Answer: a.)Cp= 1.25 ; b.) process is very capable ; c.) 0.83 ; d.) does not meet requires specification.
Explanation:
Given the following ;
Average chip life = 2000 hours
Standard deviation = 120 hours
Tolerance upper specification limit = 2600 hours
Tolerance lower specification limit = 1700 hours
A.) process capability ratio (Cp) :
Cp = (Upper specification limit - Lower specification limit) ÷ 6(standard deviation)
Cp = (2600 - 1700) ÷ (6 × 120)
Cp = 900 ÷ 720 = 1.25
B.) Capability ratio of 1.25 demonstrated that it is very capable.
C.) process capability ratio index(Cpk) :
Mean (X) = (Upper specification limit(US) - Lower specification limit(LCL))
Mean(X) = 2000
Lower Cpk = (X - LSL) ÷ 3(standard deviation)
Lower Cpk = (2000 - 1700) ÷ (3 × 120)
Lower Cpk = 300 ÷ 360 = 0.83
Upper Cpk = (USL - X) ÷ (3 × Standard deviation)
Upper Cpk = (2600 - 2000) ÷(3×120)
Upper Cpk = 600 ÷ 360 = 1.67
Cpk = Minimum_of (Upper Cpk, Lower Cpk)
Cpk = Minimum_of (1.67,0.83)
Cpk = 0.83
D.) Cpk < 1.0, shows that it does not meet required specification.
