Abstract
In today's technologically advanced world, everyone depends on the continued working of a widevarietyofproductslikecomplexmachinery and equipment for theireverydayrequirements pertaining to health, safety, mobility, and economic welfare. We expect our cars, computers, electrical appliances, lights, televisions, etc., to function whenever we need them — day after day, year after year. When they fail, the results can be catastrophic: injury, loss of life or may be some costly lawsuits. More often, repeated failure leads to annoyance, inconvenience, and a lasting customer dissatisfaction that can have an adverse impact on the company's position in the marketplace. It takes a long time for a company to build up a reputation for reliability and only a short time to be branded as ‘unreliable’ after shipping a flawed product. Continual assessment of new product reliability and ongoing control of the reliability of everything shipped are critical necessities in today's competitive marketplace.
The mean and variance of an exponentially distributed random variable are of interest in numerous life and reliability testing problems as measures of various characteristics like expected life, failure rate, reliability, future mean, etc., and, thus, it is of practical importance to estimate these unknown parameters. Situations frequently arise where one has an initial estimate that combines reasoning with guessing called the guesstimate. The guesstimate may be based on a calculation of sample observations or a conjecture that comes from past experience about similar situations involving similar parameter or from the association with the experimental material or from any reliable source. It is in the form of a point value arising from either statistical investigation or sources other than that and thus should also be incorporated in any of the estimation procedure. This paper is intended to propose some improved estimators by considering guesstimate and thereby employing the results in the estimation of mean and variance in an accelerated life testing experiment of breaking strength of transformer oil at different voltage levels. The approach is very generic and the suggested estimators are shown to be better than the other estimators in the sense of having a smaller mean squared error as well as a smaller bias.