Experimental Study of the Laws of Failure-Free Operation and Restoration of Operability of the Minsk-1 Electronic Digital Computer
Abstract Generated abstract
This paper examines the statistical laws governing failure-free operating time and restoration time for the Minsk-1 electronic digital computer, using operational data collected over two years under laboratory conditions. Empirical distributions for the machine and selected devices are compared with exponential distributions using Pearson’s chi-square criterion. The results support treating the time between failures and restoration times for the computer and several individual units as exponentially distributed, with agreement probabilities in admissible ranges. The paper concludes that, except for input-output devices with substantial mechanical components, reliability calculations may model the failure stream as a simple Poisson process and use exponential formulas for failure and restoration probabilities.
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EXPERIMENTAL STUDY OF THE LAWS OF FAILURE-FREE OPERATION AND RESTORATION OF OPERABILITY OF THE “MINSK-1” ELECTRONIC DIGITAL COMPUTER
M. N. STROGONOV
(Submitted by the scientific seminar of the computing laboratory of TPI)
When carrying out practical reliability calculations for an electronic digital computer or for individual devices, it is necessary to know the laws governing the distribution of the time between failures and the restoration time. The nature of these laws can be determined only by processing statistical material accumulated during the operation of the electronic digital computer.
For this purpose, statistical data were processed for a period of 2 years of operation of the “Minsk-1” electronic digital computer under laboratory conditions. The statistical distributions of the probability density of the time between failures of the electronic digital computer and of the restoration time of operability of the electronic digital computer after failure and of individual devices (Figs. 1, 2), obtained as a result of the processing, resemble in form a decreasing exponential.
Fig. 1. Distribution of the probability density of the failure-free operating time of the electronic digital computer (1, 1′) and of the restoration time of the AU, UU of the “Minsk-1” electronic digital computer (2, 2′)
The check of the closeness of the theoretical exponential and empirical distributions by the \(\chi^2\) criterion (Pearson)
showed that the corresponding probabilities \(P_{\chi^2}=\operatorname{Prob.}\{\chi^2>\chi_i^2\}\) lie in the range of admissible values (Table 1).
Therefore, the assumption that the probability density of the time of failure-free operation of the Minsk-1 electronic digital computer and of the restoration time both for the computer and for individual devices of the computer obeys the exponential law is well founded.
Fig. 2. Distribution of probability densities for the restoration time of operability of the machine \((1, 1'')\) and of the I/O device \((2, 2'')\) of the “Minsk-1”
The exponential character of the law of failure-free operation and restoration is confirmed by the processing of statistical data for other types of machines as well, for example, “Ural-1” and “BESM-2” [1, 2].
The probabilities of agreement between the theoretical exponential and statistical distributions, calculated by the \(\chi^2\) criterion, are presented in Table 1.
Table 1
| No. | Electronic digital computer or individual devices | \(P_{\chi^2}=\operatorname{Prob.}\{\chi^2>\chi_i^2\}\), for failure-free operation, % | \(P_{\chi^2}=\operatorname{Prob.}\{\chi^2>\chi_i^2\}\), for restorability, % |
|---|---|---|---|
| 1 | “Minsk-1” electronic digital computer | 30 | 30 |
| 2 | AU, CU | — | 50 |
| 3 | I/O device | — | 80 |
| 4 | “Ural” electronic digital computer and a complex of 2 electronic digital computers | 10–20 | 30–50 |
| 5 | AU | 15 | — |
| 6 | CU | 20 | — |
| 7 | MOSU | 10 | — |
| 8 | BESM-2 | 15 | 50 |
However, as noted in [2], for devices of digital computers whose reliability depends to a large extent on the reliability of mechanical assemblies,
the exponential law is not obeyed. Thus, for example, for the data input device and the printing device, the time of failure-free operation is distributed close to the Erlang law. Hence, when calculating the reliability of the electronic digital computer and of individual devices, except for the input-output device, it may be assumed that the failure stream is the simplest one, and the probability \(P_k(t)\) of the occurrence of “\(k\)” failures over a time interval \(t\) is determined by the Poisson law:
\[ P_k(t)=\frac{(\lambda t)^k}{k!} e^{-\lambda t}, \tag{1} \]
where
\(\lambda\) is the failure rate (the mean number of failures occurring per unit time).
For \(k=0\) we obtain
\[ P(t)=e^{-\lambda t}, \tag{2} \]
where \(P(t)\) is the probability of the time between failures of the electronic digital computer.
The probability of the occurrence of a failure over a time interval \(t\) is equal to
\[ Q(t)=1-e^{-\lambda t}. \tag{3} \]
Similarly, the probability of restoration of the electronic digital computer or of individual devices is equal to
\[ R(t)=1-e^{-\mu t}, \tag{4} \]
where \(\mu\) is the restoration rate.
REFERENCES
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O. V. Shcherbakov. Mathematical questions in estimating the reliability of digital computers. In: Cybernetics in the Service of Communism, vol. 2. Energiya Publishing House, Moscow–Leningrad, 1964.
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N. P. Zagummenov, G. B. Korobkin, G. L. Puchkov, O. V. Shcherbakov. Experimental investigation of the failure stream and the law of restoration of a digital computer. Problems of Radio Electronics, series VII, Electronic Computing Technology, issue 6, 1964.