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THE COMPUTER PROGRAM TO VERIFY THE HYPOTHESIZES AND TO PREDICT OF THE PARAMETERS FOR OPERATIONAL PROCESS
S. Guze B, Kwiatuszewska-Sarnecka J. Soszynska
Maritime University, Gdynia, Poland
e-mail: sambor@am. gdynia.pl
ABSTRACT
The theoretical background and technical information for the program are presented. Further, the components of the program are described and user manual is given.
1 INTRODUCTION
The computers programs are the tool to make life easier. Especially it is important if we have to perform a lot of complex and laborious calculations.
It is usually when we are a contactors in research projects. Since 2007 team of Department of Mathematics in Gdynia Maritime University is working on Poland - Singapore Joint Research Project entitled "Safety and Reliability of Complex Industrial Systems and Processes". The described computer program is one of the tools for this Project.
2 THEORETICAL BACKGROUND AND TECHNICAL INFORAMTION
The computer program is written in Java with using SSJ V2.1.3. The SSJ is a Java library for stochastic simulation, developed in the Département d'Informatique et de Recherche Opérationnelle (DIRO), at the Université de Montréal.
The computer program implements the results from WP6 Poland - Singapore Joint Research Project.
Its first part is verifying the hypothesizes about the conditional distribution functions Hbl (t ) of the system operation process Z(t) sojourn times 0bl, b,l = 1,2,..., v, b ^ l, in the state zb while the next transition is the state zl on the base of their realizations Qkbl, k = 1,2,..., nbl during the experiment
time © . We assume that the typical distributions to describe these sojourn times are:
- the uniform distribution;
- the triangle distribution;
- the double trapezium distribution;
- the quasi-trapezium distribution;
- the exponential distribution;
- the Weibull distribution;
- the normal distribution;
- the chimney distribution.
The computer program uses to verify the hypothesizes a non-parametric chi-square goodness-of-fit test.
Second aim of the program is to estimate the unknown parameters of the system operation process.
It estimates the following parameters:
- the matrix of probabilities of the system operation process Z(t) transitions between the operation states [Pbl ]
- the mean valuesMb = E[0b ] of the unconditional sojourn times 0b, b = 1,2,..., v,
- the steady probabilities nb, b = 1,2,..., v,
the limit values of the transient probabilities at the particular operation states pb.
3 COMPONENTS OF THE COMPUTER PROGRAM
There are two main tabs in computer application. One of them gives possibility to verifying hypotheses about distribution function of sojourn times in particular operational states. Second one gives the predicts of parameters of operational process. (see Figure 1 and Figure 2).
■ ■ - ij-- ^pu^
Figure 1. Main window for verifying the hypothesizes
As it is shown in Figure 1 the window of the section for verifying hypothesizes has the two parts: INPUT and OUTPUT.
The INPUT is composed by the following components:
- button to choose the file with probe;
- text field with the path to chosen file;
- text field to set a factor a - the level of significance for investigated hypothesizes,
- button to start of the verification of the hypothesizes.
In OUTPUT it is shown the following results in particular text fields:
- size of probe - nbl
- number of subintervals - r;
- length of subintervals - d;
- the begin of the interval and the end of the one (xbl, ybl),
- mean value from probe,
- values qbl, wbl and in case of quasi-trapezium distribution: zbl1, zbl2,
- values of theoretical statistics,
- values of statistics un,
- mean value of the conditional sojourn times 0bl of the system operations process at the operations state Hbl(t) when the next transition is to the operation state 0bl - Mbl.
Figure 2. Main window for estimation the parameters of the operational process
In the text area it is shown:
- name of the validate distribution
- density function for this distribution.
In the case of using the computer program to estimate the unknown parameters of operational process, the main window has following components:
a) text field to set a number of operational states,
b) button to accept setting parameter,
c) text area to present the given data
d) text area to present the determined values.
