1. Introduction

Nowadays, companies are in total competition aiming the development of new industry strategies especially concerning the maintenance and the production planning. In fact, general customer non satisfaction is noted to be a consequence either of random demand or sudden equipment failure. Therefore, it becomes a necessity to develop new maintenance and production strategies.

The maintenance function is largely considered as a non productive one since it does not afford us with currency directly. In fact, each company should produce goods of a certain quality and quantity required by the customer who needs to receive the product at the right time. To achieve this objective, production systems should operate efficiently and accurately by using an effective maintenance plan helping companies maximizing availability by minimizing machine downtime. Our work is the continuity of the previous one that manifested the obligation of improving availability [1, 2]. The machine suffered several failures. That's why we want to find a law that will helps us anticipate future failures and when these

failures will occur. The aim of this paper is to propose a modeling and performance evaluation method for a production site using stochastic Petri nets as a very powerful modeling tool that contributes to the improvement of the availability.

• "Assignments": assignments that modify the values of variables when crossing

To define a maintenance policy, prioritize the interventions or establish the budget, the maintenance manager must be able to choose the means and modes of intervention most suited to his machines. Similarly, a working group aimed at making machines, a line, a cell or a workshop more reliable, requires a structured method of attacking the site. Here are some simple indicators to help with the

Impact of Improving Machines' Availability Using Stochastic Petri Nets on the Overall…

Mean time between failure (MTBF) indicator measures the time elapsed between failures. It is therefore beneficial for reliability and a fortiori for

Mean time between failures <sup>¼</sup> total up time

Total up time includes stopping time off failure and micro stops time.

Maintainability means, for an entity used under given conditions, the likelihood that a given maintenance operation can be performed over a given time interval, maintenance is provided under given conditions, and use procedures and means.

Mean time To repair <sup>¼</sup> total down time

availability <sup>¼</sup> MTBF

stochastic Petri Nets proves its strength in order to increase equipment's

The notion of availability expresses the probability that an entity is in a state of "availability" under given conditions at a given time, assuming that the provision of

In this section, we present two applications in automotive and food sector where

In this first application, we present a study to improve availability of equipment that guarantees the good quality of the wiring harnesses. It is the electrical test table

number of breakdowns (1)

number of breakdowns (2)

ð Þ MTBF <sup>þ</sup> MTTR (3)

availability. Mathematically, the criterion of reliability is thus defined by the inverse of its indicator. MTBF is the mean time between consecutive failures. For a repairable system, the MTBF is the average time between completion of the repair and

2.1 Reliability index: mean time between failures (MTBF)

2.2 Maintainability index: mean time to repair (MTTR)

external means is assured. This rate is calculated using (3).

3.1 Electrical test table (automotive sector)

the next failure and is calculated using (1).

MTTR is calculated using (2).

2.3 Rate of availability

3. Applications

availability.

81

transitions.

DOI: http://dx.doi.org/10.5772/intechopen.82445

decision.

In order to exhibit the role played by the maintenance function within the company, it seems important to focus first on the huge difference between planned downtime and unplanned downtime. Unplanned downtime should be minimized. It is function of the number of breakdowns within a specified time period and related measures such as mean time between failures (MTBF) and mean time to repair (MTTR) [3]. MTBF and MTTR are claimed to be measures of equipment achievement and are related to objectives such as functional performance and process capability [4]. Thorough analysis of these two elements enables the maintenance function to improve equipment's availability by either increasing the MTBF or reducing the MTTR.

In this chapter, we show the interest of stochastic Petri nets for modeling, evaluation and performance analysis. Therefore, we will present two applications of SPNs to generate the model after having conducted a statistical study to determine transitions laws. Based on the model and after its simulation, we calculated the availability of machines after having developed a high-quality preventive maintenance plan allowing us to notice the impact of the increase value of availability on OEE.

## 2. Literature review

Petri net models have been studied extensively over the last decade [5–8]. These models have been applied to many types of systems [9–16]. A lot of analysis has been made on different states a system may occupy. These analyses had not take into consideration any study of timing. Recently, timing is integrated in some attempts [14, 17]. Merlin and Farber [18] discussed timed Petri nets. In fact, they assigned a time threshold and maximum delay to a transition. This was done to allow the incorporation of timeouts into a protocol model.

In his work, Zuberek [17] presents a fixed time for each transition to model the performance of a computer system at the register level. In another case, probability was introduced to allow a random switching of flow through the graph [19]. Shapiro limits the model to discrete time and a maximum of one token in each place. In this paper, Petri nets are extended by assigning an exponentially distributed firing rate to each transition for continuous time systems or a geometrically distributed firing rate to each transition for discrete time systems. These new stochastic Petri nets (SPNs) are isomorphic to homogeneous Markov processes [20]. In this work, SPN's are used to model the maintenance field in order to increase availability, productivity and efficiency of the production line.

Many stochastic Petri Nets classes are proposed for performance analysis of production systems. The characteristics of the different classes are essentially in the nature of transitions used, where laws other than exponential are associated [20–22].

To model our system we have used the stochastic Petri Nets with predicates because they consist of both, the immediate transitions, the deterministic transitions and the transitions with stochastic timings distributed with any law. In addition, they use variables to include two other properties:

• "Guards": variables or Boolean expressions that make the transitions uncontrollable until they are verified.

