In the recent trends, production plants in the automobile industries all over the world are facing a lot of challenges to achieve better productivity and customer satisfaction due to increasing the passenger’s necessity and demand for transportation. In this direction, the belt, tyre, and tube manufacturing plants act as vital roles in the day-to-day life of the automobile industries. Tyre production plant comprises five major units, namely, raw material selection, preparation, tyre components, finishing, and inspection. The main purpose of this research is to implement the new method to predict the most critical subsystems in the tyre manufacturing system of the rubber industry. As mathematically, any one maintenance parameter among reliability, availability, maintainability, and dependability (RAMD) parameters is evaluated to identify the critical subsystems and their effect on the effectiveness of the tyre production system. In this research, the effect of variation in maintenance indices, RAMD, is measured to identify the critical subsystem of the tyre production system based on the mathematical modeling Markov birth-death approach (MBDA), and the equations of the subsystems are derived by using the Chapman–Kolmogorov method. Besides, it also calculates the performance of certain maintenance parameters concerning time such as mean time between failures (MTBF), mean time to repair (MTTR), and dependability ratio for each subsystem of the tyre production system. Finally, RAMD analysis of the tyre production systems has been executed for predicting the most critical subsystem by changing the rates of failure and repair of individual subsystems with the utilization of MATLAB software. RAMD analysis reveals that the subsystem bias cutting is most critical with the minimum availability of 0.8387, dependability 5.19, dependability ratio 0.8701, and maximum MTTR 38.46 hours of the subsystem. In this implementation of the proposed method, a real-time case study of the industrial repairable system of tyre manufacturing system has been taken for evaluating RAMD indices of the production plant of rubber industry cited in the southern region of Tamil Nadu, India.
In the recent trends, in the last few decades, logistics and transportation have rapidly increased throughout the world due to the customers or passenger’s necessity, and the population explosion. In that situation, the demand for the automobile industrial product (tyre, tube, and belt) manufacturing also maximized. The manufacturing process of the automobile industry consists of lots of subsystems and components. The effectiveness of the entire production system closely depends on the availability of the individual machines and their critical components [
Performance evaluation of the milk production industry is described, and the reliability and availability of the milk production systems are analyzed through the application of the MINITAB software package with the different mathematical analysis techniques of RAM engineering. Also, the RAM of all individual workstations in the dairy industry is evaluated [
A real case study of planning the tunnel construction problems is described, and the suitable and optimal planning of the tunnel evacuation process is predicted through the simulation techniques such as Markov chain and Monte Carlo simulation techniques. With this proposed model, the optimal planning model has been implemented with reduced total cycle time of the tunnel evacuation process [
Conditional maintenance strategy simulation and sensitivity analysis model with energy consumption and carbon dioxide emissions of the production system are explained to the reduction of the total maintenance cost, environmental impact, and improvement of maintenance plan [
The reliability analysis of the milk powder production system is conducted in dairy plants with the application of the Markov process and RAMD approach. The proposed results identified the critical subsystem in the milk powder production system with concerning variation in the values of major maintenance parameters [
We investigate the availability and profit of the power generation in the sewage treatment plant through the application of the MBDA with exponential distribution mathematical technique. It reveals the effect of variations in the availability changes of sewage treatment plants [
This research consists of an overview of the research approaches, applications, and challenges mentioned above. This research paper is based on the performance analysis and mathematical model of the tyre manufacturing system in the rubber industry to predict the most critical subsystems in the work environment using the RAMD and Markov birth-death approach. This research technique is widely used for RAM engineering because the upcoming behaviors of a particular machine can be easily predicted by analyzing the current variables of the machine. The main motive of this research analysis is to minimize unnecessary breakdown of machines and production delay due to sudden failure of machines. Furthermore, we enhance the availability, productivity, and efficiency of the maintenance workforce through this research analysis in the rubber industry.
