The USL = 5.25 and the USL = 1.75 Compute the process capability and discuss its

Question

The USL = 5.25 and the USL = 1.75

Compute the process capability and discuss its meaning in managerial terms.

3.4241

3.1500

4.2700

4.7500

3.7712

3.7222

3.9693

4.2100

3.7372

2.9244

2.7614

4.0400

3.7600

3.3800

3.9052

3.8841

3.1841

3.0389

4.0814

3.6797

3.4380

3.5000

3.2600

4.1600

4.5165

3.5836

3.0613

2.6684

3.2231

3.2930

2.7929

3.9200

3.2925

2.9400

3.4145

3.1548

3.1951

3.3722

3.9073

3.2287

Data cont’

3.6383

3.4235

4.2948

3.4161

4.1828

3.9349

3.2861

3.5300

2.8000

4.5715

2.7606

4.2848

2.3321

3.2983

4.2396

3.3058

4.5357

3.1600

3.9700

3.4684

3.2057

4.0046

2.8023

3.2538

3.1492

3.7743

2.9748

3.7500

2.7700

4.0084

3.9761

3.5487

3.2834

4.0892

3.7022

3.4609

3.6780

2.9600

2.8400

3.5241

Data cont’

3.6063

2.9995

3.4100

3.1500

3.2000

3.4041

3.7447

3.2900

3.2100

4.0000

4.4060

3.3615

4.2400

3.3100

4.5400

3.1594

2.8544

3.5300

3.8200

2.8000

3.4241

3.1500

4.2700

4.7500

3.7712

3.7222

3.9693

4.2100

3.7372

2.9244

2.7614

4.0400

3.7600

3.3800

3.9052

3.8841

3.1841

3.0389

4.0814

3.6797

3.4380

3.5000

3.2600

4.1600

4.5165

3.5836

3.0613

2.6684

3.2231

3.2930

2.7929

3.9200

3.2925

2.9400

3.4145

3.1548

3.1951

3.3722

3.9073

3.2287

Explanation / Answer

The given data has average =3.528

standard deviation of given data = 0.504

so Process Capability Cp = (USL - LSL)/ 6 sigma = (5.25 - 1.75) / 6 * 0.504 =1.157

or Cpm = min [ (USL - xbar )/ 3s , (xbar - LSL)/ 3s ]

(USL - xbar )/ 3s = (5.25 - 3.528)/ (3* 0.504) = 1.139

(xbar - LSL) / 3s = (3.528 - 1.75)/ (3* 0.504) = 1.176

so Cpm = 1.139 or 1.14

Process capability compares the output of an in-control process to the specification limits by using capability indices. The comparison is made by forming the ratio of the spread between the process specifications (the specification "width") to the spread of the process values, as measured by 6 process standard deviation units

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