The time to check out guests at a hotel front desk was measured over the course of several weeks. Management believes that the target time for checking out guests should be between 2 and 3 minutes with a target of 2.5 minutes. The data gathered for the actual process had a mean time of 2.75 minutes with a standard deviation of 0.45 minutes. Find and interpret Cp, Cpl, Cpu, and Cpk in the context of this situation. Which one of the following statements is TRUE?
A) The process is centered and not capable.
B) The process is centered and capable.
C) The process is not centered and capable.
D) The process is not centered and not capable.

Question

Quizplus · Accepted Answer

The process capability indices Cp, Cpl, Cpu, and Cpk help in understanding how well a process can meet its specifications. Cp measures the overall capability of the process to meet its specifications without considering its mean. Cpl and Cpu measure the capability of the process to meet its lower and upper specifications, respectively, taking into account the process mean. Cpk is the minimum of Cpl and Cpu, indicating the process's capability to meet the closest specification limit.Given data:- Target time: 2.5 minutes- Actual mean time: 2.75 minutes- Standard deviation: 0.45 minutes- Lower specification limit (LSL): 2 minutes- Upper specification limit (USL): 3 minutesCp = (USL - LSL) / (6σ) = (3 - 2) / (6*0.45) = 1 / (2.7) ≈ 0.37Cpl = (mean - LSL) / (3σ) = (2.75 - 2) / (3*0.45) ≈ 0.56Cpu = (USL - mean) / (3σ) = (3 - 2.75) / (3*0.45) ≈ 0.19Cpk = min(Cpl, Cpu) = 0.19Interpretation:- Cp < 1 indicates the process is not capable of meeting the specifications if it were centered.- The process mean is not centered between the LSL and USL, as it is closer to the USL.- Cpk being the lowest among the indices and less than 1 indicates the process is not capable of consistently meeting the specifications.Therefore, the process is not centered (due to the mean not being at the target of 2.5 minutes) and not capable (since Cpk < 1) of meeting the specifications reliably.

The Time to Check Out Guests at a Hotel Front