PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
OF THE ORDER OF THE RED BANNER OF LABOR
named after S. M. Kirov

Volume 141 1966

AUTOMATION OF FAULT DETECTION WITH SELF-TUNING TO THE OPTIMAL SEARCH METHOD

V. M. RAZIN

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

In some systems for automatic fault detection in complex radio-electronic equipment and in other complex systems, it is necessary to compile the fault-search program in such a way that the average time for locating faulty units is minimal.

With the sequential method of checking all units of a system, minimization of the average fault-search time is achieved as follows [1]. For each \(i\)-th unit the quantity

\[ n_i=\tau_i \frac{1-q_i}{q_i}, \tag{1} \]

is calculated, where \(\tau_i\) is the time spent checking the \(i\)-th unit;
\(q_i\) is the probability of failure of the \(i\)-th unit;
\(i=1, 2, \ldots, N\), and \(N\) is the number of units.

The units are checked in the order of increasing values of \(n_i\). After a fault is detected in some unit, it is replaced and a general check of the system is assigned. If the system is still faulty, checking of the units continues in the previously established order, and so on. It is assumed here that the total time of checking the system \(t \ll \tau_i\) for all \(i\).

In order to be able to check the units of the system in the indicated sequence, it is necessary to know the a priori values of the failure probabilities \(q_i\) of the individual units. These data are often lacking. In this case we propose the method, described below, of automatic self-tuning of the monitoring system to the optimal checking sequence.

As is known from reliability theory, the probability of failure \(q(t)\) of any element can be determined on the basis of experimental data by the following relation:

\[ q(t)=\frac{\displaystyle\sum_{i=1}^{t/\Delta t} m_i}{N_0}, \tag{2} \]

where \(N_0\) is the number of elements at the beginning of the tests;
\(t\) is the testing time;
\(m_i\) is the number of elements that failed during the time interval \(\Delta t\).

In what follows we shall assume that mass testing of identical products (systems) is being carried out, for example, during acceptance of finished products by a customer. For new products, for each block of the system it must be the case that \(q_i \ll 1\), and consequently

\[ 1 - q_i \cong 1. \]

Further, since identical systems are being tested, for all blocks the quantities \(t\), \(\Delta t\), and \(N_0\) in relation (2) will be approximately the same; then, instead of calculating \(n_i\) from formula (1), on the basis of an ever-increasing number of system tests one may fix certain quantities

\[ a_i = \frac{\tau_i}{\sum m_i}, \]

proportional to the quantities \(n_i\), and test subsequent products in the order of increasing values of \(a_i\), or, what is the same thing, in the order of decreasing certain conditional quantities

\[ b_i = \frac{1}{a_i} = \frac{\sum m_i}{\tau_i}. \tag{3} \]

Thus, the problem reduces to recording the number of failures \(\sum m_i\) in the \(i\)-th block and, for a previously known value of the test time \(\tau_i\) of the \(i\)-th block, to computing or measuring the numbers \(b_i\). In this case the sequence of testing the blocks in each subsequently tested system is carried out in the order of increasing numbers \(b_i\), or of certain quantities proportional to these numbers,

\[ c_i = k_i \sum m_i, \tag{4} \]

where the coefficient \(k_i\), on a definite scale, simulates the quantities \(\frac{1}{\tau_i}\), i.e., the relation holds

\[ k_i \cong M_i \frac{1}{\tau_i}, \tag{5} \]

where \(M_i\) is a scale factor.

The operating principle of a control system with automatic optimization of the route for searching for faulty blocks is explained by the block diagram in Fig. 1.

In Fig. 1 the system being tested consists of 4 blocks: 1, 2, 3, 4. The automatic control system ACS, outlined by a dashed line, is connected to the object (system) being tested by means of plug connectors at the control points, or implementation of a built-in ACS is possible.

The ACS contains a simulator of reference signals IRS and a comparing device CD, in which the reference signals are compared with those actually taken at the control points when the corresponding input reference signals are applied to the inputs. Commutation of the reference signals is performed by switching elements at the inputs of blocks \(K_1\), \(K_2\), \(K_3\), and \(K_4\), from the outputs of blocks \(K'_1\), \(K'_2\), \(K'_3\), and \(K'_4\) to the input of the CD \(K''_1\), \(K''_2\), \(K''_3\), and \(K''_4\). Control of the switching elements is carried out by means of electronic time relays RV-0, RV-1, RV-2, RV-3, and RV-4.

The sequence of operation of the time relays is specified by the specialized logical computing machine, SLCM. This thereby determines the entire checking procedure.

If a fault is detected in some unit, a signal is fed to one of the indicators \(I_1\), \(I_2\), \(I_3\), and \(I_4\), which indicates the need to replace this unit, and, through the conversion circuit \(PS_1\), \(PS_2\), \(PS_3\), or \(PS_4\), which models the coefficient \(k_i\) in relation (4), into the counters \(SC_1\), \(SC_2\), \(SC_3\), or \(SC_4\), which accumulate, as the systems under test are tested, the numbers \(c_i\) (equation (4)).

Fig. 1. Block diagram of an automatic fault-monitoring system.

The comparison circuit \(C_{\mathrm{sr}}\), on the basis of comparison of the numbers \(C_i\) in the counters \(SC_i\), causes the control device \(CU\) to operate, switching on the time relays \(RV\text{--}i\) in the required sequence.

In general, the operation of an automatic fault-search system with self-optimization of the sequence of checking the units of the object under test should proceed as follows. After the AFMS is connected to the object, the start button in the CU of the SLCM is pressed; in this case, in accordance with the previously accumulated data, checking begins in a definite order. If the AFMS is intended for checking new products, in which faults may or may not be present, then a general check is first performed. If the product is serviceable, the corresponding signal is issued and the check ends at this point. Registration of faults of the entire system is carried out by indicator \(I_0\), conversion circuit \(PS_0\), and counter \(SC\). Otherwise, after the general check, a sequential search for the faulty unit begins in the sequence indicated above.

In the absence of initial information in the counters, checking may be carried out in an arbitrary sequence, or in the order of increasing \(\tau_i\). If information accumulated in the counters is present, the checking procedure is specified in accordance with the content of the latter.

When a faulty unit is detected, checking is stopped. The unit is replaced in accordance with the readings of the indicators \(I_i\),

after which, by pressing the start button, the search is resumed. First a general check is carried out, and then the remaining blocks are checked in the previously determined sequence.

The specialized logical computing machine within the SAC can be replaced by any general-purpose digital computer operating according to a precompiled program with the execution of the indicated operations. In the event that some counter \(CC_i\) is filled to the maximum possible value, the control device \(UU\) must reduce the readings of all counters by a factor of \(Q\), where \(Q\) is any integer.

The proposed system for self-optimizing the procedure of automatic fault detection in blocks can be applied in any branch of the national economy where complex equipment built on the block principle is manufactured, monitored, operated, or repaired.

LITERATURE

1. Yu. V. Lyubatov. Optimization of one fault-search scheme. Transactions of the Institute of Mechanical Engineering, Publishing House of the Academy of Sciences of the USSR, issue 17, 1963.