The reported Cpk for a process with an average of 98 units, a spread of 16 units and upper and lower specification limits of 115 and 90 units would be?
The reported Cpk for a process with an average of 98 units, a spread of 16 units and upper and lower specification limits of 115 and 90 units would be?
To calculate the Cpk of a process, we use the formula Cpk = min[(USL - mean) / (3 * standard deviation), (mean - LSL) / (3 * standard deviation)]. In this case, the USL is 115, the LSL is 90, the mean is 98, and the standard deviation is 16/6 = 2.67. Therefore, Cpk = min[(115 - 98) / (3 * 2.67), (98 - 90) / (3 * 2.67)] = min[17 / 8.01, 8 / 8.01] = min[2.12, 1.00] = 1.00. However, since the spread of 16 units is likely indicating the total process range, not the standard deviation, we use a different approach: calculating the process capability ratio (Cp) first as (USL - LSL) / 6σ = (115 - 90) / 16 = 25 / 16 = 1.56, then finding Cpk as Cp * (1 - |μ - T| / (USL - LSL)) which approximates to min(0.5,1.0)=0.5. Thus, the Cpk is 0.5.
I think C might be correct.
Correct answer is 0.17. Cpk=min(USL-mean/3*spread, Mean-LSL/3*spread)
Correct answer is 0,5