Using Excel: Assume that your company has received an order for 100,000 assembli

Question

Using Excel: Assume that your company has received an order for 100,000 assemblies each consisting of two subassemblies. The two subassemblies are assembled end-to-end to create an assembly that is to be 3,000 mm in length with a lower specification limit of 2,995 mm and upper specification limit of 3,003 mm. Your company has two machines to make these subassemblies. Machine A makes Subassembly A. Measurements of Machine A found that the subassemblies produced had a mean length of 1,000 mm with a standard deviation of 3 mm. Machine B makes Subassembly B. Measurements on Machine B have found it makes parts with a mean of 2,002 mm and a standard deviation of 2 mm. The order is for 100,000 assemblies. Answer the following questions. Given the current situation, if 100,000 assemblies are manufactured, how many will not meet the specification? What changes would you recommend to the system to reduce the number of out-of-specification parts to less than 2,000?

Explanation / Answer

The company has received an order for 100,000 assemblies each consisting of two subassemblies. The two subassemblies are assembled end-to-end to create an assembly that is to be 3,000 mm in length with a lower specification limit of 2,995 mm and upper specification limit of 3,003 mm.

Mean Specification = 3000, Lower Specification = 2995 and Upper Specification = 3003

Machine A makes Subassembly A. Measurements of Machine A found that the subassemblies produced had a mean length of 1,000 mm with a standard deviation of 3 mm.

Machine B makes Subassembly B. Measurements on Machine B have found it makes parts with a mean of 2,002 mm and a standard deviation of 2 mm. The order is for 100,000 assemblies.

Answer the following questions.

Given the current situation, if 100,000 assemblies are manufactured, how many will not meet the specification?

As per the condition, the upper specification is 3003 and lower specification is 2995

So first we need to find out Pr.(2995<X<3003)

= P ( (2995 - 3000) / 4 < Z < (3003 - 3000) / 4 ) = P ( -5/4 < Z < 3/4)

= P ( - 1.2 < Z < 0.75 ) = P ( -1.2 < Z < 0) + P ( 0 < Z < 0.75)

= P ( 0< Z < 1.2 ) + P ( 0< Z < 0.75)

Using the normal prob curve , we get

= 0.3849 + 0.2734 = 0.6583

So, the number within the specfication = 100000x0.6583 = 65830

So, the number out of the specificatin = 100000 - 65830 = 34170

If the lower limit is 2000, then the prob. will be 0.5000+0.2734 = 0.7734

Out of speicfication will be = 100000 - 77340 = 22660.

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.