This research article has been organized into seven sections. The first section presents the introductory maintenance, a critical overview of the existing literature, and the motivation of this research. In Section
It is the most widely used mathematical and stochastic process to measure the maintenance parameters (RAMD) of the production systems concerning three different state conditions. This mathematical approach was introduced by the Russian mathematician Andrey Andreyevich Markov to solve sequential problems. It analyzed the present state behavior of the system to identify the future state condition of that particular system [
Reliability is the most important maintenance parameter; it simply denotes “
Availability of the repairable systems simply defined as the ratio of the uptime to the total lifetime of the particular production system is denoted as “
The uptime of the systems is represented by the mean time to failure (MTTF) which can be measured through the failure analysis of the systems [
Equation (
Defined as the probability function of that failed system, subsystems and their components are restored into the original or operative condition in the given specific time interval (downtime) that is denoted as “
Dependability is another most important maintenance parameter measure; it is simply defined as the system’s ability to deliver the service with a specific time interval concerning the assumption of the rate of failure and repair of the production system [
The notations and assumptions used for RAMD analysis of the tyre manufacturing model are provided. The tyre manufacturing system of the rubber industry is described briefly, and maintenance problems of this system are discussed. Achieving better availability of production machinery and its equipment at this shop floor is one of the major problems of the rubber industry. The transition state diagram of the tyre manufacturing machines is illustrated in Figure
Transition state diagram of tyre production systems.
The various notations used for this RAMD analysis research in the tyre manufacturing system of the rubber industry are given as follows: SBM, SBB, SCL, SBC, SEX, SBD, and SCU working state of the machines SBM, SBB, SCL, SBC, SEX, SBD, and SCU under maintenance state of the machines ∗SBM, ∗SBB, ∗SCL, ∗SBC, ∗SEX, ∗SBD, and ∗SCU repair state of the machines BM: Banbury mixing subsystem BB: bead and belt cord manufacturing subsystem CL: calendaring subsystem BC: bias cutting subsystem EX: extruding subsystem BD: building subsystem CU: curing subsystem
Here, the RAMD analysis of the tyre manufacturing system maintenance model in this research article confirms the following assumptions: Initially, every subsystem is in the original state or good (BM, BB, CL, BC, EX, BD, and CU) The rate of repair and failure of every subsystem is constant and statistically independent ( Every repaired system is considered as good as new The single maintenance team to handle the PM of the subsystem Every subsystem has three state conditions such as original, under maintenance, and repair (e.g., S, S, and ∗S) The simultaneous failures of the subsystems are not considered The rate of PM and transition of the critical systems are taken as constant (
In this research, all the maintenance parameters measured are derived on the subsystem wise. The rate of failure and repair of all the subsystems are considered exponentially distributed. In this section, a detailed description of the tyre manufacturing plant has been presented. The tyre manufacturing plant has five major systems such as material selection, initial preparation, tyre component preparation, finishing, and inspections. The graphical representation of the tyre manufacturing system is illustrated in Figure
Manufacturing process of a tyre production system.
The tyre production system consists of these major materials such as rubber, textiles, carbon black, sulfur, and other chemical additives. Rubber is the major raw material (natural and synthetic rubber), and it has been collected from various places such as Kerala. The other ingredient is carbon black which is in a fine powder form. It has been added to the raw rubber for the softening process in the tyre production system. Then, sulfur and some chemical additives are added into the raw rubber to achieve the required tyre characteristics such as friction and ultraviolet radiation.
The tyre manufacturing process preparation is the initial operation, and it has some series operating subsystems such as Banbury mixing and bead and belt cord manufacturing. A detailed description of the subsystems is given below.
It is the initial process of the tyre manufacturing system, the mixing of raw materials (natural and synthetic rubber, carbon black, sulfur, and other chemical additives), and forming the rubber compound through the application of the computer control system. That controls the composition of rubber, and chemical mixing automatically depends upon the required tyre parts.
In this section, the mixed rubber compounds are further heated for softening the mix and evenly distributing the chemical additives. Once it is completed, that mixed compound feeds into the two sets of rollers and rotates the different directions of the powerful rolling mill that presses and squeezes the mixed rubber compound and makes the thick sheet. Those sheets are utilized to produce the specific part (bead and belt cord) of the tyre components covered with a combination of textile and fabric. This final rubberized fabric was used to build the layer of the tyre called a ply.
This section consists of the three different subsystems that the manufacturing process applied to produce the tyre components. The detailed description of the tyre component production subsystems is explained below.
