung, that is the angkot serving the route of Margahayu Raya -- Ledeng, is discussed in this thesis. Several conclusions are found, among them is that the economic life of the angkot is affected by the level of the interest rate and the utility rate used in the computation. Further, it can also be concluded that the increase of the level of the interest rate increases the computed economic life of the angkot while the increase of the utility rate decreases the computed economic life of the angkot.
The existence and uniqueness of solution is among the paramount of many mathematical problems, wi... more The existence and uniqueness of solution is among the paramount of many mathematical problems, without which quantitative and qualitative properties of the solution may not be meaningful. In this paper we discuss the existence and uniqueness of solution of an optimization problem arising in replacement theory. We search sufficient conditions for a total cost function to have a unique optimal replacement time and found that if it is positive and concave up then it always has a unique optimal replacement time.
Dalam paper ini dibahas penentuan umur ekonomis suatu kendaraan. Untuk memperoleh umur ekonomis t... more Dalam paper ini dibahas penentuan umur ekonomis suatu kendaraan. Untuk memperoleh umur ekonomis tersebut dibuat sebuah model matematika dan umur ekonomis dapat diperoleh dalam bentuk persamaan implisit. Sebuah contoh aplikasi juga diberikan.
In this paper we discuss a learning curve or manufacturing progress curve of an industrial proces... more In this paper we discuss a learning curve or manufacturing progress curve of an industrial process.
An equation describing this process will be derived by solving a modified logistic differential equation. This derivation is slightly different to that usually done in many industrial engineering literatures. It is shown that the solution to this modified equation satisfies all properties needed by a manufacturing learning curve.
In this paper we discus a method to find the values of parameters in a manufacturing progress cur... more In this paper we discus a method to find the values of parameters in a manufacturing progress curve based on three points of data. In general to find better parameter estimation we need a lot of data. However, in some circumstances, the numbers of data are limited or even scarce, especially in the beginning of a manufacturing process. For this reason, we develop a simple method to determine the values of parameters if only three data are available. The curve we are dealing with is an inverse-like sigmoid that can describe a learning process in the beginning phase and has a lower bound in the long-term phase, hence a reasonably realistic curve.
Inverted S-Curve plays important roles in industrial data analysis, e.g., the numbers of product... more Inverted S-Curve plays important roles in industrial data analysis, e.g., the numbers of production errors could be modeled using this kind of curve. In this paper we discuss how to obtain such curve and how to estimate the parameters of the resulting curve by modifying the method of the three points of data.
Uploads
Papers by Hennie Husniah
Keywords: periodic replacement, two-dimensional warranty, global solution"
Keywords: hybrid; minimal repair; age replacement; usage rate, repairable, product degradation, non-renewing failure replacement warranty, two-dimensional warranty, expected cost per unit time, renewal reward theorem, optimization.
replacement at time T , whichever occurs first. For a givenT , we obtain the optimal value 0 T which minimizes the expected cost per unit time to the buyer. A numerical example is given to illustrate the properties of the optimal solution.
Keywords: Hybrid maintenance policy, One-dimensional warranty, the expected cost per unit time.
Keywords: Periodic replacement policy, Two-dimensional warranty, Long-run average cost, Accelerated failure time (AFT) model.
Theoretically, the economic life of the public transport is studied using mathematical models within various categories, namely, discrete model, continuous model, deterministic model and stochastic model. A new approach of a continuous stochastic model is explored as a modification of a continuous deterministic model previously developed by Bethuyne.
Practically, the computation of the economic life of the public transport for certain trajectory in Bandung, that is the angkot serving the route of Margahayu Raya -- Ledeng, is discussed in this thesis. Several conclusions are found, among them is that the economic life of the angkot is affected by the level of the interest rate and the utility rate used in the computation. Further, it can also be concluded that the increase of the level of the interest rate increases the computed economic life of the angkot while the increase of the utility rate decreases the computed economic life of the angkot.
An equation describing this process will be derived by solving a modified logistic differential equation. This derivation is slightly different to that usually done in many industrial engineering literatures. It is shown that the solution to this modified equation satisfies all properties needed by a manufacturing learning curve.
Keywords: Manufacturing progress curve, curve fitting, sigmoid curve
Keywords: periodic replacement, two-dimensional warranty, global solution"
Keywords: hybrid; minimal repair; age replacement; usage rate, repairable, product degradation, non-renewing failure replacement warranty, two-dimensional warranty, expected cost per unit time, renewal reward theorem, optimization.
replacement at time T , whichever occurs first. For a givenT , we obtain the optimal value 0 T which minimizes the expected cost per unit time to the buyer. A numerical example is given to illustrate the properties of the optimal solution.
Keywords: Hybrid maintenance policy, One-dimensional warranty, the expected cost per unit time.
Keywords: Periodic replacement policy, Two-dimensional warranty, Long-run average cost, Accelerated failure time (AFT) model.
Theoretically, the economic life of the public transport is studied using mathematical models within various categories, namely, discrete model, continuous model, deterministic model and stochastic model. A new approach of a continuous stochastic model is explored as a modification of a continuous deterministic model previously developed by Bethuyne.
Practically, the computation of the economic life of the public transport for certain trajectory in Bandung, that is the angkot serving the route of Margahayu Raya -- Ledeng, is discussed in this thesis. Several conclusions are found, among them is that the economic life of the angkot is affected by the level of the interest rate and the utility rate used in the computation. Further, it can also be concluded that the increase of the level of the interest rate increases the computed economic life of the angkot while the increase of the utility rate decreases the computed economic life of the angkot.
An equation describing this process will be derived by solving a modified logistic differential equation. This derivation is slightly different to that usually done in many industrial engineering literatures. It is shown that the solution to this modified equation satisfies all properties needed by a manufacturing learning curve.
Keywords: Manufacturing progress curve, curve fitting, sigmoid curve