Reliability Analysis of a Novel Structure in an Automatic Sorting System

Xiu-fang SUN I, Li ZHENG 2 1 Department of Industrial Engineering and Logistic Management, Beijing Union University, Beijing, P.R.China,

2 Department of Industrial Engineering, Tsinghua University, Beijing, P .R.China Gdtxiufang@buu.edu.cn)

Abstract - Reliability and safety is very important for logistic equipments especially sorting system. In this paper a novel structure of automatic sorting system is designed based on Double 2 vote 2 Redundancy (D2V2R) structure. By using this structure, the reliability of the system is enhanced comparing with traditional simplex system and duplex system. Analytical results based on basic reliability analyzing theory are also given for systems using these structures.

Keywords - Reliability, Logistic equipments, Automatic sorting system, Double 2 vote 2 Redundancy

I. INTRODUCTION

Automatic sorting system has been seen as the main contributor for logistic sorting operation because of the efficiency it has brought for material and product sorting and distribution process. Nevertheless, with the complexity improving in sorting system, more and more sensors and actuator devices are equipped in the system. This trend has great influence on the system reliability because more devices cause more possible of failure. Failure will effect the transaction in many large sorting system such as airport baggage sorting, mail distributed center and big manufactory center [1] [2]. High speed, low error rate and automated operation are basic requirements for these applications.

To improve the reliability a novel structure of automatic sorting system is designed based on Double 2 vote 2 Redundancy (D2V2R) structure. The D2V2R structure has been widely used in aircraft, railway, power station, petroleum and chemical industrial. The D2V2R structure can improve system reliability by using redundant strategy and improve system safety by using 2 vote 2 method. In this paper, a novel realization of the D2V2R is given basing on field bus communication. Based on the structure the reliability is analyzed and compared with traditional sorting system which using simplex structure and duplex structure.

II. SYSTEM STRUCTURE AND PRINCIPLE

The automatic sorting system consists of one control part, a dual-net field bus and N field nodes. The structure of the automatic sorting system is shown as Fig. 1. The reliable design method is applied both in the control part and field nodes.

The control part of the automatic sorting system is designed with the D2V2R structure to enhance its reliability and safety simultaneously. The operation flow of this basic system is as following. First, the belt conveyer transfers an object to across the sorting nodes. Secondly, the sensor of the field node detects and recognizes the object. If the object is needed to process in

this node, the actuator will eject the object to the channel to the corresponding package box.

Control P3rt I Exec:ulivc ContrOller I OUIPUI Swilch Unit I

I SUbsyslc:m I I

I Output Comparison I I

I Con;:lIcr Controller I IB I ISynch Bus Sub-systcm II I

I Output Comparison II I I ConIl'OlIcr I UA lIB

Dual Net Field BIL' (CAN 2.0B)

Field Node III II II II I Input I

I Input Channel I A Chonnel B I Output I I, Output : I Channel I A Channel I B

'-. .... SensoriA Sensor IB Actuator I A AC1WIIlor I B

JI

...... Field odeN

D ,.--"'1 '----1 Belt Com'eyer c., L _ . : ... ---- --- ... - ____ r------ ... Objt L-_-: I

Fig. I. Structure of the automatic sorting system of D2V2R

The control part of the system consists of four controllers. Each filed node consists of two input channels with sensors and two output channels with actuators. Four controllers are designed in two subsystems which each subsystem consists of two controllers. The output of each subsystem is active and available when the two controllers' outputs are same. The control part's output is selected by the output switch unit according the status of two subsystems and then transferred to the active actuator of the field node by executive controller.

TABLEl SYSTEM FAILURE CONDITIONS

System I System II

IA IB ITA ITA

o 0 0 0 o o o o o o o

o o o

I o o o o

o

o o

o o

o o

o I o I o

o

o

o

o

Output Failure

o o o o o

I o

o

Failure Module

(%) o

25

25

50

25

50

50

75

25

50

50

75

50

75

75

100

This work is supported by The Natural Science Research Fund of Beijing Union University (No: 2K2009576).

978-1-4244-6484-5/10/$26.00 2010 IEEE 955

The sensors and actuators equipped in this system are smart devices which have ability to connect to field bus network CAN2.0B. The measurement data, executive command data and devices supervisory data are transferred on this data bus link. The synchronization data of the two subsystems are transferred by the high speed synchronization bus as shown in Fig. 1.

To evaluate the reliability of the control part in this sorting system, only one field node is used in the reliability analyzing process.

According to the double 2 vote 2 redundancy structure shown in Fig. 1. The whole system output failure conditions can be analyzed as table I. The data in the table shows the system output will failure only when there is fault in both two subsystems. The system can remain normal in the condition the failure module percentages get up to 50%.

Ill. RELIABILITY ANALYSIS

To analyze the reliability of the automatic sorting system the basic reliability theory is used to evaluate its performance. A. Assumptions and Notation

Before analysis, a number of assumptions which define the valid states and the possible transitions between them have to be made [3l. The assumptions used to redundant protective devices redundant protective devices are:

1) Each unit has 2 states: failed and good. 2) All units of a system are good at time O. 3) Repair of a unit is to like-new and does not damage anything. 4) All failure and repair (hazard) rates are constant in time, and unchanged by repeated failure and repair of units. 5) No two units fail or complete repair at exactly the same time (no common-cause transitions). 6) Failure and repair events are all mutually statistically independent. 7) Both units of a duplex pair have the same failure rates and same repair rates. 8) Concurrent repair can take place when more than one unit is failed. 9) Switch units and comparison units are always working.