After completing the mixed rubber compounds that will feed into the calendering operation for reducing the thickness of the rubber-mixed compound, we released the porous gases and gravidities in the rubber-mixed compounds through the application of the powerful rolling operation. This calendaring subsystem has some major activities such as (1) to create the mixed rubber compound as a uniform thick sheet with specific dimensions and (2) to prepare the initial coats of rubber on the textile fabric, to insert the steel or textile fabric in the rubber compound through friction.
In the extruding operations, the mixed rubber compound feeds into the extruder machine and then forced out through the die with the required shape of an orifice to produce the required size and shape of the tyre components. The large, flat sheet of the tyre treads is developed by the extruding process.
After the calendaring and extruding operations are completed, flat rubber sheets move into the conveyor to the bias cutting operation. In that situation, we cut the required shape and size of the flat rubber sheets with the application of the grating blade.
This section consists of the two subsystems of the final operation in the tyre manufacturing process. The detailed demonstration of the subsystems is given as follows.
This system is also called the tyre assembly process after the bias cutting process that stripped textile fabric rubber compound sheets, and other tyre components (bread, plies, sidewall, and treads) are assembled on the drum of the building machine to form the “green tyre” through this operation.
Finally, that green tyre goes to the vulcanizing process that is placed on the large mold of the curing machine that is called the bladder. That bladder filled with the high pressure and temperature steams during this operation green tyre is vulcanized up to 280° within the specified time limit. After completing the curing operation, the finished tyre will go to the cooling process and then quality checking activity.
After the vulcanizing process is completed, the finished tyre is moved into the quality and inspection process. In that situation, each tyre is thoroughly inspected with the application of various techniques such as visual inspection, destructive, and nondestructive inspection techniques, and based on these techniques, the flaws are identified such as bubbles and voids in the tyres. Once they completed the inspection and satisfy the required quality, the final product is moved into the packaging section and then stored in the warehouse for customer distribution.
The real-time case study of the RAMD analysis in the tyre manufacturing system of the rubber industry has been evaluated by applying the last five-year maintenance record data of the individual subsystems in the tyre manufacturing system [
Input numerical values of the RAMD analysis.
Subsystem | Failure rate | Repair rate | Transition rate | PM rate |
---|---|---|---|---|
Banbury mixing | 0.008 | 0.150 | 0.007 | 0.70 |
Bead and belt cord making | 0.007 | 0138 | 0.005 | 0.60 |
Calendaring | 0.004 | 0.290 | 0.006 | 0.40 |
Bias cutting | 0.005 | 0.158 | 0.003 | 0.20 |
Extruding | 0.007 | 0.144 | 0.008 | 0.50 |
Building | 0.003 | 0.244 | 0.004 | 0.30 |
Curing | 0.002 | 0.310 | 0.002 | 0.20 |
This research analyzed the performance of the tyre production systems in the rubber industry. The description of the tyre production system is presented in the previous section. That production system has seven numbers of subsystems to achieve tyre production. All the subsystems are arranged in the series configuration production process in the manufacturing plant. Hence, the maintenance parameters (RAMD) of all the subsystems are measured through the utilization of the Markov birth-death process and the mathematical equations are derived by using the differential-difference equations [
Sample transition state diagram of the subsystem.
In initial state conditions, apply time
Now, applying the normalizing state conditions where
Derive equations (
Maintainability of the tyre manufacturing subsystems is derived as follows:
Other maintenance performance parameter measures of the tyre manufacturing subsystems are as follows:
Similarly, we measured the all other individual subsystem maintenance parameters through the application of equations (
Since the seven subsystems are arranged in the series configuration of the tyre manufacturing system and if failed, any one of the subsystems causes the entire production system to fail. The reliability of the tyre production system is equal to the product of each subsystem’s reliability. Hence, the overall reliability of the tyre production systems is achieved by using the following equation:
The effect of changes of all the subsystems and total system reliability concerning the time between 30 and 75 days are analyzed, and results are illustrated in Table
Effect of changes in the reliability of tyre production system.
