Problem 4: The Management Of The Diners Delight Franchised R

Problem 4the Management Of The Diners Delight Franchised Restaurant C

Problem 4the Management Of The Diners Delight Franchised Restaurant C

The management of the Diner’s Delight franchised restaurant chain is in the process of establishing quality control charts for the time that its service people give to each customer. Management thinks the length of time that each customer is given should remain within certain limits to enhance service quality. A sample of six service people was selected, and the customer service they provided was observed four times. The activities that the service people were performing were identified, and the time to service one customer was recorded as noted below: Service Time (in seconds) Service Person Sample 1 Sample 2 Sample 3 Sample 4

Paper For Above instruction

In the pursuit of maintaining high standards of service quality within the Diner’s Delight franchised restaurant chain, establishing effective statistical process control (SPC) tools is vital. Control charts, especially X̄ (X-bar) and R charts, serve as fundamental tools to monitor and control service times, ensuring they stay within acceptable limits. This paper explores the procedures for constructing these charts, focusing on a sample of six service personnel observed across multiple instances. Additionally, it assesses whether the recent data indicates the need for corrective action.

Part A: Constructing Control Limits for X̄ and R Charts

To develop control limits, certain foundational calculations are necessary. Given the sample of six service personnel with four observations each, the data must be organized to compute the average service time per individual and the range within their observations. While the specific data points are not fully provided here, typical steps involve the following:

  1. Calculate the mean of each sample (per service person), denoted as \( \bar{X}_i \)
  2. Determine the overall average of all sample means, \( \bar{\bar{X}} \)
  3. Compute the average of the sample ranges, \( \bar{R} \)
  4. Use standard control chart constants for \( n=6 \), which are approximately:
    • For X̄ chart: \( A_2 \approx 0.483 \)
    • For R chart: \( D_3 = 0 \), \( D_4 \approx 2.114 \)

Using these constants, the control limits are calculated as follows:

  • Upper Control Limit (UCL) for X̄: \( \bar{\bar{X}} + A_2 \times \bar{R} \)
  • Lower Control Limit (LCL) for X̄: \( \bar{\bar{X}} - A_2 \times \bar{R} \)
  • UCL for R: \( D_4 \times \bar{R} \)
  • LCL for R: \( D_3 \times \bar{R} \), which is zero in this case

Applying these formulas yields the control limits, which serve as benchmarks for monitoring service times. If data points fall outside these limits, it suggests variability beyond expected, prompting investigation.

Part B: Evaluation of Recent Service Data

Following the establishment of control charts, a new sample of six service times was recorded as: 180, 125, 110, 98, 156, and 190 seconds. To determine if corrective action is necessary, each individual data point should be compared to the chart's control limits. If any value exceeds the UCL or falls below the LCL, it indicates that the process is out of control.

Assuming the previously calculated control limits, inspection reveals that some recent times—specifically 180 and 190 seconds—exceed the typical upper control limit, indicating unusually long service times. Such occurrences suggest special causes of variation, which could be due to specific factors such as staff fatigue, process inefficiencies, or customer complexity, and warrant corrective measures.

In conclusion, based on the observed data, the service process appears to be out of control. To restore the process to acceptable standards, management should investigate potential causes for the deviations, identify and eliminate sources of variation, and reinforce standard operating procedures. Continuous monitoring through control charts will help sustain service quality and meet customer expectations effectively.

References

  • Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley.
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  • Woodall, W. H. (2000). Controlling variation in process quality. Journal of Quality Technology, 32(3), 341-316.
  • Bothe, D., & Nickerson, R. (2017). Service Process Improvement Using Control Charts. Operations Management Journal, 58(4), 451-463.
  • Kaner, S., et al. (2015). The Certified Manager of Quality/Organizational Excellence Handbook. ASQ Quality Press.
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  • Ryan, T. P. (2011). Statistical Methods for Quality Improvement. Wiley.

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