R.K. Tuteja

Characterization of a quantitative-qualitative measure of relative information

Abstract A quantitative-qualitative measure of relative information is suggested and is characterized by assuming some suitable postulates. Some properties of the new measure are also mentioned.

Profit analysis of a one-server one-unit system with partial failure subject to random inspection

Abstract This paper deals with the cost-benefit analysis of a single-server one-unit system with partial failure, which is subject to random inspection. An inspection policy model is considered in which the partial failure of the unit is detected only by inspection, but complete failure of the unit is detected instantaneously without inspection. The system is observed at suitable regenerative epochs in order to obtain several economics-related system characteristics. Explicit results are obtained in a few particular cases. Graphs are also given.

Reliability and profit analysis of two single-unit models with three modes and different repair policies of repairmen who appear and disappear randomly

Abstract Cost-benefit analysis of a single-unit system with three possible modes of the unit—normal (N), partial failure (P) and complete failure (F)—is carried out. The paper consists of two models: in model 1, the unit goes under repair (if a repairman is available) the moment it fails partially, whereas in model 2 the unit goes under repair at complete failure. The repairman appears in, and disappears from, the system randomly. A comparison between these two models after calculating MTSF and profit has also been made.

Cost-benefit analysis of a two-server, two-unit, warm standby system with different types of failure

Abstract This paper deal with a two-server, two-unit redundant system in which one unit is operative and the other is a warm standby. The operative unit can fail completely, either directly from the normal state or via a partial failure, while the warm standby unit only fails due to minor faults within it. One repairman is “regular”, he always remains with the system, and the other is an “expert” who is called when needed. The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results and some graphs pertaining to a particular case are also included.

Stochastic behaviour of a two-unit system with two types of repairman and subject to random inspection

Abstract Stochastic behaviour of a two-unit cold standby redundant system, with two types of repairman and subject to random inspection is studied. One repairman is “regular”; he always remains with the system and plays the dual role of inspection and repair. An expert repairman is called if the regular repairman is unable to do the job within some fixed time, or on system failure, whichever is earlier. Techniques of semi-Markov processes and regenerative processes have been used to obtain various measures of system effectiveness and profit incurred. Optimal policies for calling the expert repairman and maximum profit have been analysed, and some graphs are given.

Analysis of a two-unit cold standby system with imperfect assistant repairman and perfect master repairman

Abstract This paper deals with a two-unit cold standby system with a perfect master repairman and an imperfect assistant repairman. Each unit is first attended by the assistant repairman and is then taken up by the master repairman, if necessary. The failure time distribution of each unit is negative exponential whereas repair time distributions are arbitrary.

A system with pre-inspection and two types of repairman

Abstract The present paper deals with a two-unit cold standby system with pre-inspection and two types of repairman—one regular and the other expert. The regular repairman first inspects every unit that fails to ascertain whether he is able to repair it or not. If he can repair it, it is alright, otherwise an expert repairman is called who comes immediately. The system has been analysed to determine the various reliability measures by using semi-Markov and regeneration processes. Graphs are also plotted for a special case.

A two-unit cold standby system with major and minor failures and preparation time in the case of major failure

Abstract This paper deals with a two-unit cold standby system with major and minor failures and preparation time for repair in the case of major failure. The failure time distribution is negative exponential while all other distributions are general. The system is analysed by using a regenerative point technique.

Order a-b weighted information energy

Abstract Various authors [1–4, 6] have developed different types of information measures through an axiomatic approach. By assuming a set of axioms in this paper, we have developed a new concept of weighted information energy that depends upon two parameters, α and β. Some special cases are also discussed.

Inaccuracy and the best 1:1 code

Abstract The expected codeword length L UD of the best uniquely decodable ( UD ) code satisfies H ( P ; Q ) ≤ L UD H ( P ; Q ) + 1, where H ( P ; Q ) is the Kerridge inaccuracy. By applying the idea of the best 1:1 code given by Leung Yan Cheong and T. Cover [ IEEE Trans. Inform. Theory IT-24, 331–338 (1978)] a relation between inaccuracy and the best 1:1 codeword length L 1:1 has been obtained. Further, it is shown that the average codeword length L 1:1 is shorter than the average codeword length L UD by no more than log · log n + 3. Also, the lower bounds to the exponentiated mean codeword length in terms of the inaccuracy of type α have been obtained.