Notation A failure rate, failure rate of unit 11 repair rate, repair rate of unit R(t) reliability function A(t) availability function

B. The Calculation of Failure Rate The failure rate A is the most important element to

evaluate the reliability, availability, and MTTF (Mean Time to Failure). The failure rate is represented in (1) as the inverse of the operating time T of components.

A = (1) T

956

The reliability of systems and components, when they operate correctly at t, is a conditional probability for the correct operation between to and T [4l. The system reliability is defined in (2).

R(t) = e -At (2) Reliability of system is the ability of system to

complete stated functions under stated condition and stated time limit. Reliability is a qualitative concept. But in practice it always needs to use quantificational reliability to indicate level of reliability. The reliability of system, when it operates correctly at to, is a conditional probability for the correct operation between to and t. It is defined to be Rs(t). The reliability of series system that consists of n modules is defined in (3).

n

R,(t) = IT R;(t) (3) ;=1

The reliability of parallel system that consists of n modules is defined in (4).

n

Rp(t) = 1- IT[l- R;(t)] (4)

MTTF (Mean Time To Failure) is the expected time that a system will operate before the first failure. This is a useful parameter to specify the quality of a system. MTTF is evaluated in the integral of reliability. It is shown in (5).

MTTF = r R(t)d(t) (5) The availability of systems is the probability to

operate a task correctly on the instance of time t. As it were, it is the time ratio for the system to be operated correctly. It has a close relation with repair rate. If a failed simplex system is not repaired then its availability state transition diagram is identical to its reliability state transition diagram in Fig. la, and A(t) =R(t). [3J

For calculate the reliability of the D2V2R system shown in Fig. 1. Its serial and parallel structure can be shown as Fig. 2a, 2b and 2c.

c .! ;f

i

Vl . OJ

Fig.2a. Serial and parallel structure of the D2V2R system

Assume the reliability of different elements is same. The elements include sensor, main controller and actuator. Assume the reliability of comparison unit and switch unit is 1. Assume the element without redundant is not reparable during the automatic sorting system is running. Assume the repair rate of the element with redundant is 0.9 and it can be replaced online.

According to the serial and parallel structure of the system configuration the reliability of these three structures can be calculated as following [5l.

For simplex system shown in Fig. 2b, the reliability of each controller is as following

as

(6) The reliability of the simplex system can be calculated

RSimplex (t )=Rsensor (t) X Rcantroller (t) X Roctuator (t) (7) For duplex system shown in Fig. 2c, the reliability

can be calculated base on the serial model of input part, controller part and executive part. Among these three parts the controller part is base on a parallel model of two hot standby controllers [5] [6]. Then the reliability of main controller is as following

RDuplex (t) = R"nwr (t)x [ 1- (1- Rcontroller(t))2 Jx R actuator (t) (8) For D2V2R system shown in Fig. 2a, sensors, main

controllers and actuator parts have redundant configuration. The reliability can be calculated as following

RD2v2R (t) = RIN (t)RMC (t)RoUT (t) Where

R IN (I) = 1 - [1 - R"",or (t) r RMc(t) = 1-(1-RSl/bsystem )2

Rsubsystem (t) = Rcol1trolle/ ROUT (t) == 1- [1-Ractl/ator (t) t s Controller 1 ------[E!i=:J Single I I Actuator

Fig.2b. Reliability model of simplex system

Fig.2e. Reliability model of duplex system

IV. NUMERICAL RESULTS

(9)

(10)

(11)

(12) (13)

To illustrate the magnitude of the error III the predicted system reliability, consider the data presented in Fig. 3. Assume the life cycle of these elements is 10000 hours. Then, the reliabilities of these three systems are as the table II.

t(hours)

o

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

TABLE II SYSTEM FAILURE CONDITIONS

RSinglc

0.74081822

0.54881164

0.40656966

0.30119421

0.22313016

0.16529889

0.12245643

0.09071795

0.06720551

0.04978707

RDuplcx

0.811316395

0.648294308

0.511945108

0.400491906

0.310925037

0.239879823

0.184102794

0.140673703

0.107087303

0.081258498

RD2V2R

0.96714146

0.891311127

0.796429059

0.696761408

0.600423597

0.511670468

0.432383863

0.363030829

0.303274051

0.252354925

957

As the Fig. 3 shown, under the same condition, the reliability of the system is much higher than simplex system and also the duplex system. The system is believable.

In practical application, because of the easychangeable of the components in D2V2R system, the reliability is even higher than the irreparable condition.

1.20

1.00 -+--R_Sillgle

0.80 ,q

-R_Dllplcx

-+-R_D2V2R 0.60 'ii

0.40

0.20

0.00 0 2000 4000 6000 8000 10000

Tilllc (Hours) Fig.3. Reliability model of three control systems

V. CONCLUSION

In this paper, an automatic sorting control system with D2V2R structure is proposed in order to improve the reliability of the sorting system especially for busy sorting applications. And an applied reliability model for D2V2R control system is created based on basic reliability model. Reliability analysis results shows that the reliability of the proposed D2V2R system is higher than that of the simplex system and the duplex system described in this paper.

ACKNOWLEDGMENT

Xiufang SUN Author thanks Dr Ze LIU and Ms Ping WANG's part work in the development of the structure.

REFERENCES

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