30 | 0.7866 | 0.8106 | 0.8869 | 0.8607 | 0.8106 | 0.9139 | 0.9418 | 0.3396 |
35 | 0.7558 | 0.7827 | 0.8694 | 0.8395 | 0.7827 | 0.9003 | 0.9324 | 0.2837 |
40 | 0.7261 | 0.7558 | 0.8521 | 0.8187 | 0.7558 | 0.8869 | 0.9231 | 0.2369 |
45 | 0.6977 | 0.7298 | 0.8353 | 0.7985 | 0.7298 | 0.8737 | 0.9139 | 0.1979 |
50 | 0.6703 | 0.7047 | 0.8187 | 0.7788 | 0.7047 | 0.8607 | 0.9048 | 0.1653 |
55 | 0.6440 | 0.6805 | 0.8025 | 0.7596 | 0.6805 | 0.8479 | 0.8958 | 0.1381 |
60 | 0.6188 | 0.6570 | 0.7866 | 0.7408 | 0.6570 | 0.8353 | 0.8869 | 0.1153 |
65 | 0.5945 | 0.6344 | 0.7711 | 0.7225 | 0.6344 | 0.8228 | 0.8781 | 0.0963 |
70 | 0.5712 | 0.6126 | 0.7558 | 0.7047 | 0.6126 | 0.8106 | 0.8694 | 0.0805 |
75 | 0.5488 | 0.5916 | 0.7408 | 0.6873 | 0.5916 | 0.7985 | 0.8607 | 0.0672 |
Reliability changes of the tyre production system.
The availability of the individual subsystems will affect the entire production system because of the series configuration of the manufacturing process in the industry. The availability of the tyre production system equals the product of the individual subsystem’s availability. Hence, the overall availability of the tyre production system is demonstrated in the following equation:
The effect of changes of all the subsystems and total system availability concerning the specific rate of failure and repair of the subsystems are analyzed, and results are illustrated in Table
Effect of changes in the availability of tyre production system.
Subsystem | Availability at faulty state | Availability at ideal state |
---|---|---|
Banbury mixing | 0.8827 | 0.9206 |
Bead and belt cord making | 0.8859 | 0.9153 |
Calendaring | 0.9344 | 0.9528 |
Bias cutting | 0.8387 | 0.8523 |
Extruding | 0.8555 | 0.8982 |
Building | 0.9339 | 0.9485 |
Curing | 0.9535 | 0.9594 |
Availability variation of the tyre production system.
The overall maintainability of the tyre production system can be obtained by utilizing the following equation:
The effect of changes of all the subsystems and total system maintainability concerning the time between 30 and 75 days are analyzed, and results are illustrated in Table
Effect of changes in the maintainability of a tyre production system.
30 | 0.9889 | 0.9841 | 0.9998 | 0.9913 | 0.9867 | 0.9993 | 0.9999 | 1.0000 |
35 | 0.9948 | 0.9920 | 1.0000 | 0.9960 | 0.9935 | 0.9998 | 1.0000 | 1.0000 |
40 | 0.9975 | 0.9960 | 1.0000 | 0.9982 | 0.9968 | 0.9999 | 1.0000 | 1.0000 |
45 | 0.9988 | 0.9980 | 1.0000 | 0.9992 | 0.9985 | 1.0000 | 1.0000 | 1.0000 |
50 | 0.9994 | 0.9990 | 1.0000 | 0.9996 | 0.9993 | 1.0000 | 1.0000 | 1.0000 |
55 | 0.9997 | 0.9995 | 1.0000 | 0.9998 | 0.9996 | 1.0000 | 1.0000 | 1.0000 |
60 | 0.9999 | 0.9997 | 1.0000 | 0.9999 | 0.9998 | 1.0000 | 1.0000 | 1.0000 |
65 | 0.9999 | 0.9999 | 1.0000 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 1.0000 |
70 | 1.0000 | 0.9999 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
75 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
Maintainability changes of a tyre production system.
The overall dependability of the series configured tyre production system can be obtained by utilizing the following equation:
The MTTR of repairable tyre production subsystems concerning the specific availability changes in the subsystems of the tyre production systems is derived through the application of equations (
MTTR changes in the tyre production system.
The summary of all the subsystem maintenance parameters of the tyre production system in the rubber industry is appended in Table
RAMD indices for the tyre production system.
