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Statistical analysis of reliability of container refrigeration units
ELSEVIER
lnt J. Refrig. Vol. 19, No, 6, pp. 407-413, 1996 Copyright © 1996Published by ElsevierScienceLtd and IIR Printed in Great Britain. All rights reserved 0140-7007(96)00014-X 0140-7007/96/$15.00 + .00
Statistical analysis of reliability of container refrigeration units Jiang Yan-Qiao S h a n g h a i M a r i t i m e University, S h a n g h a i , P R C
W a n g Shi-Liang Shanghai Ocean Shipping Company, Shanghai, P R C Received 5 N o v e m b e r 1993; revised 21 December 1995; accepted 10 February 1996
Emphasis has been given to the reliability of a wide range of products in recent years. However, little has been studied so far in the field of reliability of refrigerated containers. The characteristics of the reliability of container refrigeration units used in marine transportation are described in this paper. Field censored data collected from 4318 self-owned and long-time leasing refrigerated containers of a shipping company with 4 years' operation time are analysed. Analysis techniques for censored lifetime data are presented and applied to obtain the parameter estimates for the entire population when only a portion of that population has failed. Reliability characteristics for four principal types of container refrigeration units, i.e. Daikin, Paul Klinge, Mitsubishi and Carrier, are observed and studied. The reliability probability density function for some main components, such as the evaporator, the expansion valve, and the compressor, is also presented and discussed. Copyright © 1996 Published by Elsevier Science Ltd and IIR
(Keyworfls: refrigerated containers; reliability; censored data processing; Weibull distribution; maximum-likelihood estimation)
Analyse statistique de la fiabilit6 de conteneurs frigorifiques Ces demikres ann~es, la fiabilit~ de bon nombre de produits est devenue un crit~re important. Cependant, jusqu 'a ce jour, peu de travaux ont ~t~ r~alisOs sur la fiabilit~ des conteneurs frigorifiques. On d~crit dans l'article les caract~ristiques de la fiabilitO de conteneurs frigorifiques utilis~s pour la transport maritime. On a analysO les donn~es relevdes sur le terrain, sur 4318 conteneurs frigorifiques d'une compagnie maritime (dont elle est propri~taire ou qu'elle a en leasing), sur une dur~e de 4 ans. On pr~sente les techniques d'analyse de la dur~e de via, et on les utilise pour obtenir les estimations des param~tres pour la ~ population ~ enti~re, lorsque seule une portion de cette population a montr~ des d~faillances. On observe et on ~tudie les caracteristiques de fiabilitO de quatre types principaux de conteneurs frigorifiques. Daikin, Paul Klinge, Mitsubishi et Carrier. On pr~sente et on discute ~galement la probabilitO de fiabilite de queiques composants importants tels que l'~vaporateur, le d~tendeur et le compresseur.
(Mots d+s: transport frigorifique;transport maritime; conteneur; fiabilit+) The refrigerated container is a container for the transport of cold or frozen cargo that needs to be kept in a specific range of temperatures. Under field conditions, the inside temperature will remain at any degree within - 2 5 to +25°C. To ensure exchangeability of the containers in world transportation, the International Organization for Standardization (ISO) has recommended some international standards for containers. In recent years, the refrigerated containers which are widely used in marine transportation are 1AA (40f) and 1CC (20f), which are in conformity with the standards. The refrigeration units of the refrigerated container for long-distance transportation are mostly of the mechanical type with air-cooling or water-cooling systems. In view of the various transportation conditions, the voltage is set at 220 or 440 V. Maintenance and inspections should be done in order to keep the refrigerated containers always in a satisfactory condition: pre-trip inspection (PTI) (an overall inspection to be done pre-load and after-load), yard monitoring and repairing, as well as periodic inspection. Though it is required that only those refrigerated
containers whose technical conditions are satisfactory could be loaded on board the ship, some of them are liable to be out of order because of the following causes:
1.
2.
3. 4.
407
In the case of multi-mode transportation, the refrigeration units may be damaged by the impact of the acceleration of railroad traffic and various vibrations during loading and unloading, and the vibrations both from the chassis during land transportation and from the hull. Moreover, the duration of the voyage is longer than that of the land transportation. The effects that should not be neglected are the variation of the environmental conditions (temperature, humidity, etc.) and corrosion from sea water and wind I . Some deficiency in design rationality and the imperfection of manufacturing technology concerning the refrigeration units. Human errors from the ship's crew, such as maloperation, incorrect judgement or improper response, etc.
408
Jiang Yan-Oiao and Wang Shi-Liang
Table 1 Failure data category and detail
Tableau 1 Cat~gorie et description des donn~es de dffaillance Category
Detail
1
Source power
11
Control electriccircuits
III IV
Instrumentation equipment Pressure switch
V
Evaporator, etc.
VI
Compressor
VII
Expansion valve, etc.
VIII
Pipe leakage, refrigerant charging
IX
Others
1. Power cable 2. Plug or receptacle 3. Power change over S.W. 4. Circuit breaker 5. Trans. 440/220V 6. Main contactor 7. Insulation 8. Control circuit, trans. (control) 9. Contactor 10. Temperature sensor 11. Phase sensor and relay 12. Recordingthermostat, partlow, clock, etc. 13. Dual P.S.W. 14. Oil P.S.W. 15. Pressure differentialswitch (air) 16. Evaporator (fan, motor, etc.) 17. Condenser(fan, motor, etc.) 18. Motor heat protector and conjunctionbox 19. Defrost failure (heater resistance, defrost relay, etc.) 20. Compressor 21. Compressormotor 22. Valve plate 23. Compressorconjunctionbox 24. Dryer 25. Solenoidvalve 26. Expansion valve 27. Pipe, leakage detecting,nitrogen charging 28. Refrigerantcharging, vacuuming 29. Lub oil charging 30. Others
In marine transportation, the refrigerated containers have the above-mentioned features, and from those it could be deemed that the failure and repair reports from ships can fully show the container performance characteristics during loaded operation. Therefore, it is significant, after collecting and analysing this failure and repair data, to study the reliability of the refrigerated containers and improve transportation quality. A total of 1478 failure and repair reports have been collected from 4318 self-owned and long-time leasing refrigerated containers of a shipping company with an operation period of around 4 years (30 June 1988-13 April 1993). The total failure and repair data include 2889 reports. The main types of refrigeration units used for these refrigerated containers are: Paul Klinge: T N E 505, T N E 555; Mitsubishi: CPE10-3BA1, CPE522BAA, CPE13-3BAA; Carrier: 69NT40-424, 69NT40-464, 69NT40-484, 69NT20-284, 69NT20-254-8, 69NT20-284; Daikin: L K A E 8CD1, L K A E N 5BD5. In order to avoid any possible business dispute, A, B, C and D are used here in the following instead of the real models (not necessarily representing the above four items in the same order). For example, A8940 represents one type of refrigerated unit which was built in 1989, and installed on a 40 f container.
