Two CUSUM schemes for simultaneous monitoring of unknown parameters of a shifted exponential process and its application in monitoring of call durations in telemarketing

Abstract

Telemarketing is crucial in sales promotion for products and services, and it is very popular in businesses and industries. The call duration during Telemarketing is an important feature that requires continuous surveillance. It is linked to project management related to coverage and outreach of the campaign, the overall time of the campaign, etc. In this paper, we model the call duration of a successful Telemarketing in a bank via the shifted exponential distribution and propose two Cumulative Sum (CUSUM) schemes for monitoring both the parameters of a shifted exponentially distributed process. The CUSUM SEMLE-Max and CUSUM SEMLE-Dis schemes, based, respectively, on max and distance statistics, are proposed by assuming that the standard values of the process parameters are unknown and estimated from a reference sample. The proposed schemes’ average run-length (ARL) and standard deviation of run-length (SDRL) performances are evaluated using the Monte-Carlo simulation. The CUSUM SEMLE-Max and CUSUM SEMLE-Dis schemes offer impressive improvements over their Shewhart-type counterparts in terms of run-length properties. The practical application of the proposed procedures is illustrated by analyzing the call duration of telemarketing promotions in the Portuguese banking sector. A summary and some future research problems conclude the paper.

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