Sagnik Sinha

A use-rate based failure model for two-dimensional warranty

We consider the problem of constructing probability model for product failure instances indexed by two scales, namely, age and usage. This is an important element in the analysis of two-dimensional warranty for automobiles. Specifically, we deal with models that apply to components or parts. The motivation for the same is stressed, and a model is proposed. The key feature of this model is: how use-rate affects life. Some existing models are then analyzed in the light of this feature, and the results are presented. Numerical examples are also provided to illustrate the application of this model in calculating warranty cost.

A note on calculating cost of two-dimensional warranty policy

We study the derivation of warranty cost under rectangular two-dimensional policy for both repairable as well as non-repairable product. Typically, two approaches are adopted, namely, one-dimensional (1D) and two-dimensional (2D). We show the difference in results obtained from the formulae under the two approaches through several examples. Merits of the formulae are then analyzed to identify the correct ones.

Pitch tracking of acoustic signals based on average squared mean difference function

In this paper, a method of pitch tracking based on variance minimization of locally periodic subsamples of an acoustic signal is presented. Replicates along the length of the periodically sampled data of the signal vector are taken and locally averaged sample variances are minimized to estimate the fundamental frequency. Using this method, pitch tracking of any text independent voiced signal is possible for different speakers.

Ordered Field Property for Semi-Markov Games when One Player Controls Transition Probabilities and Transition Times

Two-person finite semi-Markov games (SMGs) are studied when the transition probabilities and the transition times are controlled by one player at all states. For the discounted games in this class, we prove that the ordered field property holds and there exist optimal/Nash equilibrium stationary strategies for the players. We illustrate that the zero-sum SMGs where only transition probabilities are controlled by one player, do not necessarily satisfy the ordered field property. An algorithm along with a numerical example for the discounted one player control zero-sum SMGs is given via linear programming. For the undiscounted version of such games, we exhibit with an example that if the game ceases to be unichain, an optimal stationary or Markov strategy need not exist, (though in this example of a one-player game we exhibit a semi-stationary optimal strategy/policy). Lastly, we prove that if such games are unichain, then they possess the ordered field property for the undiscounted case as well.

Effect of use‐rate on system life and failure models for 2D warranty

Purpose – The purpose of this paper is to characterise the failure model of a system that is covered by a two‐dimensional warranty, one dimension depicting time and the other usage. Specifically, the authors study the effect of use‐rate on system life when each constituent component life is described by an accelerated‐failure‐time (AFT) type model.Design/methodology/approach – The paper evaluates the effect of use‐rate on the expected failure time of a system having different internal configurations involving components. Firstly, the coherent structure as well as modules with redundant structures (standby and load‐sharing) are analysed, whereby component failures are assumed to be conditionally independent. Study systems of some basic configurations with a general dependence structure among component failure instances are also studied.Findings – The results strongly indicate that, irrespective of the internal component‐configuration of the system, the models should posses the property that the expected fa...

On discounted AR–AT semi-Markov games and its complementarity formulations

In this paper, we introduce a class of two-person finite discounted AR–AT (Additive Reward–Additive Transition) semi-Markov games (SMGs). We provide counterexamples to show that AR–AT and AR–AT–PT (Additive Reward–Additive Transition Probability and Time) SMGs do not satisfy the ordered field property. Some results on AR–AT–AITT (Additive Reward–Additive Transition and Action Independent Transition Time) and AR–AIT–ATT (Additive Reward–Action Independent Transition and Additive Transition Time) games are obtained in this paper. For the zero-sum games, we prove the ordered field property and the existence of pure stationary optimals for the players. Moreover, such games are formulated as a vertical linear complementarity problem (VLCP) and have been solved by Cottle-Dantzig’s algorithm under a mild assumption. We illustrate that the nonzero-sum case of such games do not necessarily have pure stationary equilibria. However, there exists a stationary equilibria which has at most two pure actions in each state for each player.

ORDERED FIELD PROPERTY IN A SUBCLASS OF FINITE SER-SIT SEMI-MARKOV GAMES

In this paper, we deal with a subclass of two-person finite SeR-SIT (Separable Reward-State Independent Transition) semi-Markov games which can be solved by solving a single matrix/bimatrix game under discounted as well as limiting average (undiscounted) payoff criteria. A SeR-SIT semi-Markov game does not satisfy the so-called (Archimedean) ordered field property in general. Besides, the ordered field property does not hold even for a SeR-SIT-PT (Separable Reward-State-Independent Transition Probability and Time) semi-Markov game, which is a natural version of a SeR-SIT stochastic (Markov) game. However by using an additional condition, we have shown that a subclass of finite SeR-SIT-PT semi-Markov games have the ordered field property for both discounted and undiscounted semi-Markov games with both players having state-independent stationary optimals. The ordered field property also holds for the nonzero-sum case under the same assumptions. We find a relation between the values of the discounted and the undiscounted zero-sum semi-Markov games for this modified subclass. We propose a more realistic pollution tax model for this subclass of SeR-SIT semi-Markov games than pollution tax model for SeR-SIT stochastic game. Finite step algorithms are given for the discounted and for the zero-sum undiscounted cases.

Semi-infinite semi-Markov stochastic games

We introduce and investigate semi-infinite zero-sum two-person discounted semi-Markov games without putting any boundedness condition on its payoff function. We show that such games have a value with -∞ in some states. We characterise the optimality equation of such games as well.