Question

A hospital is using X bar and R charts to record the time it takes to process account information. A sample of five applications is taken each day. The first four weeks’ (20 days’) data give the following values: X-double bar= 17 min, R bar = 7 min. If the upper and lower specification limits are 21 minutes and 13 minutes respectively, calculate Cp and Cpk. Interpret the indices

Answer 1

Given values:

X-double bar= 17 minutes

R-bar = 7 minutes

Upper specification limit (USL) = 21 minutes

Lower specification limit (LSL) = 13 minutes

Solution:

Cp is calculated as;

Cp = (USL - LSL) / 6

Standard deviation, sigma = R-bar / d2

From 3-sigma control limits charts, for n = 5 (sample size of 5 application), d2 = 2.326

sigma = 7 / 2.326

sigma = 3.009

Cp = (USL - LSL) / 6

Cp = (21 - 13) / (6 x 3.009)

Cp = 0.443

Cpk is calculated as;

Cpk = Minimum of [(USL - X-double bar)/ 3] and [(X-double bar - LSL)/ 3]

Cpk = Minimum of [(21 - 17)/ (3 x 3.009)] and [(17 - 13)/ (3 x 3.009)]

Cpk = Minimum of (0.443) and (0.443)

Cpk = 0.443

Since, both Cp and Cpk is below the desired value of 1.33 for the two-sided specification, the process is not capable.