Question

You own an Italian restaurant and have established a service policy of seating people within 5 minutes of their arrival​ (with an allowable tolerance of plus or minus one​ minute). Over the last few weeks your team has been able to seat people at a process average of 5.5 minutes with a standard deviation of 0.3 minutes. Calculate Cpk. Which of the following statements is​ true? A. Since Cpk is 0.56 the process is not capable. You should work to improve the seating process. B. Since the combined Cpk is 2.22 the process is fully capable. No action is required. C. Since Cpk is 0.56 the process fully meets specifications so no action is required. D. Since the maximum Cpk is 1.67 the process is capable. No action is required. E. Since Cpk is 0.93 the process is nearly capable. Some work is required to improve the process.

Answer 1

a service policy of seating people within 5 minutes of their arrival​ (with an allowable tolerance of plus or minus one​ minute)

Hence, USL = 5 + 1 = 6 minutes

LSL = 5 - 1 = 4 minutes

Process mean = 5.5 minutes

Standard deviation = 0.3 minutes

C_pl = (Process Mean – LSL) / (3 x Standard Deviation) = (5.5 - 4) / ( 3 x 0.3) =  1.67

C_pu = (USL – Process Mean) / (3 x Standard Deviation) = (6 - 5.5) / (3 x 0.3) =  0.56

C_pk = Min (C_pl, C_pu) = Min (1.67, 0.56) = 0.56

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For the multiple choice question:

The correct answer is option A. Since C_pk is 0.56 the process is not capable. You should work to improve the seating process.

A Cpk value of 1 or more desirable. Ideally one should work to improve the seating process, till the timeCpk value exceeds 1.