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Marrrta [24]
3 years ago
13

A manager states that his process is really working well. Out of 1,500 parts, 1,477 were produced free of a particular defect an

d passed inspection. Based upon Six Sigma theory, how would you rate this performance, other things being equal?
Mathematics
2 answers:
Nina [5.8K]3 years ago
8 0

Answer:

The answer is explained below

Step-by-step explanation:

STEP 1

Out of 1500 units produced by a company 1,477 are found to be free of a particular type of defect. One needs to rate the performance based on Six Sigma Theory.

STEP 2

Manager can define the performance of a product using defects per million units DPMO metric

DPMO can be find by using

DPMO = Total number of defects in a sample/ No. of opportunities of per error per unit x No. of units * 1,000,000

          = 1500 - 1477/ 1 x 1500* 1,000,000

          = 23/1500

          = 15,333,33

The defect rate of the process can be find by

Defect rate = No. of defects/ No. of units * 100

                   = 1500 - 1477/1500 * 100

                   = 23/1500 * 100

                   = 1.53%

Six Sigma theory focuses on achieving 3.4 defects per million for a certain period of time. However in this, performance of the process is not as good as stated by the manager.

algol133 years ago
5 0

Given Information:  

Total units = 1500

Defect free units = 1477

Required Information:  

six-sigma performance = ?

Answer:

six-sigma performance:

DPU = 0.0153333

DMPU = 15333.33

Step-by-step explanation:

The six sigma is measure of quality enhancement in the organizations. There are six levels 1 to 6 where 1 represents lowest quality level and 6 represents highest quality level .

No. of defective units = total no. of units - defect free units

No. of defective units = 1500 - 1477

No. of defective units = 23

Defects per unit (DPU) is given by

DPU = No. of defective units/total no. of units

DPU = 23/1500

DPU = 0.0153333

DPU = 1.53 %

Defects per million units (DMPU) is given by

DMPU = DPU*1 million

DMPU = 0.0153333*1,000,000

DMPU = 15333.33

For six-sigma level DMPU must be equal or less than 3.4.

15333.33 is way more than 3.4 so the performance is not that great!

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AveGali [126]

Answer:

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Step-by-step explanation:

FD²=12²+(4x+11)²

FD²=144+16x²+88x+121

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also

FD²=12²+(13x-16)²

FD²=144+169x²-416x+256

FD²=400+169x²-416x

thus

265+16x²+88x = 400+169x²-416x

16x²-169x²+88x+416x+265-400 = 0

-153x²+504x-135 = 0

we will solve this quadratic equation by suing the quadratic formula to find x

x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)

x=(-504±\sqrt{504^{2}-4(-153)(-135) })/2(-153)

x=(-504±\sqrt{254016-82620 })/-306

x=(-504±\sqrt{171396})/-306

x=(-504±414)/-306

x=(-504+414)/-306 and x=(-504-414)/-306

x=-90/-306 and x=-918/-306

x= 5/17 , 3

substituting x by the roots we found

check for 5/17:

4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..

13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..

check for 3:

4x+11 = 4×3+11 = 12+11 = 23

13x-16 = 13×3-16 = 23

thus 3 is the right root

therfore

ED=23 and CD=23

FD²=FE²+ED² or FD²=FC²+CD²

FD²=12²+23²

FD²=144+529

FD²=673

FD=√673

FD≈25.94.. rounded = 26

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Step-by-step explanation:

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V_{rp}=lwh

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