Impact of Improving Machines' Availability Using Stochastic Petri Nets on the Overall… DOI: http://dx.doi.org/10.5772/intechopen.82445

• "Assignments": assignments that modify the values of variables when crossing transitions.

To define a maintenance policy, prioritize the interventions or establish the budget, the maintenance manager must be able to choose the means and modes of intervention most suited to his machines. Similarly, a working group aimed at making machines, a line, a cell or a workshop more reliable, requires a structured method of attacking the site. Here are some simple indicators to help with the decision.

#### 2.1 Reliability index: mean time between failures (MTBF)

Mean time between failure (MTBF) indicator measures the time elapsed between failures. It is therefore beneficial for reliability and a fortiori for availability. Mathematically, the criterion of reliability is thus defined by the inverse of its indicator. MTBF is the mean time between consecutive failures. For a repairable system, the MTBF is the average time between completion of the repair and the next failure and is calculated using (1).

$$\text{Mean time between failures} = \frac{\text{total up time}}{\text{number of breathdown}}\tag{1}$$

Total up time includes stopping time off failure and micro stops time.

#### 2.2 Maintainability index: mean time to repair (MTTR)

Maintainability means, for an entity used under given conditions, the likelihood that a given maintenance operation can be performed over a given time interval, maintenance is provided under given conditions, and use procedures and means. MTTR is calculated using (2).

$$\text{Mean time To repair} = \frac{\text{total down time}}{\text{number of breathdown}}\tag{2}$$

#### 2.3 Rate of availability

failures will occur. The aim of this paper is to propose a modeling and performance

In this chapter, we show the interest of stochastic Petri nets for modeling, evaluation and performance analysis. Therefore, we will present two applications of SPNs to generate the model after having conducted a statistical study to determine transitions laws. Based on the model and after its simulation, we calculated the availability of machines after having developed a high-quality preventive maintenance plan allowing us to notice the impact of the increase value of

Petri net models have been studied extensively over the last decade [5–8]. These models have been applied to many types of systems [9–16]. A lot of analysis has been made on different states a system may occupy. These analyses had not take into consideration any study of timing. Recently, timing is integrated in some attempts [14, 17]. Merlin and Farber [18] discussed timed Petri nets. In fact, they assigned a time threshold and maximum delay to a transition. This was done to

In his work, Zuberek [17] presents a fixed time for each transition to model the performance of a computer system at the register level. In another case, probability was introduced to allow a random switching of flow through the graph [19]. Shapiro limits the model to discrete time and a maximum of one token in each place. In this paper, Petri nets are extended by assigning an exponentially distributed firing rate to each transition for continuous time

systems or a geometrically distributed firing rate to each transition for discrete time systems. These new stochastic Petri nets (SPNs) are isomorphic to homogeneous Markov processes [20]. In this work, SPN's are used to model the maintenance

Many stochastic Petri Nets classes are proposed for performance analysis of production systems. The characteristics of the different classes are essentially in the

To model our system we have used the stochastic Petri Nets with predicates

nature of transitions used, where laws other than exponential are associated

because they consist of both, the immediate transitions, the deterministic transitions and the transitions with stochastic timings distributed with any law.

• "Guards": variables or Boolean expressions that make the transitions

In addition, they use variables to include two other properties:

uncontrollable until they are verified.

field in order to increase availability, productivity and efficiency of the

allow the incorporation of timeouts into a protocol model.

evaluation method for a production site using stochastic Petri nets as a very powerful modeling tool that contributes to the improvement of the availability. In order to exhibit the role played by the maintenance function within the company, it seems important to focus first on the huge difference between planned downtime and unplanned downtime. Unplanned downtime should be minimized. It is function of the number of breakdowns within a specified time period and related measures such as mean time between failures (MTBF) and mean time to repair (MTTR) [3]. MTBF and MTTR are claimed to be measures of equipment achievement and are related to objectives such as functional performance and process capability [4]. Thorough analysis of these two elements enables the maintenance function to improve equipment's availability by either increasing the

MTBF or reducing the MTTR.

Maintenance Management

availability on OEE.

2. Literature review

production line.

[20–22].

80

The notion of availability expresses the probability that an entity is in a state of "availability" under given conditions at a given time, assuming that the provision of external means is assured. This rate is calculated using (3).

$$\text{availableality} = \frac{\text{MTBF}}{(\text{MTBF} + \text{MTTR})} \tag{3}$$

#### 3. Applications

In this section, we present two applications in automotive and food sector where stochastic Petri Nets proves its strength in order to increase equipment's availability.

#### 3.1 Electrical test table (automotive sector)

In this first application, we present a study to improve availability of equipment that guarantees the good quality of the wiring harnesses. It is the electrical test table

#### Maintenance Management

whose role is to check the flow of the electric current and therefore it ensures the main technical function of the wiring harnesses produced.

To achieve this result, we present the electrical test table and its components. Then, availability is calculated based on the history provided by the company. After this, we find the law that will help us anticipate future failures and when these failures will occur. This law enables us to develop a high-quality preventive maintenance plan in order to increase the availability of the equipment.