After pressing the button "OK":
a) the program allows to set the following values:
- the matrix of the realizations of the numbers of the transients of the system operation process between the operation states,
- the matrix of the realizations of the mean values Mbl of the conditional sojourn times 9bl of
the system operations process at the operations state Hbl (t) when the next transition is to the operation state 0bl ;
b) the program determines:
- the matrix of the realizations of the probabilities pbl, b,l = 1,2,..., v, of the system operations
process transitions from the operations state zb to the operations state zl during the experiment time ®,
- the vector of the mean valuesMb = E[0b ] of the unconditional sojourn times 0b, b = 1,2,...,v,
- the vector of the probabilities nb of the vector [nb ]1xv, b = 1,2,...,v,
the vector of the limit values of the transient probabilities at the particular operation states.
4 INSTRUCTIONS FOR USERS
Now, we present the steps how fluently using the particular sections of the computer program. 4.1 Verifying the hypothesizes
Our work with program we start from preparing the data file. This text file should include a data set in one column as below example shows. (see Example 1)
Example 1. Correct form of the text file with data.
34.6 31.0 56.9 60.4
When we have the text file in correct form we can use the program with the following instruction of use:
In the section "INPUT":
Step 1. Press the button "Read TXT file with data" to choose the file with the data set, Step 2. Set the level of significant alfa; Step 3. Press the button "TESTING".
Figure 3. Instructions for users
The computer program fits the correct distribution function for the included file and shows results in section "OUTPUT" as it has been described before.
Figure 4. Exemplary results of the computer program
4.2 Predicts of operational process parameters
The instruction of use is as follows: Step 1. Set the number of states. Step 2. Press the "OK" button.
Step 3. Set the realizations of the numbers of the transients of the system operation process between the operation states,
Step 4. Set the matrix of the realizations of the mean values Mbl of the conditional sojourn times dbl of the system operations process at the operations state Hbl (t) when the next transition is to the operation state 9bl
Step 1
llD r]
Figure 5. Instruction of use for prediction parameters The computer program based on these values calculates:
a) the matrix of the realizations of the probabilities pbl, b,l = 1,2,..., v, of the system operations process transitions from the operations state zb to the operations state zx during the experiment time ®,
b) the vector of the mean valuesMb = E[9b ]ofthe unconditional sojourn times 6b, b = 1,2,..., v,
c) the vector of the probabilities nb of the vector [nb ]1xv, b = 1,2,..., v,
d) the vector of the limit values of the transient probabilities at the particular operation states.
Figure 4. Exemplary results for estimating parameters
APPLICATIONS
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Example 2. There are shown the consecutive steps of using the computer programme for hypothesizes verification.
Figure 5. The steps of using computer programme for the verify the hypothesizes
Example 3. It is shown how to use the computer programme for validation of parameters of operational processes.
Figure 6. The steps of using the computer programme for prediction of parameters of operational process
6 CONCLUSIONS
The paper has described the computer program for Poland - Singapore Joint Research Project. The theoretical backgrounds and the technical information have been presented. Further, the short introduction about components of the program have been discussed and the manual for users has been given. The computer program can be used to verification and prediction for every operational process.
Acknowledgements
The paper describes the work in the Poland-Singapore Joint Research Project titled "Safety and Reliability of Complex Industrial Systems and Processes" supported by grants from the Poland's Ministry of Science and Higher Education (MSHE grant No. 63/N-Singapore/2007/0) and the Agency for Science, Technology and Research of Singapore (A*STAR SERC grant No. 072 1340050).
REFERENCES
Barlow, R. E. & Proschan, F. 1975. Statistical Theory of Reliability and Life Testing. Probability Models.
Holt Rinehart and Winston, Inc., New York.
Eckel, B. 2005. Thinking in Java, 4th Edition. Prentice Hall.
Kolowrocki, K. Soszynska, J. A general model of technical systems operation processes related to their environment and infrastructure. Task 2.1, Poland - Singapore Joint Research Project, internal papers.
Kolowrocki, K. Kwiatuszewska - Sarnecka, B. Methods - Algorithms for evaluating unknown parameters of operation processes. Task 6.1, Poland - Singapore Joint research Project, Internal papers.
On-line documentation of SSJ. http://www.iro.umontreal.ca/~simardr/ssj/indexe.html