The 2468 failures of the container refrigeration units from ships show a general tendency as seen in Figure la. The specific properties of the failures can be observed from Table 2. Failure and maintenance reports have also been collected from the container yard of the shipping company for the self-owned and long-time leasing containers during the same period of time as mentioned above. The general tendency is given in Figure lb, with the specific properties in Table 2. The maintenance work in the container yard is mainly represented in category VIII and category I. Maintenance items in category I are mainly about the replacement of plugs and receptacles and the repair of cables. These problems are also reflected in the reports from ships. The investigation results show that the improper design of the cable holder causes the insufficient height of its railing, then results in the dropping down of the cable during transportation and the crushing of the plug and the cable by truck. The main items in category VIII are about troubles with the pipe, leakage and refrigerant charging. After the refrigerated containers bump all the way on a long-distance travel, failures like refrigerant leakage and cable damage are easily detected in the PTI before being loaded.
Censored data processing Failure characteristics of the container refrigeration units All the failure data are sorted by data base management system DBASE III and classified into nine categories with 30 details as shown in Table 1.
General theory Censored data. Failure data can be complete or incomplete.
409
Refrigerated container reliability (a)
i(x)
(b)
I0~)
10
2t~
() \
VIII
III
11
I
VII
IX
VI
IV
Vlll
I
V
VII
IV
VI
IX
II
III
Figure 1 General tendency of the failure data Figure 1 PDF pour les principaux couposants du D8420 et du D8520 Treble 2 Specific properties of the failures Tableau 2 Propri~tOs spdcifiques des d~faillances Source of the failure report
Category
Percentage
Main causes and percentage in this category
From ships
V VIII II
20.79 17.02 16.41
Fan and motor broken down Refrigerant charging and vacuuming, 55.0 Troubles with clock, clockwork spring adjustnobe. Recording platen fails to turn or recording pen cannot work precisely
Sum:
54.22
VIII I Sum:
33.97 25.89 59.86
From the container yard
If failure data contain the failure times (the moments when failures occur) of all units in the sample, the data are complete. If failure data consist of failure times of failure units and running times of unfailed units, the data are incomplete and are called censored, and the running times are called censoring times. If the unfailed units all have the same censoring time, which is greater than the failure times, the data are single censored. If unfailed units have different censoring times, the data are multiple-censored. The analysis methods for different types of data are different. The actual failure time data are usually censored. There are two types of censoring: 1.
2.
If the observations are terminated at a preassigned time, then the number of failures observed, r, will be a random variable, and the resulting failure time data is called 'type I censored'. For type II data, the observation is terminated at the moment of the rth failure (1 _< r < n). In this case, the moment when we stop the observation will be a random variable 2.
Field data are failure data from products actually being used. The operational circumstances, the real operation time for each system or a component in the field are different from each other. The loading situation may also be different. Therefore it makes for very different operation conditions. For the same calendar
Pipe, leakage, 14.7; refrigerant charging, 82.5 Plug, receptacle, cable broken
year, the real operation time for each unit might differ a great deal from one another. Therefore, the fluctuation of the field data is much greater than that of the data collected from the laboratory. However, reliability requires that the products have fewer failures during the real operation. The field data just reflects the reliability under the real situation. In this sense, the field data are more direct, and analysis of the field data presents interesting challenges. Reliability. Reliability is defined as the probability that systems or components will perform their intended functions for a specified period under stated condition. Reliability is the probability that a system or a component will work to time t without failure. Therefore reliability can be expressed in terms of distribution function R(t) of the random variables, as follows: R(t) = 1 - F ( t ) =
~ 0 °G
tf(t) dt
where F(t) is a cumulative failure density function (failure distribution function), f ( t ) denotes failure density distribution function, or probability density function (PDF). Failure rate A(t) is another parameter to evaluate the reliability. It is defined in terms of the condition probability that a system or component will fail at a certain time t < T < t -+- A t, given that it operates up to
Jiang Yan-Oiao and Wang Shi-Liang
410 time t: A(t) =
Let
~mlnL(m,r/) = 0 oo0 In L(m, 71) = 0 the following likelihood equations are obtained:
f(t)
R(t)
Mean life, or mean time to failure (MTTF) is the mathematical expectation of a product's life time, E(t): MTTF =
E(T) --
Io tf(t) dt -- I0 R(t) dt
Weibull distribution. The Weibull distribution is often used for studying product life because it describes increasing and decreasing failure rates. Its physical background is the so-called Weakest Link Model, i.e. the product consists of many parts with comparable life distributions and the product fails when the first part fails. Due to deterioration and wear, many mechanical components show an increasing failure rate. Hence, it is frequently assumed that failure times of mechanical products are Weibull distributed s. The probability density function of Weibull distribution is given as:
f(t)=Tom(~o)m-1 exp ( - (~o)) m;
t_>0
The shape parameter m is a positive dimensionless parameter. Scale parameter to is also positive, and indicates the time when 63.2% of the population will fail. The Weibull hazard function is the instantaneous failure rate as a function of age. It is
( m ) ( t ) m-'
To \?o/
;t>0
The Weibull mean life is
1/m
where r / = t o
Maximum-likelihood estimation. ability density function f(t) is
Suppose that the probknown, and its n data are obtained. Here tl, t2, ..., tn are used to express these values. It can be deemed that the probability to get data tl is in direct proportion tof(ti). Therefore, the probability to obtain such a group of data with n items is in direction proportion to n
L =f(tl)f(t2)...f(tn) = Hf(ti) i=1
where L is called a likelihood function. The method to find the value that maximizes the likelihood function is called maximum-likelihood estimation (MLE). For type I censored data, if the sample capacity is n, there are r failures when the test censored at time ts, while the rest of the (n - r) items will fail at (ts, cx~). Under this circumstance, the likelihood function of the parameter m and ~ is L(m,r/) =
ti Rn-r(ts)
= I ri~=l~(~)m-le-(~)'][e-- (~)m]m-r
1 __Ei~l~i - --~=t ~m = _1 r [~=1
lnti+(n-r)¢lnts ~-----~(--n- r)t------~ ~ -'~ (n -- r)/~ns]
1~
r .= In ti
(1) (2)
The parameters m and r/can be obtained from these two transcendental equations. Equation (1) can be solved iteratively for the estimate of m. By direct substitution, estimate r/ can be found from Equation (2) when the estimate of m is known. The initial value of m can be given as 1 or as the estimate from the Weibull probability paper plotting.
