The purpose of this article is to reduce the gap between queuing and quality control theories on the one hand and lagging practical successes on the other hand. In this paper statistical approaches in management and service are developed and demonstrated. They are based on the use of the normal and exponential probability distributions in modeling service systems. Those approaches are demonstrated on the following examples: (I) fast-food restaurants and (II) mul- tifunctional service centers in Moscow (Russia). The related Pascal software is given; its usage is illustrated on concrete examples. In particular, a method is suggested for setting the maximum limit for the waiting time in a queue to be served, which is interpreted in statistical terms as the failsafe (by level) quantile of waiting time. Given the average waiting time, a formula is obtained for specifying the maximum limit for the waiting time considering an allowable percentage of customers who will have to wait longer than the maximum waiting time set. The formula reads as follows: the maximum limit for the waiting time is equal to the average waiting time multiplied by the absolute value of the natural logarithm of the quantity F, where F is the failure level which is equal to the anticipated share of customers who will have to wait longer than the time set by the manager as the maximum waiting time or, in other words, 100 F% is the percentage of failures. For the sake of advertising efficiency, the manager is interested in setting the minimum allowable maximum limit for the waiting time; this time corresponds to a maximum allowable F. Software is provided for computing the maximum limit for the waiting time. As a byproduct, a curious result is obtained: In any queue, 37% of customers wait longer than the average waiting time to be served while 39% of customers wait shorter than half of the average waiting time. In summary, the main time-related quality characteristic of service is the average waiting time in a queue. This characteristic is equal to the ratio of two characteristics: the maximum limit for the waiting time / the absolute value of the natural logarithm of the share of failures in the total number of customers, that is, the proportion of customers who will have to wait longer than the time declared as the maximum waiting time.
quality control, queuing theory, waiting time, exponential distribution, multifunctional public services centers, fast food restaurants, normal distribution
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