BASIS OF RELIABILITY ANALISIS
OF BALNEOTECHNICAL SYSTEMS
SAFETY
Tchórzewska-Cieślak B.
Politechnika Rzeszowska, Poland
Abstract: Balneotechnology is the science that covers the whole of the technological problems
concerning design, operation and development of health resorts, especially the exploitation of balneological raw materials and the technological conditions for their usage in health resorts therapeutics. The creation of the optimum therapeutic and technological conditions to use health resort natural resources in therapeutics is a complex task which requires the cooperation of experts from many fields (doctors, geologists, chemists, biologists and engineers from different branches, including sanitary engineers). Observations of the operation of balneotechnical systems in many health resorts in Poland and European countries reveal the difficulties in their work. More and more often the random failures having very extensive negative consequences are reported. The popular balneological treatments using mineral waters, thermal and therapeutic mud often carry the threat of infection. One can name trichomoniasis, mycosis and legoneliosis. To estimate the threat resulting from such event and the accompanying risk it becomes necessary to elaborate the methodology to assess reliability measures for proper balneotechnical system operation.
1. Introduction
Health resort therapeutics has got a specific character and thanks to the natural resources (therapeutic waters and peloids), climate and facilities it has proper conditions to carry out the complex balneological therapy. Balneotechnology is the science that covers all technological problems concerning design, operation and development of health resorts, especially the exploitation of balneological raw materials and the technological conditions for their usage in health resorts therapeutics.Observations of the balneotechnical systems operation in many health resorts in Poland and another European countries reveal the significant difficulties in their functioning.. More and more often the random failures having very extensive negative consequences are reported. To estimate the threat resulting from such events and the accompanying risk it becomes necessary to elaborate the methodology to assess reliability rating for proper balneotechnical system operation. Safety and risk connected with it derive from the theory of reliability which started its
existence as a discipline in 1955 when the first symposium on reliability was held in the USA. The first works in Polen on water supply systems reliability were presented by a team of authors Jeżowiecki J., Tiukało A. and Zalewski J.from the Technical University in Wrocław [3,4] in the conference “Reliability of water supply systems and sewage systems “.This subject was developed, among others, by the authors of works [1,2,6,8,9].
2.Characteristic of balneotechnical systems
The basic elements of the health resort infrastructure are the following: mineral water intakes, therapeutic gases and sea water intakes, peloid resources, treatment rooms, patients lodging houses, fitness clubs, medical diagnostics institutions, mineral, curative and table water bottling plants, environmental protection units and systems. In heath resort treatment the following curative sources are used: mineral and curative waters, curative gases, peloids, sea water, regular water, health resort products [5].The basic balneotechnical systems are: curative raw materials exploitation and utilization system that was divided into subsystems: mineral and curative water installation subsystem ,curative gases installation subsystem ,sea water installation subsystem ,peloid installation subsystem .Each of the named subsystems can be divided into components performing some defined functions.
¨ Curative water installations can be divided according to water composition into the following types :
balneotechnical system
- for oxalic (water containing CO2), - for hydrogen sulphide waters , - for radioactive waters, - for specific waters, - for iodide waters, - for thermal waters.
¨ Installations for curative waters exploitation consist of the following elements [5]: - curative waters pumping stations and hydrophore stations,
- curative water storage tanks, - outside and inside pipelines, - curative water heater,
- hyper thermal water cooling facilities.
3.Operational analysis of balneotechnical systems reliability and safety
Balneotechincal systems reliability tests belong to the category of operating tests which means that they are performed in form of observation during the real operation and they need a long time interval. These tests should be carried out in such extent that enables to
obtain quantity and quality characteristics for different kinds of failures. The important problem connected with these tests is to determine the reasons and consequences of the particular kinds of failures. The exemplary program of balneotechnical systems operating reliability tests is the following:
· Preliminary stage
- Purpose and range of research
· Analysis of balneotechnical system structure - Subsystems distinction
- Determination of up states of balneotechnical system and components - Reliability measures selection
· Operating data obtaining - Data sources
- Research range determination - Data accuracy and reliability · Data processing
- Data statistical verification
- Determination of reliability measures for balneotechnical system components
To analyse balneotechnical system reliability and safety the following reliability measures have been suggested [2,9]:
Mean time between failures Tp is a mean value of random variable Tp determining system ( or its elements ) operating time ( up time ) between two successive failures.