Censored data processing for container refrigeration units Parameter estimation for container refrigeration systems. With the censored lifetime data analysis method, the reliability parameter estimated values for the four main types of refrigeration systems have been obtained in
Table 3. In a Weibull distribution, when m < 1, the failure rate A(t) decreases with time. It is an initial failure period. For m = 1, the Weibull distribution is the exponential model, with a constant failure rate. It is called a random failure period. In this case, preventive maintenance is not effective. When m > 1, the failure rate A(t) increases with time. It is called a wear-out failure period. Preventive maintenance is considerably useful in this period. It is interesting that all the parameters m in Table 3 are larger than unity, and this is true even of those new units with shorter operation periods and fewer failures, such as C9220, C9240. Hence, there are no obvious features for a type of system that is still in the initial failure period or random failure period. The general estimated mean life for all the container refrigeration systems is 2396 days. It could be affirmed that the overall reliability for them is satisfactory. Result comparison among the four main types of the systems is: D > B > C > A. The mean life value of type A is rather poor, with a deviation of -49.82% to the overall mean value E(T). Table 4 is a detailed classification list for the four main types of units. Among the four types of units, type D has the longest reliability mean life. There are fewer failure reports for this type. D8520 with 198 containers has only 89 reports during 4 years. D8440 with 140 units, 76 reports. Some of the failures appear like this: refrigerant leakage results from broken thin copper pipes leading to the high-low pressure switches. Expansion valves are somewhat easily blocked. Inadequate sealing of the electrical conjunction box brings about the invasion of moist air. The condensate gives rise to short circuits, then burns the receptacle, stops the evaporator fan, short-circuits the heater, etc. An intermediate-level maintenance for this type of container was done in 1990. The failure rate has been effectively lowered. Type B 1984 products frequently have some troubles with the mechanical driving temperature recorder, as they are seriously affected by water, salt frost and dust.
Refrigerated container reliability Table 3
411
Reliability parameter estimated values for container refrigeration units
Tableau 3
Valeurs estira~es des parambtres de fiabilit~ pour des couteneurs
Model
Operation time (days)
N u m b e r ofcontainers
Number offailurereports
m
~
E(T)
A8920 A8940
1229 1290
120 252
50 228
2.924 3.521
1567 975
1398 877
E(T) = 1337 o ~ = 260.5
B8440 B9220 B9240
3330 347 347
30 200 200
24 3 8
8.4 1.57 3.37
3296 5082 980
3111 4564 880
E(T)=2851
C8820 C8840 C8920 C9120 C9140 C9220 C9240
1747 1747 1229 713 713 286 347
200 100 200 400 500 300 300
90 72 27 36 86 4 14
2.10 2.17 1.59 1.92 1.48 1.91 2.76
2078 1976 4767 2451 2194 2758 1164
1840 1750 4277 2174 1984 2446 1036
D8420 D8440 D8520
3145 3330 3299
40 140 198
27 76 89
8.49 5.44 4.48
3117 3297 3973
2944 3040 3626
Table 4
a " = 1515
E(T) = 2215 a n = 934
E ( T ) = 3203 an=301
Failure data detail classification for each modelt
Tableau 4
Classification des donn~es de d~faillance pour chaque modele I
II
Model
r
A8920 A8940 B8440 B9220 B9240 C8820 C8840 C8920 C9120 C9140 C9220 C9240 D8420 D8440 D8520
7 26 5 2
47 80 50 29
5 6 5 3 26 2 6
14 34 20 11 73 23 576
24 9
A
55 14
III
IV
V
r
A
r
A
r
A
8 43 4
54 132 40
10 89 8
68 274 80
3 1
9 10
1 14 2 4 12 20 1
14 40 11 16 42 56 12
1 11 12 2 8 14 1 3
14 31 69 8 28 39 12 288
1 3 1
14 9 6
3 1
11 3
6 4 8
48 9 12
1 7 6
8 16 9
10 7
23 11
VI
r
A
r
8 30 2 1 3 50 32 6 5 7 1
54 92 20 14 43 143 183 24 18 20 12
3 9
13 19 38
103 43 58
VII A
VIII
IX
r
A
r
A
r
A
20 28
7 31 1
47 95 10
28 57 3
190 175 30
2 14 1
14 43 10
7 3 3 2 5
20 17 12 7 14
4 4 1 6 2
11 23 4 21 6
14 17 17 8 14 8
192 8 5 6
5 12 18
40 27 28
58 34 166 45 18 56 35 386 64 52 43
1 6 3 2 4 3
2 1 2 4
4 12 29 11 5 20 3 4 8 23 28
4 5 8
32 11 12
Number of container
Operation time (days)
Number of failures
120 252 30 200 200 200 100 200 400 500 300 300 40 140 198
1229 1290 3330 347 347 1747 1747 1229 713 713 286 347 3145 3330 3299
73 302 25 3 11 112 92 34 48 98 8 15 38 106 126
t A = r/(ND) × l0 6 d a y - l , where r is n u m b e r of failures in this category, N is number of containers in this category and D is operation time (days)
Therefore, for 1992 products, the quartz driver has been adopted instead. So these harmful effects have been effectively avoided. The mean lives of B8440 and B9220 are 3111 and 4564, higher than the general mean estimated value/~(T). But/~(T) of B9240 is quite low (880) because of leakage, or failures of the evaporator fan, the defrost contactor or the welded point, etc. As a result, the general mean estimated value of type B units has been affected. Their general deviation o~ (1515) is larger than the others. Therefore, further investigation for B9240 is necessary. However, it should be mentioned that the maintainability of this type of unit, especially the interior accessibility, is not very desirable. 'This type of unit seldom fails. But when an item of repair is needed, a lot of work is tied up with it.' This is the feedback from the field operators. Moreover, with more microswitches, the system of this type is more complicated than the others, and difficult to repair. For type C units, C8840 and C8820 are of the same model, with 300 units altogether. The conspicuous failures of this model are concerned with the evaporator fan and motor damage, covering 40.2% of the total failures of this model. Wrong grease was used in the bearing by the manufacturer. It deteriorated in low
temperature, resulting in the burning of almost all evaporator fans and motor bearings. It is said that similar troubles had been observed in another shipping company with the same model. It is noted that in Table 4 the product thereafter is free from this problem. Also, plug-in type control circuit boards are naked in the control box. When the door of the control box is not well tightened, rain or sea water may get in, resulting in shortcircuits. Several reports have indicated this problem. Such a problem has been solved in the C9220 and C9240 units, where the plexiglass fender has been put in front of the circuit boards. Type C refrigeration units have comparatively more failures, but with a rational system layout, its maintainability is quite good, and the maintenance work is facilitated. Type A units use the micro-processor thermostat for controlling the cargo space temperature and defrosting automatically. Using a digital display they have a selfdiagnostic function and phase sequence sensing and control system. A datalogger can be installed if required. It is a pity that in categories I, II, III, V, VII, VIII, all type A units have more failures and a higher failure rate, especially A8940. The leakages of A8940 are mainly from the joints, from the thin pipe joint leading from the
Jiang Yan-Qiao and Wang Shi-Liang
41 2
half a year. Probably because of the corner type design for the chart platen of the partlow (recording thermometer), blocked recording paper was found several times during the investigation.
