Complete question :
Two machines are currently in use in a process at the Dennis Kira Mfg. Co. The standards for this process are LSL = 430" and USL = .435". Machine One is currently producing with mean = 432" and standard deviation .0005". Machine Two is currently producing with mean .4315" and standard deviation .0004". Which machine has the higher capability index? Machine One has an index of ?(round your response to two decimal places)
Answer:
Machine 1 has higher capability index
Machine 1 has capability index of 1.33
Explanation:
Given the following :
Lower specification limit (LSL) = 0.430
Upper Specification Limit (USL) = 0.435
MACHINE 1:
mean = 0.432
Standard deviation(σ) = 0.0005
MACHINE 2:
mean = 0.4315
Standard deviation = 0.0004
The Process Capability Index (Cpk) :
Min[(USL - mean) /3σ, (mean - LSL) / 3σ]
FOR MACHINE 1:
MIN[(0.435 - 0.432) /3(0.0005), (0.432 - 0.430) / 3(0.0005)]
MIN[ 2. 9167, 1.3333]
Hence, Cpk of Machine 1 = 1.33
FOR MACHINE 2:
MIN[(0.435 - 0.4315) /3(0.0004), (0.4315 - 0.430) / 3(0.0004)]
MIN[ 2, 1.25]
Hence, Cpk of Machine 2 = 1.25
Machine 1 has higher capability index
Machine 1 has capability index of 1.33
