RELIABILITY IN A HIERARCHICAL MANAGEMENT

1

LITERATURE REVIEW & METHODS

THE RESULTS OF THE PRESENTATION

CONTENT

2

3

INTRODUCTION AND OBJECTIVE

• In contemporary management, in whatever system is employed, we must consider the possibility that the required output may not always be reliably obtained.

• The objective of this lecture is to introduce the principle of the methodology for static reliability measurement of a large system ( for example, which would have a serious environmental impact in the case of a defect).

1 OBJECTIVE

LITERATURE REVIEW & METHODS

• In general, we can formalize the uncertainty of the output system to be like the probability of a failure of the system element during its activity time.

• If we know the probability of any component's failure-free working during its lifetime (p), then we can determine a value of the component’s unreliability (h), by way of simple subtraction from the expected reliability:

h=1- p. • For example the management of a vehicle servicing

organization can statistically calculate that a modern, best selling car does not need to be repaired during the duration of the guarantee in 96 of 100 cases. The reliability of the car during the guarantee period is therefore p =0.96, and its measure of unreliability is then h=0,04.

2

• This data about the unreliability of a system (here about manufactured product) is very valuable for a manager. The date about unreliability allows the manager to identify what additional costs must be added to production costs for the purposes of calculating profit.

• Shown diagrammatically, it is possible to represent a methodology for reducing unreliability in the following way:

• I. Couplers' safety optimalization,• II. Adding duplicate or standby components.

Two methods of increasing system reliability from the structure point of view

h2=0,0016

h2=

0,0016

X

T(X)

X

Y= f(T) with the probability p1 = 0.9600

Y= f(T)with the probability p2 = 0.9984

Improving the reliability of element

e.g. Constructional

adjustment

h1=0,0400 T(X)

Y= f(T)with the probability p1 = 0.9600

T(X) T(X)

Y= f(T) with the probability p2 = 0.9984

T(X)

X

I.) Increasing the reliability optimization of the element

itself

II.) Increased reliability by adding the redundant

elementX

• We can consider the unreliability of two elements connected in parallel, where one appears as a redundant element.

(1)

• If we have n-1 redundant elements the resulting uncertainty would be obtained by multiplying together the unreliability associated with each interconnected parallel element:

(2)

• If we use formula (2) needed to determine the reliability of a system composed entirely of parallel elements, we can identify it as a complement to the unreliability of the resulting h, namely:

(3)

21 hhh

n

iin hhhhh

121 ...

n

iihp

1

1

• Indicating partial unreliability hi-shaped reliability (h = 1 - p) and by (3), we obtain the formula:

(4)

• In an organizational system, generally there are not only the redundant elements. Some elements of the organizational system are connected in series. For example, to transmit the information needed to implement the strategic plan for the operational processes is necessary to inform the strategic organization’s tactical unit and then operational unit. There is a need to overcome the interference of three organizational elements.

(5)

)1(11

n

iipp

n

iin ppppp

121 ...

Functional structure of the organization, with three levels of management and seven organizational units

Sps= 0.95

T1

pT1= 0.92

O1

PO1= 0.86

O2

PO2= 0.85

T2

pT2= 0.87

O3

PO3= 0.80

O4

PO4= 0.81

The strategy: level of

functional unit

Tactic: level of

functional groups

Operational management:

level management

features

• To determine how information is manipulated by the content of the resulting behavior measured in the operational organization, we will spread the structure into three series-

connected blocks, with each block represents one level of management. • In terms of information, the final link reliability of each block is

based on the formula (5):

• Reliablity of the first block: • Reliablity of the second block:

• Reliablity of the third block:

• The product of the reliability of individual blocks:

95,01 spp

9896.0)87,01()92,01(1)1(12

12

iiTpp

864522.0)81,01()80,01()85,01()86,01(1)1(14

13

iiOpp

I%818128,0864522,09896,095,0321

3

1

ofpppppi

i

• Based on this progress, we can create a formula for the general result of the determination of any system composed of interconnected elements in both parallel and serial links. There is a need to know only the reliability of the individual elements:

(6)

where m is a variable number of elements connected in parallel (in our example it is the number of elements in 3 blocks), and n is the number of elements connected in series

)1(111

m

iij

n

j

pp

Diagram of the information transmission between organizational units

Feedback - the measurement of the resulting behavior

–pS

0.95

pT1

0.92

pT2 0.87

pO1 0.86 pO2 0.85 pO3 0.80 pO4 0.81

The resulting behavior of channeling 81% of the contents of the information I

I: input of the information on the business planControl deviation

First block

Second block

Third block

The resulting reliability of information transmission in terms of the probability transferring information to the operational management

• The number of standby units must continue to respect the requirement that the implementation and maintenance costs demand minimum resources, namely to achieve the result of what was the cheapest.

• It is based on a combination of two strategies mentioned above - from optimization of the reliability of the serial link, as well as the involvement of additional parallel links generating standby elements.

4 RESULTS

nOij

n

j

Oij

o

iij

n

j

pppp )1(1)1(1)1(1111

• Approximation of RESULTING reliability if we know – Average reliability of a component , number of

managerial levels (blocks) n and number of organization units for one level:

(7)

• Obviously, we can design an organizational system, when we ask p, know either pij+o or pij +n and must calculate n or o (by the expression from formula (7)).

4 RESULTS

nOij

n

j

Oij

o

iij

n

j

pppp )1(1)1(1)1(1111

ijp

Practical Example:Diagram of functional units block of power

plant, consisting of two cycles

2. secondary circuit

P2

S

C P1

R

PT

G

1. primary circuit

PG

The units of the primary circuit are: R - nuclear reactor, PG - steam generator, P1 - pump (in the primary circuit). The secondary circuit units are: PG - steam generator, S - steam separator, PT - steam turbine, G - generator of electricity, C - condenser, P2 - pump (in the secondary circuit).

heat surface of PG

direction of the circulation of coolant (radioactive water) in

the primary circuit

direction of circulation of

inactive steam in the secondary

circuit

Diagram of the analysis of the resulting radiation leakage in the block of power plant

1st block: the reliability of the management of

fission in the reactor

2nd block: the reliability of the reactor cooling

3rd block:According to the criteria

of proofing reliability

p11 p12

p21 p24 p27 p210

p22 p25 p281 p211

p23 p26 p29 p212

p37

p36

p35

p34

p33

p32

p31

p38

p39

p310

p311

Input into the analysis: the reliability of components and sub-links of primary circuit in

accordance with the criteria of safe control (control, cooling, impermeability)

Output from the analysis: the resulting reliability of the block

of nuclear power plant p