RAMD indices | |||||||
---|---|---|---|---|---|---|---|
Reliability | |||||||
Maintainability | 1 − | 1 − | 1 − | 1 − | 1 − | 1 − | 1 − |
Availability (faulty) | 0.8827 | 0.8859 | 0.9344 | 0.8387 | 0.8555 | 0.9339 | 0.9535 |
Availability (ideal) | 0.9206 | 0.9153 | 0.9528 | 0.8523 | 0.8982 | 0.9485 | 0.9594 |
Dependability | 7.52 | 7.76 | 14.24 | 5.19 | 5.92 | 14.12 | 20.5 |
MTTR (faulty) | 16.61h | 18.28h | 17.55h | 38.46h | 23.98h | 23.59h | 24.38h |
MTTR (ideal) | 10.78h | 13.21h | 12.38h | 29.34h | 16.09h | 18.09h | 21.15h |
125.0h | 142.8h | 250.0h | 200.0h | 142.0h | 333.3h | 500.0h | |
Dep. ratio | 0.9025 | 0.9049 | 0.9429 | 0.8701 | 0.8823 | 0.9422 | 0.9582 |
The RAMD analysis of the numerous subsystems and tyre production systems has been carried out for a real-time case study of the small- and medium-scale rubber industry by assigning the numerical values of the maintenance parameters of the tyre production system as shown in Table
Effect of changes in the MTTR of a tyre production system.
Subsystem | MTTR at faulty state (hours) | MTTR at ideal state (hours) |
---|---|---|
Banbury mixing | 16.16 | 10.78 |
Bead and belt cord making | 18.28 | 13.21 |
Calendaring | 17.55 | 12.38 |
Bias cutting | 38.46 | 29.34 |
Extruding | 23.98 | 16.05 |
Building | 23.59 | 18.09 |
Curing | 24.38 | 21.15 |
Availability variations of the subsystem BC concerning the rate of failure and repair.
0.002 | 0.003 | 0.004 | 0.005 | 0.006 | 0.007 | 0.008 | |
---|---|---|---|---|---|---|---|
0.128 | 0.8956 | 0.9015 | 0.9068 | 0.9113 | 0.9154 | 0.9191 | 0.9224 |
0.138 | 0.8653 | 0.8730 | 0.8798 | 0.8858 | 0.8912 | 0.8960 | 0.9003 |
0.148 | 0.8370 | 0.8463 | 0.8544 | 0.8616 | 0.8681 | 0.8740 | 0.8792 |
0.158 | 0.8105 | 0.8211 | 0.8304 | 0.8388 | 0.8463 | 0.8530 | 0.8592 |
0.168 | 0.7857 | 0.7974 | 0.8078 | 0.8171 | 0.8255 | 0.8331 | 0.8400 |
0.178 | 0.7623 | 0.7750 | 0.7863 | 0.7965 | 0.8057 | 0.8140 | 0.8216 |
0.188 | 0.7402 | 0.7538 | 0.7660 | 0.7769 | 0.7868 | 0.7958 | 0.8040 |
That result shows the availability of the subsystem BC approximately decreases from 3.03 to 2.21% with an increased repair rate of the particular subsystem. However, the availability of the subsystem will increase from 0.59 to 1.36% with an increased failure rate of the subsystem, and the MTTR will decrease by 4.87% approximately. The graphical representation of the availability changes in the subsystem BC concerning the rate of failure and repair is shown in Figure
Availability variation of the subsystem BC.
In this RAMD analysis of research, the utilization of the MBDA in measuring the
In the future, this proposed mathematical technology will be used to establish the predictive maintenance management process of smart machines and the health prediction system of its vital components. We intend to implement it with the help of the latest industrial revolution (Industry 4.0) technologies such as Industrial Internet of Things, Cyber-Physical Production Systems, and Internet Communication Technology.
The detailed input numerical data used in this RAMD analysis of the real-time industrial case study are available from the corresponding author upon request. Due to the actual fact that data were collected from the industry, it is used for research purposes only.
The authors declare that there are no conflicts of interest regarding the publication of this research article.
The authors wish to thank the Management of Kalasalingam Academy of Research and Education (KARE), Krishnankovil, Tamil Nadu, India, and Vellore Institute of Technology (VIT), Vellore, Tamil Nadu, India, for their support in this research.