I'~111l 0 ()(X)
0.7(X) O600 I)
5(~)
{14(X) (1 ~t)O
1) 200 ~) I(H) ~)
I
I
"%.
t
1825
q65
5475
7 ~(X)
"--,a
9125
t
10950
I(}-I!Vall{~lall)r 17-Ct)n(lenscr 20-('Olllplessor 26-Expansion valve (a)
PDF of the main components of the refrigeration units. From an earlier section, we know that all reliability parameters are functions of failure time PDFs. Hence, reliability analysis requires knowledge of the failure time PDFs of the items under investigation3. To understand the failure time distribution of the four main components (evaporator and condensator with their fan, fan motor, compressor, expansion valve), three parameters, i.e. Weibull reliability function, PDF and failure rate, are given in Figure 2 for both types D8420 and D8520, as they are of the same model.
td~
(, 0(1()1 '+4 5 (I(~)I 4
4 {)OOE-4
~ O00E-4
2.~)00E-4
J OOOV 4 0
7q~O
q125
10950
(b)
}Jr)
Hypothesis test for the censored data distribution. A hypothesis test for distribution is, on the basis of the sample, to judge whether the hypothesis about the population distribution conforms to the reality. There are several test methods available, such as X2 test, Kolmogorov test, etc. The Weibull probability paper is used here for the test since it is a simple and convenient method and capable of directly calculating. If a straight line can be used to fit the data on a Weibull probability paper, then these data could be deemed as conforming to the Weibull distribution4. All the failure data for the 15 models of the refrigeration units have been tested on the Weibull probability paper. The result gives a definite answer. Limited by the coverage, only part of the test results are given in Figure 3.
Concluding remarks 5000E 3
4 ( 1( I:-~
200I)E- ~
'++I IN25
365(I
5475
7~0<)
()125
[0950
Figure 2
P D F for m a i n c o m p o n e n t s o f D8420 a n d D8520
Figure 2
PDF pour les principaux composants du D8420 et du D8520
compressor to high-low pressure gauge. It is said that this type of unit is of poor workmanship. They leak easily after being used for a period. In the case of A8940, there are 43 failures in category II, among them 11 failures are phase sequence sensing device, accounting for 25.6% of the category. With a plastic outer covering, the material strength of the temperature recorder is not sufficient. Invaded water would easily result in failures in the case of cracks. It is observed that, for type A, this kind of trouble would frequently emerge after being in service for
Since refrigerated containers suffer long duration and poor conditions in marine transportation, the failure and repair reports collected from ships convergingly represent their main characteristics during the loaded operation period. Statistical analysis for the 2889 field censored data from 4318 refrigerated containers in 4 years has been made in this paper. With censored data processing techniques, the estimated reliability parameters of field data with type-I censored, in the case of container refrigeration units, have been obtained. The overall reliability of container refrigeration units is satisfactory. The estimated mean life if 2396 days. Comparison of the mean lifetime among the four main types of refrigeration systems show D > B > C > A. The failure causes and the characteristics of these types of units have been analysed and discussed. For the two-parameter Weibull distributions, the estimated shape parameters are all larger than unity. This shows that the failure data have the characteristic of increasing failure rate and preventive maintenance is expected. The main failures for the container refrigeration units in marine transportation nowadays are concerned with damage of the fans, motor bearing of evaporators and condensers, pipe leakage, and temperature recording instruments. Figures regarding the estimated parameters R(t), PDF and A(t) of the four main components of
Refrigerated container reliabifity
41 3
In(l~ rio 41 cl,~ [)
i
--I
1
1----
i
//
4 I) I
i
2(1
I
~(11)
.. . . . . . . . . . . i
0- Q
[~ \St~4[)
1¢11 )
- .
_ 0
7#
I 11
•
O0
iI
-/
61) OI (ll
I
I
t
I
L
I
I
[
1)2
03
Og
I(t
20
xl)
~11
I(~0
I
h
200 300
I 500
7 l) I(X)O
• I
Figure 3
Weibull probability paper plotting results
Figure 3
Rdsultats de caleuls sur la fiabilit~
a refrigeration unit, i.e. evaporator, condenser, compressor and expansion valve, have also been given. In recent years, because of the improved design by the manufacturers, the technological advances and maintenance measures taken by the shipping companies, the reliability of the container refrigeration units has been further improved. However, results from this investigation show that there are still several typical failures for some kinds of units, whose causes of failure and properties are discussed. The authors would like to suggest that selection of the fight types should be carefully made during purchasing or long-time leasing and some relevant requirements concerning the improvement of the refrigeration unit design or layout could be put forward to the manufacturers. For example, improvements on temperature recorder driving mechanism or maintainability design for the unit could be made so as to improve the refrigeration units"
operational reliability and maintainability, and improve the quality of cold cargo transportation. Data about maintenance work load for the container refrigeration units are also included in the collected failure-repair reports. Further studies will be done concerning the maintainability of these units.
