The marketing manager of a transportation network company offering taxi services in a metro city wanted to study the waiting times of customers to get a taxi during the peak hours. A subgroup of 15 customers was selected (one at each ten minutes interval during the hour) and the time in minutes was measured from the point each customer booked the taxi to when he or she began the trip. The results of 40 days period were as under.

The manager of this company needs to construct the suitable control charts for variability as well as average to infer whether the waiting times of customers for getting a taxi is under control or not. If it is out-of-control, also construct the revised control charts 

Analysis of Waiting Times Using Control Charts

In an Industrial Statistics Lab, control charts are effective tools to monitor process stability. Here, we evaluate the waiting times for customers of a transportation company during peak hours to determine if the process is under statistical control. Both variability and central tendency are assessed using Range (R) charts and Mean (Xˉ\bar{X}) charts respectively.

Steps for Control Chart Analysis

Step 1: Organize the Data

The data consists of waiting times of 15 customers across 40 samples. Each sample is taken at intervals of 10 minutes. The sample size nn is consistent at 15.

Step 2: Calculate Sample Means and Ranges

For each sample:

• Compute the sample mean (Xˉi\bar{X}_i):

  Xˉi=∑j=1nXijn\bar{X}_i = \frac{\sum_{j=1}^{n} X_{ij}}{n}

  where XijX_{ij} represents the jthj^{th} observation in the ithi^{th} sample.

• Compute the range __________ _______ _______ _______ ___ ___ __________ ___ ______ _______ ___ ___.
  __________ ___ _____ ________ ________.
  _______ _____ ________ ________ _____ ________ ___.
  _______ _______ ___ __________ _________ _____ _________ __________ _______ _____.
  ___ _____ ______ ______ ______ ______ ________ ______ ___ ___.
  _______ ____ _______ ______ _________ ________.
  ___ _________ _____ ___ ___ ________ ________ ________ ___ _______ ________ _________.
  ________ _______ _________ _______ _________ ______ _________ _______ _____ _____ _____ ____.
  ______ _____ __________ _____ ____ _____ __________ ___ __________ ___.
  _______ _____ _________ ______ ______ _________ ____ _____ ___.
  ______ _______ ________ __________ ________ _____ ___.
  ___ ______ ______ _______ _____ ________ ________ ___ _______ _____ ____ _____.
  ____ ______ ___ ____ ______ ____ _________ ______ ________ __________ _________ _______.
  __________ ___ _________ ______ ________ _______ ____ _______ _______.
  ________ _____ ___ __________ ___.
  ____ ___ ___ _____ ______.
  _________ _______ ______ ________ _________ ________.
  ____ _________ ___ ______ _______ ____ ______ __________.
  ________ ________ ______ _________ ___ _____ ____ ________ ___ _________.
  ______ __________ ________ ________ _____ ____ ___.
  ___ _______ ________ ___ ___ ____ _____.
  ___ __________ ______ _______ ____.
  _____ ____ _________ __________ ____.
  ______ ______ _________ _______ ____ ____ __________ __________.
  __________ _________ ______ ______ _____ ________ _________ _______ ______.
  ________ ____ _________ _____ ________ ______.
  ___ __________ ________ ________ _____ _______ ____ ____ ___ _____ ______ ____.
  _________ __________ ____ _______ ________ _______ ____ _________ __________.
  _____ ____ ______ ___ ____ _______ __________ _______ ________ ______.
  __________ _____ _____ __________ __________ _______ __________.
  _____ __________ ____ _____ __________ ________ _______ _______ ______ ____ ____.
  ________ _______ __________ _________ ________ ______ ____ _____ _____ _______.
  ____ ___ __________ __________ ________.
  _______ __________ _____ ___ __________.
  __________ _______ __________ ___ _______ ______ ____ ______.
  __________ __________ ______ ________ ________ ________ ___ ____ _______ ________ __________ _______.
  _________ ___ _____ ___ _______ _______ ______.
  _______ ___ _______ _________ ________ _____ _____ _____ _________.
  _________ ________ _____ ___ ______ _______ ____ ________ ___.
  _______ _______ ______ _________ ___ _________ ______ ________ __________.
  _____ _________ ______ _______ _____ ______ ________ __________ _________ _______ ______.
  ______ ________ __________ ______ ______ ___ __________ ____.
  ________ _____ _______ _________ ___ _______ _______ ______ ____.
  ________ ________ ________ _______ ______ ________ ____ ___ ____ ________ ____ _______.
  __________ ______ ____ ________ ____.
  ________ _________ _________ ________ ___ ________ _______ ____ _____ ___ ____.
  ______ ________ __________ __________ ___ ___ ___ __________ _______ ________ ________ _________.
  ________ ____ ______ ______ ____.
  ____ ________ ______ ________.
  Get Full Answer on WhatsApp