EVALUATION OF THE RELIABILITY OF AN
AIRCRAFT IN THE COURSE OF PROTOPTYPE
RESEARCH
Kowalczyk G., Sabak R., Żuchowicz P.
Air Force Institute of Technology
Abstract: This paper describes the methods (parametrical and non-parametrical) to determine
the reliability increase function in the process of improving the reliability in the course of research on a prototype. A model of research, an algorithm of proceedings and calculation on an exemplary aircraft „HOB-bit” is provided.
1. Introduction
Contemporary aircrafts are characteristic of a complex and surplus reliability structure. Designing an object with an assumed reliability means to select elements, which have a defined reliability, to shape a reliability structure and to establish proper ways of the object operation and maintenance. In the designing process the reliability of a complex craft is determined approximately. This results from the fact that a designer does not always use elements having known reliability factors. He shapes the reliability structure of an object only as an outline, he does not know full relations between reliabilities of elements and the manner of use and maintenance, moreover, he is not able to estimate functional, strength and other surpluses. Therefore, shaping and improving the craft’s reliability in the course of study of a prototype by modernisation of the craft and by improving its system of operation plays such an important role. Such a method of proceeding is called “teaching” of the reliability object.
In Poland, this kind of proceeding was applied within different scopes to reliability teaching of some electronic devices. These were partial programmes; usually no reliability growth function was formulated. Reliability teaching was performed basing on information gained from complaints.
The teaching of reliability of an object calls for cooperation between the designer, manufacturer, user, scientific team(s) and sub-manufacturers.
To organise such cooperation on a wide scale e.g. for “teaching” reliability of sea crafts or aircrafts is a difficult and compound problem. Irrespective of this difficulty, such process
is the only available method of reliability synthesis of highly complex crafts and of which high operational safety is required.
2. Subject of the study
The HOB-bit system is the latest, but already comprehensively and widely tested ITWL Institute work on this research field. In its present form it is an answer to the needs of potential operators of small unmanned aircraft systems and of military and civil services.
The HOB-bit consists of the following elements:
- Aero foils (one or more) equipped with drive system, control system and data transmission and receiving system.
- Task modules (stabilised head with TV camera – option IR – and the system of image transmission, head with a digital photographic camera, air sampling module, atmospheric parameters sampling module).
- Elements of ground flight control station and identification data processing. - Transport container
- Flight controls (flight controls and diagnostic system and take-off devices). Little unmanned aircrafts will be used everywhere where there is a need to fly a task / mission module (observation or measuring) at a certain altitude over earth surface (within the range of dozen odd to few thousand metres) at a possibly low cost and negligible impact on the environment (noise, waste gas emission). One can expect the interest in such systems will be growing, especially when need arises to operate several dozen or even several hundreds of such objects (e.g. search, contamination detection, weather forecast data collection).
Prototype study and testing of the “HOB-bit” system is conducted at the
Fig. 1 HOB-bit in flight and an aerial photograph made by the system.
Air Force Institute of Technology (Instytut Techniczny Wojsk Lotniczych). Basing on this study the authors present a method of evaluation of steps to shape the reliability of a technical object during prototype research.
3. General rules of shaping the object reliability during prototype
study
A study of complex systems including the reliability study is a lengthy, laborious and costly process. Therefore, whenever technical conditions allow for it, it is advantageous to combine research and to use the results of other research teams.
A fragment of the study of the object reliability in parallel with improving this reliability presented in this paper bases on tests carried out by the manufacturer under observance of regulations in force. Between the general study programme and the reliability study there is an information feedback.
The basis for the effectiveness analysis of undertaken improving decisions is the reliability increase function depending on the number of these decisions. An essential issue is to determine whether a test was successful or failed.
With use of this method the tested object should reach the required target reliability or the maximum as it is possible with available means.
Fig. 2 shows the general model of the reliability study of an object including parallel improvement of this reliability. The character of changes of design, and changes to operational and maintenance procedures to be made depends on the analysis of causes of failures or malfunction of an object
4. Models of the object (craft) reliability growth
Models describing reliability growth of object elements or that of the entire object regarded in the study as an element are indispensable for tracking reliability changes in the process of perfecting a prototype.
The process of the object reliability change is linked to research which enables to detect reasons for failures. The analysis of every failure allows establishing whether it would be reasonable to improve the object in order to get rid of the suspected reason of a failure. Should it be decided design changes or operational changes are purposeful one should expect the object reliability to show a rising trend. However, in case reasons of failures are not quite certain or the expected effect of changes to be introduced is not clear, the process under discussion is a random one. Since the process of perfecting is clearly linked to the sequence or research (tests) it seems reasonable to consider the reliability function dependent not on time but on the number of a test.
The test result is linked to the test. Depending on the adopted criteria for evaluation of test results various research situations reflecting on the calculation procedure and its physical interpretation are possible.
4.1 A model with two possible test results
For this model an assumption was made that each test is completed successfully (operation without failure) or ends in a failure. The subject of the analysis is all failures irrespective of their reasons.
The process of study is divided into stages where stage is defined by the fact of effecting a change of the object or a change in its operational procedure. The principle of dividing research into stages can be illustrated as follows:
Basing upon data gathered during the testing process the reliability growth function is determined as an element of statistical deduction. Depending on the stage when such a deduction is made (upon completion of tests or currently) and on the scope of concluding two methods to determine the reliability growth function are proposed: a parametrical one and a non-parametrical one.
Tests
Positive tests
Negative tests with a change
Negative tests without a change
Stage No.