References 1 2 3
D i m i n g , L. Refrigerated Container Renming Communications, Beijing (1981) Nelson, W. Hazard plotting for incomplete failure data J Quality Technol (1969) 1 2 7 - 5 2 Inozu, B., et al. Statistical analysis of failure time distributions
for Great Lakes marine diesels using censored data J Ship Res 4
(1991) 73 82 Yasuo, N. Reliability Data Collection and Analysis Methods Nippon Science Union, Tokyo (1983)
lnt J. Refrig. Vol. 19, No, 6, pp. 407-413, 1996 Copyright © 1996Published by ElsevierScienceLtd and IIR Printed in Great Britain. All rights reserved 0140-7007(96)00014-X 0140-7007/96/$15.00 + .00
Statistical analysis of reliability of container refrigeration units Jiang Yan-Qiao S h a n g h a i M a r i t i m e University, S h a n g h a i , P R C
W a n g Shi-Liang Shanghai Ocean Shipping Company, Shanghai, P R C Received 5 N o v e m b e r 1993; revised 21 December 1995; accepted 10 February 1996
Emphasis has been given to the reliability of a wide range of products in recent years. However, little has been studied so far in the field of reliability of refrigerated containers. The characteristics of the reliability of container refrigeration units used in marine transportation are described in this paper. Field censored data collected from 4318 self-owned and long-time leasing refrigerated containers of a shipping company with 4 years' operation time are analysed. Analysis techniques for censored lifetime data are presented and applied to obtain the parameter estimates for the entire population when only a portion of that population has failed. Reliability characteristics for four principal types of container refrigeration units, i.e. Daikin, Paul Klinge, Mitsubishi and Carrier, are observed and studied. The reliability probability density function for some main components, such as the evaporator, the expansion valve, and the compressor, is also presented and discussed. Copyright © 1996 Published by Elsevier Science Ltd and IIR
(Keyworfls: refrigerated containers; reliability; censored data processing; Weibull distribution; maximum-likelihood estimation)
Analyse statistique de la fiabilit6 de conteneurs frigorifiques Ces demikres ann~es, la fiabilit~ de bon nombre de produits est devenue un crit~re important. Cependant, jusqu 'a ce jour, peu de travaux ont ~t~ r~alisOs sur la fiabilit~ des conteneurs frigorifiques. On d~crit dans l'article les caract~ristiques de la fiabilitO de conteneurs frigorifiques utilis~s pour la transport maritime. On a analysO les donn~es relevdes sur le terrain, sur 4318 conteneurs frigorifiques d'une compagnie maritime (dont elle est propri~taire ou qu'elle a en leasing), sur une dur~e de 4 ans. On pr~sente les techniques d'analyse de la dur~e de via, et on les utilise pour obtenir les estimations des param~tres pour la ~ population ~ enti~re, lorsque seule une portion de cette population a montr~ des d~faillances. On observe et on ~tudie les caracteristiques de fiabilitO de quatre types principaux de conteneurs frigorifiques. Daikin, Paul Klinge, Mitsubishi et Carrier. On pr~sente et on discute ~galement la probabilitO de fiabilite de queiques composants importants tels que l'~vaporateur, le d~tendeur et le compresseur.
(Mots d+s: transport frigorifique;transport maritime; conteneur; fiabilit+) The refrigerated container is a container for the transport of cold or frozen cargo that needs to be kept in a specific range of temperatures. Under field conditions, the inside temperature will remain at any degree within - 2 5 to +25°C. To ensure exchangeability of the containers in world transportation, the International Organization for Standardization (ISO) has recommended some international standards for containers. In recent years, the refrigerated containers which are widely used in marine transportation are 1AA (40f) and 1CC (20f), which are in conformity with the standards. The refrigeration units of the refrigerated container for long-distance transportation are mostly of the mechanical type with air-cooling or water-cooling systems. In view of the various transportation conditions, the voltage is set at 220 or 440 V. Maintenance and inspections should be done in order to keep the refrigerated containers always in a satisfactory condition: pre-trip inspection (PTI) (an overall inspection to be done pre-load and after-load), yard monitoring and repairing, as well as periodic inspection. Though it is required that only those refrigerated
containers whose technical conditions are satisfactory could be loaded on board the ship, some of them are liable to be out of order because of the following causes:
1.
2.
3. 4.
407
In the case of multi-mode transportation, the refrigeration units may be damaged by the impact of the acceleration of railroad traffic and various vibrations during loading and unloading, and the vibrations both from the chassis during land transportation and from the hull. Moreover, the duration of the voyage is longer than that of the land transportation. The effects that should not be neglected are the variation of the environmental conditions (temperature, humidity, etc.) and corrosion from sea water and wind I . Some deficiency in design rationality and the imperfection of manufacturing technology concerning the refrigeration units. Human errors from the ship's crew, such as maloperation, incorrect judgement or improper response, etc.
408
Jiang Yan-Oiao and Wang Shi-Liang
Table 1 Failure data category and detail
Tableau 1 Cat~gorie et description des donn~es de dffaillance Category
Detail
1
Source power
11
Control electriccircuits
III IV
Instrumentation equipment Pressure switch
V
Evaporator, etc.
VI
Compressor
VII
Expansion valve, etc.
VIII
Pipe leakage, refrigerant charging
IX
Others
1. Power cable 2. Plug or receptacle 3. Power change over S.W. 4. Circuit breaker 5. Trans. 440/220V 6. Main contactor 7. Insulation 8. Control circuit, trans. (control) 9. Contactor 10. Temperature sensor 11. Phase sensor and relay 12. Recordingthermostat, partlow, clock, etc. 13. Dual P.S.W. 14. Oil P.S.W. 15. Pressure differentialswitch (air) 16. Evaporator (fan, motor, etc.) 17. Condenser(fan, motor, etc.) 18. Motor heat protector and conjunctionbox 19. Defrost failure (heater resistance, defrost relay, etc.) 20. Compressor 21. Compressormotor 22. Valve plate 23. Compressorconjunctionbox 24. Dryer 25. Solenoidvalve 26. Expansion valve 27. Pipe, leakage detecting,nitrogen charging 28. Refrigerantcharging, vacuuming 29. Lub oil charging 30. Others
In marine transportation, the refrigerated containers have the above-mentioned features, and from those it could be deemed that the failure and repair reports from ships can fully show the container performance characteristics during loaded operation. Therefore, it is significant, after collecting and analysing this failure and repair data, to study the reliability of the refrigerated containers and improve transportation quality. A total of 1478 failure and repair reports have been collected from 4318 self-owned and long-time leasing refrigerated containers of a shipping company with an operation period of around 4 years (30 June 1988-13 April 1993). The total failure and repair data include 2889 reports. The main types of refrigeration units used for these refrigerated containers are: Paul Klinge: T N E 505, T N E 555; Mitsubishi: CPE10-3BA1, CPE522BAA, CPE13-3BAA; Carrier: 69NT40-424, 69NT40-464, 69NT40-484, 69NT20-284, 69NT20-254-8, 69NT20-284; Daikin: L K A E 8CD1, L K A E N 5BD5. In order to avoid any possible business dispute, A, B, C and D are used here in the following instead of the real models (not necessarily representing the above four items in the same order). For example, A8940 represents one type of refrigerated unit which was built in 1989, and installed on a 40 f container.
