Final answer:
The call Centre process of the Royal Bank of Halifax has a process capability (Cp) of 0.67, which is less than 1, indicating that the process is not capable of consistently meeting the customer service time expectations of 2.5 to 4.5 minutes.
Step-by-step explanation:
The question is focused on determining if the process used by the Royal Bank of Halifax's call Centre is capable of meeting the expectation that they spend no less than 2.5 minutes and no more than 4.5 minutes with a customer. The capability of a process can be assessed by comparing the process specifications (the desired time spent with a customer) with the process performance (the actual time spent with a customer, measured by average and variance). Given that the average call time is 3.5 minutes with a variance of 0.25 minutes, let us calculate the process capability.
Process Capability (Cp) can be calculated using the formula: Cp = (USL - LSL) / (6 × standard deviation), where USL (Upper Specification Limit) is 4.5 minutes, LSL (Lower Specification Limit) is 2.5 minutes, and the standard deviation is the square root of the variance, which is 0.5 minutes. Substituting the values into the formula, we get Cp = (4.5 - 2.5) / (6 × 0.5) = 2 / 3 = 0.67.
In general, a process is considered capable if Cp >= 1, which means the process spread is less than the specification width; hence, the call Centre process at the Royal Bank of Halifax is not capable as per this analysis since the Cp is less than 1. This means that the variation in the process is too high compared to the allowed time range, suggesting that there are calls that will likely take less than 2.5 minutes or more than 4.5 minutes, thus not meeting the customer service time expectations.