0 dt ) t f( t ) ' p T ( E p T (1)
or from the operating data [2] :
k 1 i pi pk
1
z
(
t
z
t
)
T
(2)E(Tp) – a mean value of random variable Tp ,
t – observation time
tpi –value of operating period i for objects with failures k – a number of operating periods for objects with failures z – a number of operating periods for objects without failures f(t) – density of probability of random variable Tp
Mean repair time Tn is a sum of time to repair Td and time of repair (by the moment when element starts working again) T0.
Tn = Td + T0 (3)
Mean repair time is a mean value of random variable Tn, determining repair time. 0 o ' n) tf (t)dt T ( E Tn (4)
or according to the operating data:
o n 1 i ni o nn
1
t
T
(5) E(Tn’) - a mean value of random variable Tn,fo(t) - density of random variable T0,
n0 - a number of repairs in the tested period tni - repair time for i repair
Failure rate l(t) dt ) T ( dE ) t ( ' p l , (6)
or according to the operating data:
pś T 1 l , (7) t N ) t t , t ( n ) t ( l (8) Tpś – mean operating time between successive failures = E(Tp),
n(t,t+t) –a number of all failures within time interval t ,
N- a number of tested elements or in case of linear system length in km t - observation time.
Recovery rate m (t) describes a number of failures in a time unit , it can be calculated from the operating data according to the formula :
t ) t ( n ) t t , t ( n ) t ( m (9) n (t,t+t) – a number of elements whose recovery has been finished within time interval (t,t+t),
n (t) - a number of elements whose recovery has been finished by time t, t - observation time.
Availability K(t) describes the probability that system will be in the state of reliability.
When the time of system operating increases the availability K(t) heads for the boundary value called the stationary availability K [9].
l m l m l m exp[ ( ) t] ) t ( K (10)
l
m
m
K
(
t
)
lim
K
t T Tn T p p (11)Unreliability rate U describes the probability that system will be in the down state ,
U = 1- K (12)
Reliability (NF) means system ability to perform its functions in determined operational
conditions, in any moment (then we use availability K(t) or in the specific time range (then we use reliability function R(t)).
Uunreliability (ZF) means a state in which system is not able to perform its functions. Safety (NB) is defined as the probability that such losses like human health or lives will
not take place as a result of the undesirable events.
Unsafety (ZB ) means that the catastrophic events appear in system. There is a
dependence between a measure of safety and a measure of reliability [9].
NB = NF+ ZF/(C = 0) (13)
While the loss of unsafety ZB is determined from the formula:
ZB = 1 – NB (14)
ZF/(C = 0) - probability assigned to unreliability events provided that no significant social costs, health hazard or loss of life are connected with it
ZB - unsafety identified with the probability connected with the risk of loss of safety, ZF - unreliability identified with the probability connected with the risk of unreliability
ZF = 1 – NF (15)
Safety can also be defined as [8]:
P X(t) ; Y(t) ) t ( B (16)X(t) - external influence of the source of threat X(t) does not exceed the required safety level
The speed of external threat influence in the given time interval does not exceed the speed of system adaptation which is written as follows :
dt ) t ( dY dt ) t ( dX (17)
System reliability can be defined as system feature corresponding with confidence
which is placed in this system , that means the conviction of its users that the system will perform its functions according to the requirements and in a safe way. Therefore the measures of system reliability are: accessibility (at any time convenient to user), reliability, safety and protection against the possible failures.
4. Confidence limits
In statistical studies for the given significance level the confidence level 100(1-)% is determined and for this level the confidence intervals and limits are determined. [10]: Upper limit of confidence internal for failure rate lU1 is
T 2 ) 2 r 2 ( 2 1 1 U l (18) Lowerlimit of confidence internal for failure ratelL1 is
T 2 ) r 2 ( 2 1 L l (19) Lowerlimit of confidence internal formean operating time betweenfailures TPL
) 2 r 2 ( 2 1 T 2 PL T (20)
Upper limit of confidence internal formean operating time between failures
T
PU) r 2 ( 2 T 2 PU T (21)
r - a number of observed failures, T- accumulated time of test, 2- - fractile distribution 2 for a defined number of freedom degrees.