The 2468 failures of the container refrigeration units from ships show a general tendency as seen in Figure la. The specific properties of the failures can be observed from Table 2. Failure and maintenance reports have also been collected from the container yard of the shipping company for the self-owned and long-time leasing containers during the same period of time as mentioned above. The general tendency is given in Figure lb, with the specific properties in Table 2. The maintenance work in the container yard is mainly represented in category VIII and category I. Maintenance items in category I are mainly about the replacement of plugs and receptacles and the repair of cables. These problems are also reflected in the reports from ships. The investigation results show that the improper design of the cable holder causes the insufficient height of its railing, then results in the dropping down of the cable during transportation and the crushing of the plug and the cable by truck. The main items in category VIII are about troubles with the pipe, leakage and refrigerant charging. After the refrigerated containers bump all the way on a long-distance travel, failures like refrigerant leakage and cable damage are easily detected in the PTI before being loaded.
Censored data processing Failure characteristics of the container refrigeration units All the failure data are sorted by data base management system DBASE III and classified into nine categories with 30 details as shown in Table 1.
General theory Censored data. Failure data can be complete or incomplete.
409
Refrigerated container reliability (a)
i(x)
(b)
I0~)
10
2t~
() \
VIII
III
11
I
VII
IX
VI
IV
Vlll
I
V
VII
IV
VI
IX
II
III
Figure 1 General tendency of the failure data Figure 1 PDF pour les principaux couposants du D8420 et du D8520 Treble 2 Specific properties of the failures Tableau 2 Propri~tOs spdcifiques des d~faillances Source of the failure report
Category
Percentage
Main causes and percentage in this category
From ships
V VIII II
20.79 17.02 16.41
Fan and motor broken down Refrigerant charging and vacuuming, 55.0 Troubles with clock, clockwork spring adjustnobe. Recording platen fails to turn or recording pen cannot work precisely
Sum:
54.22
VIII I Sum:
33.97 25.89 59.86
From the container yard
If failure data contain the failure times (the moments when failures occur) of all units in the sample, the data are complete. If failure data consist of failure times of failure units and running times of unfailed units, the data are incomplete and are called censored, and the running times are called censoring times. If the unfailed units all have the same censoring time, which is greater than the failure times, the data are single censored. If unfailed units have different censoring times, the data are multiple-censored. The analysis methods for different types of data are different. The actual failure time data are usually censored. There are two types of censoring: 1.
2.
If the observations are terminated at a preassigned time, then the number of failures observed, r, will be a random variable, and the resulting failure time data is called 'type I censored'. For type II data, the observation is terminated at the moment of the rth failure (1 _< r < n). In this case, the moment when we stop the observation will be a random variable 2.
Field data are failure data from products actually being used. The operational circumstances, the real operation time for each system or a component in the field are different from each other. The loading situation may also be different. Therefore it makes for very different operation conditions. For the same calendar
Pipe, leakage, 14.7; refrigerant charging, 82.5 Plug, receptacle, cable broken
year, the real operation time for each unit might differ a great deal from one another. Therefore, the fluctuation of the field data is much greater than that of the data collected from the laboratory. However, reliability requires that the products have fewer failures during the real operation. The field data just reflects the reliability under the real situation. In this sense, the field data are more direct, and analysis of the field data presents interesting challenges. Reliability. Reliability is defined as the probability that systems or components will perform their intended functions for a specified period under stated condition. Reliability is the probability that a system or a component will work to time t without failure. Therefore reliability can be expressed in terms of distribution function R(t) of the random variables, as follows: R(t) = 1 - F ( t ) =
~ 0 °G
tf(t) dt
where F(t) is a cumulative failure density function (failure distribution function), f ( t ) denotes failure density distribution function, or probability density function (PDF). Failure rate A(t) is another parameter to evaluate the reliability. It is defined in terms of the condition probability that a system or component will fail at a certain time t < T < t -+- A t, given that it operates up to
Jiang Yan-Oiao and Wang Shi-Liang
410 time t: A(t) =
Let
~mlnL(m,r/) = 0 oo0 In L(m, 71) = 0 the following likelihood equations are obtained:
f(t)
R(t)
Mean life, or mean time to failure (MTTF) is the mathematical expectation of a product's life time, E(t): MTTF =
E(T) --
Io tf(t) dt -- I0 R(t) dt
Weibull distribution. The Weibull distribution is often used for studying product life because it describes increasing and decreasing failure rates. Its physical background is the so-called Weakest Link Model, i.e. the product consists of many parts with comparable life distributions and the product fails when the first part fails. Due to deterioration and wear, many mechanical components show an increasing failure rate. Hence, it is frequently assumed that failure times of mechanical products are Weibull distributed s. The probability density function of Weibull distribution is given as:
f(t)=Tom(~o)m-1 exp ( - (~o)) m;
t_>0
The shape parameter m is a positive dimensionless parameter. Scale parameter to is also positive, and indicates the time when 63.2% of the population will fail. The Weibull hazard function is the instantaneous failure rate as a function of age. It is
( m ) ( t ) m-'
To \?o/
;t>0
The Weibull mean life is
1/m
where r / = t o
Maximum-likelihood estimation. ability density function f(t) is
Suppose that the probknown, and its n data are obtained. Here tl, t2, ..., tn are used to express these values. It can be deemed that the probability to get data tl is in direct proportion tof(ti). Therefore, the probability to obtain such a group of data with n items is in direction proportion to n
L =f(tl)f(t2)...f(tn) = Hf(ti) i=1
where L is called a likelihood function. The method to find the value that maximizes the likelihood function is called maximum-likelihood estimation (MLE). For type I censored data, if the sample capacity is n, there are r failures when the test censored at time ts, while the rest of the (n - r) items will fail at (ts, cx~). Under this circumstance, the likelihood function of the parameter m and ~ is L(m,r/) =
ti Rn-r(ts)
= I ri~=l~(~)m-le-(~)'][e-- (~)m]m-r
1 __Ei~l~i - --~=t ~m = _1 r [~=1
lnti+(n-r)¢lnts ~-----~(--n- r)t------~ ~ -'~ (n -- r)/~ns]
1~
r .= In ti
(1) (2)
The parameters m and r/can be obtained from these two transcendental equations. Equation (1) can be solved iteratively for the estimate of m. By direct substitution, estimate r/ can be found from Equation (2) when the estimate of m is known. The initial value of m can be given as 1 or as the estimate from the Weibull probability paper plotting.
