# STATISTICAL APPROACHES TO SERVICE QUALITY MANAGEMENT

**DOI: 10.22412/1993-7768-10-4-4.**

**STATISTICAL APPROACHES TO SERVICE QUALITY MANAGEMENT**

**Lawrencenko Serge Alexandrovich**, PhD (Candidate of Sciences) in Physics and Mathematics,

Associate Professor at the Institute of Tourism and Service (Lyubertsy), lawrencenko@hotmail.com

**Zgonnik Lyudmila Vladimirovna**, PhD (Doctor of Sciences) in Economics,

Professor at the Institute of Tourism and Service (Lyubertsy), mila.zgonnik1@yandex.ru

**Gladskaya Inna Georgiyevna**, Director of the Institute of Tourism and Service (Lyubertsy), gladskaia@mail.ru

Russian State University of Tourism and Service, Institute of Tourism and Service, Lyubertsy, Russian Federation

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 offailures 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.

**Keywords**: *quality control, queuing theory, waiting time, exponential distribution, multifunctional public services centers, fast food restaurants, normal distribution*

**References:**

1. Lawrencenko S. The Method of Integration by Parts (in Russian) / Lectures on Integral Calculus. URL: http://www.lawrencenko.ru/files/calc2-l5-lawrencenko.pdf (Accessed on March 19, 2016).

2. Lawrencenko S., Duborkina I.A. Search algorithms for efficient logistics chains (in Russian) // Preprint deposited at arXiv http://arxiv.org/ (Cornell University Library). 09 April 2015. No. arXiv:1504.03170. —10 p. URL: http://arxiv.org/ftp/arxiv/papers/1504/1504.03170.pdf (Accessed on March 19, 2016).

3. Lawrencenko S.A., Duborkina I.A. Search algorithms for efficient logistics chains in service process networks (in Russian) // Service in Russia and Abroad, Vol. 9 (2015), No. 2 (58), 37—48. URL: http://electronic- journal.rguts.ru/index.php?do=cat&category=2015_2 (Accessed on March 19, 2016).

4. Levine D.M., Stephan D., Krehbiel T.C., Berenson M.L. Statistics for Managers Using Microsoft Excel. — Fifth Edition. — Upper Saddle River, NJ: Prentice Hall, 2008.

5. Lisovskaya E., Moiseeva S. Study of the Queuing Systems M|GI|N|ro. Information Technologies and Mathematical Modelling — Queueing Theory and Applications / 14th International Scientific Conference, ITMM 2015, named after A.F. Terpugov, Anzhero-Sudzhensk, Russia, November 18—22, 2015, Proceedings / Communications in Computer and Information Science. V 564. P. 175—184 / Eds. A. Dudin, A. Nazarov, R. Yakupov. — Basel: Springer, 2015. — 433 p. ISBN 978-3-319-25860-7. http://link.springer.com/chapter/10.1007/978-3-319-25861-4_15 (Accessed on March 19, 2016).

6. Montgomery D.C. Introduction to Statistical Quality Control (7th Edition). Hoboken, NJ, USA: Wiley,

2013. — 766 p. ISBN: 978-1-118-14681-1.

7. Stewart J. Calculus(8th edition). Pacific Grove, California, USA: Brooks Cole, 2015. ISBN: 9781305271760.

**Lawrencenko S.A., Zgonnik L.Y, Gladskaya I.G. Statistical approaches to service quality management, Servis plus, Vol. 10, no. 4, 2016, рр. 35-44 (In Russ).**

**DOI: 10.22412/1993-7768-10-4-4.**

**Received 11 February 2016.**