5. Characteristic of the basic reliability structures
Reliability diagram shows the interactive logical connections between individual elements of the technological system considering the impact of their failures on the reliable system operation. While the reliability diagram is made its element are treated as the links working with defined probability describing failure free event .
a) Series structure – if failure of any element causes failure of the whole subsystem then the corresponding reliability links should be placed in the series reliability structure.
n 1 i iK
K
(22)if for every ,,i”:
Ki = Ko then K = Ko n (23)
i = 1,2,3,...,n., n – a number of elements.
b) Threshold structure – if failure of subsystem happens when element “k”, out of all the “M” homogeneous elements is damaged then all reliability links corresponding to these elements should be placed in the homogeneous threshold structure type ,,M-k out of M”. dop k 0 k k 0 p k M 0 S k K K M K (24)
where: k - a number of damaged elements,
kdop - an acceptable number of damaged elements, KS - availability measure for threshold structure, K0 - availability measure for an individual element, Kp0 - downtime measure for an individual element. M- a number of all elements
)! k M ( ! k ! M k M
- binomial factor value (25) c) Parallel structure – if subsystem failure happens when all homogeneous elements are damaged then individual links corresponding to these elements should be placed in the parallel reliability structure
M 1 j j S 1 (1 K ) K (26)
where : KS - availability measure for parallel structure. Kj,- availability measure for an individual element
M- a number of all elements
6. Computational example
In fig. 1 you can see the simplified diagram of the therapeutic tank using brine. The availability measures for the individual elements are the following:
Pumping engines K3,
Cut –off valves KZO ,
Sand filters K1a,
Anthracite filters K1b,
Overflow tank K2,
Circulating water heater K4,
Chlorinators K5,
Tank basin K6,
Fig.1 The simplified diagram of the therapeutic tank
For the diagram shown in fig.1 the reliability diagram according to the rules given in point 5 fig. 2 has been made:
Fig.2 The reliability diagram
To calculate the availability measure for the technological system of the therapeutic tank operation the formulas (12) ,(22) ,(23), (26).were used :
For series structure
KZO-1a-ZO-ZO-1b-ZO= KZO K1a KZO2 K1b KZO= KZO4 K1a K1b K2-ZO-3-ZZ-ZO-ZO-1a-ZO-1b-ZO-4-ZO= K2 K3 KZZK1a KZO6 K1b K4 Parallel structure
Series structure
K A =K2-ZO-3-ZZ-ZO-ZO-1a-ZO-1b-ZO-4-ZO- ZO-5= K2 K3 KZZK1a KZO6 K1b K4KZO-5 Parallel structure
KB= K2-ZO-3-ZZ-ZO-ZO-1a-ZO-1b-ZO-4-ZO- ZO-5’ = 1-(1- KA)2 Finally the series structure is obtained:
K= KZO-1a-ZO-ZO-1b-ZO KBK6
Unreliability index U acc. to (12) is: U=1-K
7. Conclusions
Reliability engineering is widely applied in many technological systems. In the environmental engineering the reliability theory was developed most of all for water supply systems [1,6], for its internal systems [3]. Unfortunately there are not any reports in literature concerning the usage of this theory to analyse the balneological systems which also have failures[7]. Competition in the health resort market causes that consumers requirements will increase. Therefore it seems advisable to apply the reliability theory to analyse the balneological systems safety.
References
[1] Al-Zahrani M., Syed J.L. Hydraulic reliability analysis of water distribution system. Journal of the Institution of Engineers . Singapore. Vol 1issue 1 2004. s 76-92
[2] Kwietniewski M., Roman M., Kłoss-Trębaczkiewicz H. Niezawodność wodociągów i kanalizacji. Arkady. Warszawa 1993r
[3] Jeżowiecki J., Tiukało A., Zalewski J.: O symulacyjnej metodzie określania niezawodności instalacji wodociągowych. Materiały konferencyjne „Niezawodność systemów wodociągowych i kanalizacyjnych” Wydawnictwo NOT Kielce, Cedzyna 1986 r., str. 329-339.
[4] Jeżowiecki J., Tiukało A., Zalewski J.: Standardowe charakterystyki dobowego poboru wody jako funkcje niezawodności dostarczania wody w instalacjach wodociągowych. Materiały konferencyjne „Niezawodność systemów
wodociągowych i kanalizacyjnych” Wydawnictwo NOT Kielce, Cedzyna 1986 r., str. 348-356..
[5] Madeyski A.: Podstawy inżynierii uzdrowiskowej. Wydawnictwo Arkady. Warszawa, 1979 r
[6] Mays L.W Reliability analysis of water distribution systems. ASCE. New York 1989.
[7] Tchórzewska–Cieślak. Podstawy analizy niezawodności systemów
balneotechnicznych. II Kongres Inżynierii Środowiska. Wydawnictwo PAN. Lublin 2005
[8] Rak J.: Podstawy bezpieczeństwa systemów zaopatrzenia w wodę. Wydawnictwo PAN - Komitet Inżynierii Środowiska t.28, s.1-215, 2005.
[9] Wieczysty A., Niezawodność systemów wodociągowych i kanalizacyjnych, tom I i II Skrypt. Wydawnictwo PK. Kraków 1990r