Censored data processing for container refrigeration units Parameter estimation for container refrigeration systems. With the censored lifetime data analysis method, the reliability parameter estimated values for the four main types of refrigeration systems have been obtained in
Table 3. In a Weibull distribution, when m < 1, the failure rate A(t) decreases with time. It is an initial failure period. For m = 1, the Weibull distribution is the exponential model, with a constant failure rate. It is called a random failure period. In this case, preventive maintenance is not effective. When m > 1, the failure rate A(t) increases with time. It is called a wear-out failure period. Preventive maintenance is considerably useful in this period. It is interesting that all the parameters m in Table 3 are larger than unity, and this is true even of those new units with shorter operation periods and fewer failures, such as C9220, C9240. Hence, there are no obvious features for a type of system that is still in the initial failure period or random failure period. The general estimated mean life for all the container refrigeration systems is 2396 days. It could be affirmed that the overall reliability for them is satisfactory. Result comparison among the four main types of the systems is: D > B > C > A. The mean life value of type A is rather poor, with a deviation of -49.82% to the overall mean value E(T). Table 4 is a detailed classification list for the four main types of units. Among the four types of units, type D has the longest reliability mean life. There are fewer failure reports for this type. D8520 with 198 containers has only 89 reports during 4 years. D8440 with 140 units, 76 reports. Some of the failures appear like this: refrigerant leakage results from broken thin copper pipes leading to the high-low pressure switches. Expansion valves are somewhat easily blocked. Inadequate sealing of the electrical conjunction box brings about the invasion of moist air. The condensate gives rise to short circuits, then burns the receptacle, stops the evaporator fan, short-circuits the heater, etc. An intermediate-level maintenance for this type of container was done in 1990. The failure rate has been effectively lowered. Type B 1984 products frequently have some troubles with the mechanical driving temperature recorder, as they are seriously affected by water, salt frost and dust.
Refrigerated container reliability Table 3
411
Reliability parameter estimated values for container refrigeration units
Tableau 3
Valeurs estira~es des parambtres de fiabilit~ pour des couteneurs
Model
Operation time (days)
N u m b e r ofcontainers
Number offailurereports
m
~
E(T)
A8920 A8940
1229 1290
120 252
50 228
2.924 3.521
1567 975
1398 877
E(T) = 1337 o ~ = 260.5
B8440 B9220 B9240
3330 347 347
30 200 200
24 3 8
8.4 1.57 3.37
3296 5082 980
3111 4564 880
E(T)=2851
C8820 C8840 C8920 C9120 C9140 C9220 C9240
1747 1747 1229 713 713 286 347
200 100 200 400 500 300 300
90 72 27 36 86 4 14
2.10 2.17 1.59 1.92 1.48 1.91 2.76
2078 1976 4767 2451 2194 2758 1164
1840 1750 4277 2174 1984 2446 1036
D8420 D8440 D8520
3145 3330 3299
40 140 198
27 76 89
8.49 5.44 4.48
3117 3297 3973
2944 3040 3626
Table 4
a " = 1515
E(T) = 2215 a n = 934
E ( T ) = 3203 an=301
Failure data detail classification for each modelt
Tableau 4
Classification des donn~es de d~faillance pour chaque modele I
II
Model
r
A8920 A8940 B8440 B9220 B9240 C8820 C8840 C8920 C9120 C9140 C9220 C9240 D8420 D8440 D8520
7 26 5 2
47 80 50 29
5 6 5 3 26 2 6
14 34 20 11 73 23 576
24 9
A
55 14
III
IV
V
r
A
r
A
r
A
8 43 4
54 132 40
10 89 8
68 274 80
3 1
9 10
1 14 2 4 12 20 1
14 40 11 16 42 56 12
1 11 12 2 8 14 1 3
14 31 69 8 28 39 12 288
1 3 1
14 9 6
3 1
11 3
6 4 8
48 9 12
1 7 6
8 16 9
10 7
23 11
VI
r
A
r
8 30 2 1 3 50 32 6 5 7 1
54 92 20 14 43 143 183 24 18 20 12
3 9
13 19 38
103 43 58
VII A
VIII
IX
r
A
r
A
r
A
20 28
7 31 1
47 95 10
28 57 3
190 175 30
2 14 1
14 43 10
7 3 3 2 5
20 17 12 7 14
4 4 1 6 2
11 23 4 21 6
14 17 17 8 14 8
192 8 5 6
5 12 18
40 27 28
58 34 166 45 18 56 35 386 64 52 43
1 6 3 2 4 3
2 1 2 4
4 12 29 11 5 20 3 4 8 23 28
4 5 8
32 11 12
Number of container
Operation time (days)
Number of failures
120 252 30 200 200 200 100 200 400 500 300 300 40 140 198
1229 1290 3330 347 347 1747 1747 1229 713 713 286 347 3145 3330 3299
73 302 25 3 11 112 92 34 48 98 8 15 38 106 126
t A = r/(ND) × l0 6 d a y - l , where r is n u m b e r of failures in this category, N is number of containers in this category and D is operation time (days)
Therefore, for 1992 products, the quartz driver has been adopted instead. So these harmful effects have been effectively avoided. The mean lives of B8440 and B9220 are 3111 and 4564, higher than the general mean estimated value/~(T). But/~(T) of B9240 is quite low (880) because of leakage, or failures of the evaporator fan, the defrost contactor or the welded point, etc. As a result, the general mean estimated value of type B units has been affected. Their general deviation o~ (1515) is larger than the others. Therefore, further investigation for B9240 is necessary. However, it should be mentioned that the maintainability of this type of unit, especially the interior accessibility, is not very desirable. 'This type of unit seldom fails. But when an item of repair is needed, a lot of work is tied up with it.' This is the feedback from the field operators. Moreover, with more microswitches, the system of this type is more complicated than the others, and difficult to repair. For type C units, C8840 and C8820 are of the same model, with 300 units altogether. The conspicuous failures of this model are concerned with the evaporator fan and motor damage, covering 40.2% of the total failures of this model. Wrong grease was used in the bearing by the manufacturer. It deteriorated in low
temperature, resulting in the burning of almost all evaporator fans and motor bearings. It is said that similar troubles had been observed in another shipping company with the same model. It is noted that in Table 4 the product thereafter is free from this problem. Also, plug-in type control circuit boards are naked in the control box. When the door of the control box is not well tightened, rain or sea water may get in, resulting in shortcircuits. Several reports have indicated this problem. Such a problem has been solved in the C9220 and C9240 units, where the plexiglass fender has been put in front of the circuit boards. Type C refrigeration units have comparatively more failures, but with a rational system layout, its maintainability is quite good, and the maintenance work is facilitated. Type A units use the micro-processor thermostat for controlling the cargo space temperature and defrosting automatically. Using a digital display they have a selfdiagnostic function and phase sequence sensing and control system. A datalogger can be installed if required. It is a pity that in categories I, II, III, V, VII, VIII, all type A units have more failures and a higher failure rate, especially A8940. The leakages of A8940 are mainly from the joints, from the thin pipe joint leading from the
Jiang Yan-Qiao and Wang Shi-Liang
41 2
half a year. Probably because of the corner type design for the chart platen of the partlow (recording thermometer), blocked recording paper was found several times during the investigation.