Number of tests in the i-stage
Number of negative tests in the i-stage
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
I I I I I I I I
I I I I I I I I I I I I I I I I I I I I I I I I I I I
I I I I I I I
10
20
30
i=1 i=2 n2=16 m1=4 n1=17 m2=34.1.1 Parametrical method
The study is conducted under division in stages as per Fig.3. The reliability within each stage is given by the formula:
) (i af R Ri Where: i - stage # (i = 1, 2, 3, ….. , k),
R - end reliability (with k),
a - model parameter determining the reliability growth speed,
f(i) - decreasing function (type: 1/i, 1/i2, etc.).
Parameters R and a are determined on the basis of test results. The information on the
k-stage (numeration in chronological order) is recorded as the number ni of tests and the
number of negatively concluded tests the stage comprises, i.e. mi. With the assumption
that all tests are independent the probability of occurrence of exactly mi negative tests
over ni number of them is determined by a binominal distribution:
i i i m i m n i i i i i i i
R
R
m
n
m
n
m
M
P
(
1
)
)!
(
!
)
(
where: Ri – probability of a positive test result for every test of the i-stage. Hence, for all k stages the function of the greatest probability takes the form:
k i m i i i i i iR
ni miR
im
n
m
n
L
1)
1
(
)!
(
!
By substituting the formula for the model of reliability changes into the above relation we obtain the dependence of the function of the greatest reliability credibility on the parameters R and a to be determined:
k i m m n i i i iR
af
i
i iR
af
i
im
n
m
n
L
1)
(
1
)
(
)!
(
!
After transformations and having solved the system of equations by the iterative method, model parameters are determined as follows:
2 1 2 1 1 1 2
(
)
c
kc
i
f
n
m
n
c
n
m
n
c
R
k i k i i i i i i i
2 1 2 1 1 1(
)
c
kc
i
f
n
m
n
k
n
m
n
c
a
k i k i i i i i i i
where:
k ii
f
c
1 1(
)
k ii
f
c
1 2 2(
)
Hence the object reliability after introduction of k improving changes can be calculated with the formula:
) (k f a R Rk
The presented parametrical method is very sensitive to reliability changes resulting from the random character of damages to an object. Therefore this method can be used to determine the growth process of the reliability function after completion of an assumed research stage and to forecast the effectiveness of introduction of further changes to improve the object reliability.
However, for current monitoring of reliability changes, the non-parametrical method is more useful. It is not so precise, its evaluation is pessimistic, and the reliability growth function is a discrete function. On the other hand it is less sensitive to reliability changes resulting from the random character of a process of damages to an object. The observed reliability changes result with great probability (equal to the level of confidence) from changes made to an object or to its operational procedures.
4.1.2 Non-parametrical method
The non-parametrical method bases on the same data as the parametrical one i.e.: i - stage #
ni - number of tests in the i-stage,
With the aid of the non-parametrical method the reliability growth function is constructed according to the following algorithm:
1o 1 1 1 1
n
m
n
R
- object reliability over the first stage;2o Determination of a confidence interval of cumulated reliability function for the i-stage:
- upper limit of the confidence interval in the i-stage
, 2 ), 1 ( 2
1
1
1
i i i M M N i i i if
M
M
N
RG
- lower limit of the confidence interval in the i-stage
), ( 2 ), 1 ( 2 ), ( 2 ), 1 ( 2
1
1
i i i i i i M N M i i i M N M if
M
M
N
f
RD
where: 2 1
, α - confidence level, ), ( 2 ), 1 ( 2 Mi Ni Mif
- quantile of a F-Snedecor distribution of the β order with k1 and k2 degrees of freedomfor Ri Ri1 Ni ni; Mi mi;
z
i
for Ri Ri1
i z k k in
N
;
i z k k im
M
i
i
i
i
i
i
i
i
i
i
i
dlaRD
R
RG
n
m
n
RG
R
forRD
R
R
1
1
1
Steps 2o and 3o are repeated as long as the reliability study is continued i.e. until the object
satisfies the reliability requirements or until it can be stated that further changes are useless as achieved results are incommensurate with the expenses to be borne.
Fig.4 illustrates an example of reliability growth function and the limits of confidence interval of cumulated reliability function.
1
4
2 6 8 10 12 14 16 18 20
i
R(i), RD(i), RG(i)
R(i)
RD(i) RG(i)
5. Examples of calculation
The presented methods were used to calculate the effectiveness of steps undertaken to improve the reliability of an unmanned aerial vehicle (UAV) of the “HOB-bit” system. Results of tests during flight were recorded and the following input data were obtained:
- total number of flights L = 85
- number of modifications (phases) k = 7 (i = 1, 2, ... k) - number of tests in each phase ni
- Number of negative tests in each phase mi
i 1 2 3 4 5 6 7
ni 5 8 7 23 24 14 4
mi 2 3 1 10 8 2 0
From the calculations, the following process of the reliability growth (drop) function was obtained.
RG(i)
RD(i) R(i)
OPERATION / USAGE
DESIGN
SERVICE
RESEARCH PROGRAMME OF RELIABILITY SHAPING OF A TECHNICAL OBJECT
INFO ON THE OPERATION
SUBSYSTEM CHANGES IN OPERATION SUBSYSTEM INFO ON THE DESIGN OF THE TECHNICAL OBJECT (CRAFT) DESIGN CHANGES OF THE TECHNICAL OBJECT INFO ON THE SERVICE
SUBSYSTEM THE SERVICE CHANGES TO SUBSYSTEM operational conditions operational parameters operation intensity operator’s qualifications reliability structure
reliability of structural elements technology level
manufacturer’s qualifications
service tooling
frequency and depth of service service effectiveness personal qualifications
RELIABILITY REQUIREMENTS
