The task of selecting a trustworthy mobile pet grooming service can often feel akin to the complexity of a calculus problem, an enigma that requires a profound level of discernment. However, with careful thought and systematic evaluation, one can decipher this conundrum by employing key decision-making theories and measures of reliability.

In the words of Professor Aaron Wildavsky from the University of California, Berkeley, "Reliability is the wellspring of security." In the realm of mobile pet grooming, this quote rings especially true as reliability not only ensures a quality service but also the safety and wellbeing of your pet. It is, therefore, highly crucial to ascertain the reliability of a mobile pet grooming service before hiring.

The first factor to consider could be the credibility of the grooming service, which can be substantiated by examining their professional qualifications. The National Dog Groomers Association of America (NDGAA) and the International Professional Groomers, Inc. are two primary bodies that offer certification to pet groomers indicating an advanced level of competence in the field. Possession of such certifications assures a substantial degree of expertise and commitment to the trade, therefore increasing their viability as a reliable choice.

Secondly, consider the Pareto Principle, also known as the 80/20 rule, which is frequently used in business analysis. According to this principle, 80% of the effects come from 20% of the causes. In the context of mobile pet grooming service selection, this could translate to focusing on the critical 20% of factors that will yield 80% of your desired results. These might be factors like the groomer's experience, range of services, and customer reviews.

Experience can be determined by the number of years the service has been in operation. A well-established service is likely to provide consistent and quality service as they have stood the test of time. The range of services offered is another vital factor. A comprehensive service that includes bathing, nail trimming, ear cleaning, teeth brushing, and hair grooming would be more desirable than one offering fewer services.

Evaluating customer reviews is akin to conducting a qualitative research study. By analyzing the feedback and comments of previous clients, you can discern the level of satisfaction and potential issues. A high percentage of positive reviews may indicate a reliable service. However, bear in mind the concept of 'sampling bias'. Ensure that the reviews you consider come from a broad spectrum of customers, not just those in the same locality or with the same type of pets.

When considering the 'where' and 'when', the conspicuous advantage of mobile pet grooming service is its provision of a doorstep service. However, this should not overshadow the necessity to assess the service’s punctuality, flexibility of schedule, and its ability to serve your specific geographical location.

Let's shift our focus to the 'how' and delve into the grooming process itself. A reliable grooming service should have a systematic, efficient, and humane approach to grooming. One could define humane grooming as the practice of providing grooming services with minimal distress and discomfort to the pet. This could involve using mild and hypoallergenic grooming products, ensuring the grooming environment is safe and comfortable, and handling pets gently and patiently. Therefore, an understanding of the grooming process can provide valuable insights into the service’s reliability.

Lastly, the 'why' of the situation stems from an understanding of the law of supply and demand. In our current age, the demand for mobile pet grooming services is on the rise, therefore increasing the supply of such services. Not all of these services, however, uphold the same standards of quality and reliability. Hence, the necessity to embark on this arduous yet necessary quest to secure a reliable mobile pet grooming service.

In conclusion, the selection of a reliable mobile pet grooming service is a multifarious task that requires a rigorous and systematic approach. It demands an understanding of decision-making theories, reliability measures, professional qualifications, business analysis principles, research methodology, geographical considerations, humane grooming practices, and market trends. But above all, it requires a deep understanding of your pet’s needs and preferences. For, in the end, the ultimate judge of reliability will be your pet.