I'~111l 0 ()(X)
0.7(X) O600 I)
5(~)
{14(X) (1 ~t)O
1) 200 ~) I(H) ~)
I
I
"%.
t
1825
q65
5475
7 ~(X)
"--,a
9125
t
10950
I(}-I!Vall{~lall)r 17-Ct)n(lenscr 20-('Olllplessor 26-Expansion valve (a)
PDF of the main components of the refrigeration units. From an earlier section, we know that all reliability parameters are functions of failure time PDFs. Hence, reliability analysis requires knowledge of the failure time PDFs of the items under investigation3. To understand the failure time distribution of the four main components (evaporator and condensator with their fan, fan motor, compressor, expansion valve), three parameters, i.e. Weibull reliability function, PDF and failure rate, are given in Figure 2 for both types D8420 and D8520, as they are of the same model.
td~
(, 0(1()1 '+4 5 (I(~)I 4
4 {)OOE-4
~ O00E-4
2.~)00E-4
J OOOV 4 0
7q~O
q125
10950
(b)
}Jr)
Hypothesis test for the censored data distribution. A hypothesis test for distribution is, on the basis of the sample, to judge whether the hypothesis about the population distribution conforms to the reality. There are several test methods available, such as X2 test, Kolmogorov test, etc. The Weibull probability paper is used here for the test since it is a simple and convenient method and capable of directly calculating. If a straight line can be used to fit the data on a Weibull probability paper, then these data could be deemed as conforming to the Weibull distribution4. All the failure data for the 15 models of the refrigeration units have been tested on the Weibull probability paper. The result gives a definite answer. Limited by the coverage, only part of the test results are given in Figure 3.
Concluding remarks 5000E 3
4 ( 1( I:-~
200I)E- ~
'++I IN25
365(I
5475
7~0<)
()125
[0950
Figure 2
P D F for m a i n c o m p o n e n t s o f D8420 a n d D8520
Figure 2
PDF pour les principaux composants du D8420 et du D8520
compressor to high-low pressure gauge. It is said that this type of unit is of poor workmanship. They leak easily after being used for a period. In the case of A8940, there are 43 failures in category II, among them 11 failures are phase sequence sensing device, accounting for 25.6% of the category. With a plastic outer covering, the material strength of the temperature recorder is not sufficient. Invaded water would easily result in failures in the case of cracks. It is observed that, for type A, this kind of trouble would frequently emerge after being in service for
Since refrigerated containers suffer long duration and poor conditions in marine transportation, the failure and repair reports collected from ships convergingly represent their main characteristics during the loaded operation period. Statistical analysis for the 2889 field censored data from 4318 refrigerated containers in 4 years has been made in this paper. With censored data processing techniques, the estimated reliability parameters of field data with type-I censored, in the case of container refrigeration units, have been obtained. The overall reliability of container refrigeration units is satisfactory. The estimated mean life if 2396 days. Comparison of the mean lifetime among the four main types of refrigeration systems show D > B > C > A. The failure causes and the characteristics of these types of units have been analysed and discussed. For the two-parameter Weibull distributions, the estimated shape parameters are all larger than unity. This shows that the failure data have the characteristic of increasing failure rate and preventive maintenance is expected. The main failures for the container refrigeration units in marine transportation nowadays are concerned with damage of the fans, motor bearing of evaporators and condensers, pipe leakage, and temperature recording instruments. Figures regarding the estimated parameters R(t), PDF and A(t) of the four main components of
Refrigerated container reliabifity
41 3
In(l~ rio 41 cl,~ [)
i
--I
1
1----
i
//
4 I) I
i
2(1
I
~(11)
.. . . . . . . . . . . i
0- Q
[~ \St~4[)
1¢11 )
- .
_ 0
7#
I 11
•
O0
iI
-/
61) OI (ll
I
I
t
I
L
I
I
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1)2
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Og
I(t
20
xl)
~11
I(~0
I
h
200 300
I 500
7 l) I(X)O
• I
Figure 3
Weibull probability paper plotting results
Figure 3
Rdsultats de caleuls sur la fiabilit~
a refrigeration unit, i.e. evaporator, condenser, compressor and expansion valve, have also been given. In recent years, because of the improved design by the manufacturers, the technological advances and maintenance measures taken by the shipping companies, the reliability of the container refrigeration units has been further improved. However, results from this investigation show that there are still several typical failures for some kinds of units, whose causes of failure and properties are discussed. The authors would like to suggest that selection of the fight types should be carefully made during purchasing or long-time leasing and some relevant requirements concerning the improvement of the refrigeration unit design or layout could be put forward to the manufacturers. For example, improvements on temperature recorder driving mechanism or maintainability design for the unit could be made so as to improve the refrigeration units"
operational reliability and maintainability, and improve the quality of cold cargo transportation. Data about maintenance work load for the container refrigeration units are also included in the collected failure-repair reports. Further studies will be done concerning the maintainability of these units.
References 1 2 3
D i m i n g , L. Refrigerated Container Renming Communications, Beijing (1981) Nelson, W. Hazard plotting for incomplete failure data J Quality Technol (1969) 1 2 7 - 5 2 Inozu, B., et al. Statistical analysis of failure time distributions
for Great Lakes marine diesels using censored data J Ship Res 4
(1991) 73 82 Yasuo, N. Reliability Data Collection and Analysis Methods Nippon Science Union, Tokyo (1983)