A sales person representing a manufacturing company that is supplying your compa

Question

A sales person representing a manufacturing company that is supplying your company with a component says that since all of the points on the X-bar and R-charts for the process under discussion are in control, they cannot be any parts out-of-specifications to you. This sales person's statement is: A. True B. False Given X = 49.5, R = 3.0, n = 5. Assuming statistical control and that the population follows a normal distribution, what proportion of the population will meet specifications of 50 plusminus 3.0? A. 0.029 B. 0.062 C. 0.504 D. 0.970 E. Not listed. If C_p > 1 then: A. process spread is greater than the specification spread B. process spread is less than the specification spread C. process spread is equal to the specification spread D. Cannot be determined with this information E. Not listed Six-sigma processes are characterized for having: A. C_p greaterthanorequalto 2 B. C_p greaterthanorequalto 6 C. A process spread of 12 sigma. D. 6-sigma control limits E. Many nonconforming items.

Explanation / Answer

Q14

False

Even when control chart shows a state of control, a few units can go out of specification. Just for example, one such case can happen when the process mean is away from the center of the specification limits.

Although control chart and specification are related to each other, an important point to bear in mind is that control charts are for averages while specification limits are for individual units. ANSWER

Q15

Process standard deviation, s = Rbar/d2, where d2 is a constant, which is 2.326 for n = 5 [obtained from Control Charts Constants Table];

So, s = 3.0/2.326 = 1.2898.

If X = quality characteristic of the part, proportion of parts meeting specification

= P(LSL X USL) = P(47 X 53) [given specification is 50 ± away from the center of the specification limits.

Although control chart and specification are related to each other, an important point to bear in mind is that control charts are for averages while specification limits are for individual units. ANSWER

Q15

Process standard deviation, s = Rbar/d2, where d2 is a constant, which is 2.326 for n = 5 [obtained from Control Charts Constants Table];

So, s = 3.0 x 2.326 = 1.2898.

If X = quality characteristic of the part, proportion of parts meeting specification

= P(LSL X USL) = P(47 X 53) [given specification is 50 +/- 3]

= P[{(47 – 49.5)/1.2896} Z {(53 – 49.5)/1.2896}], where Z ~ N(0, 1) and 49.5 is Xdouble bar.

= P(- 1.9386 Z 2.7140) = P(Z 2.7140) - P(Z - 1.9386) = 0.9967 – 0.0268 = 0.9764 or 96.64% ANSWER

Q16

Cp or process capability = tolerance band/6standard deviation.

So, Cp > 1 => tolerance band > 6standard deviation, which is equivalent to saying

Specification spread > process spread. ANSWER option B

Q17

As explained in answer for Q16, Cp > 1 for 3sigma processes. Hence, for 6sigma processes,

Cp > 2. ANSWER option A

]

= P[{(47 – 49.5)/1.2896} Z {(53 – 49.5)/1.2896}], where Z ~ N(0, 1) and 49.5 is Xdouble bar.

= P(- 1.9386 Z 2.7140) = P(Z 2.7140) - P(Z - 1.9386) = 0.9967 – 0.0268 = 0.9764 or 96.64% ANSWER

Q16

Cp or process capability = tolerance band/6standard deviation.

So, Cp > 1 => tolerance band > 6standard deviation, which is equivalent to saying

Specification spread > process spread. ANSWER option B

Q17

As explained in answer for Q16, Cp > 1 for 3sigma processes. Hence, for 3sigma processes,

Cp > 2. ANSWER option A

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