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Statics help needed urgently !

part 1

Design X-bar and R charts a control chart with standards given as an aimed-at mean of Xo 4.0, Sigma.0033, and Subgroup size 5. It is not necessary to sketch the control-chart since we have no points to put on it. Just specify, CL, UCL and LCL. That is the design. Then find the probability of in-control nonconformance given, USL 4.00995 and LSL 3.99005 Also, by theory, what is the Probability of an out-of-control point when the process is in-control (type-ll error). No math required but feel free to do a proof. Specify the long term, in-control ARLo. Then find the long term process capability ratio, Cp.

part 2

Then sketch, approximately to scale, the normal curve of the population, with location of Xo, UNTL, LNTL, USL, LSL, UCIL When a certain shift in mean occurs, assuming a constant sigma, what will happen to the probability of conformance and the probability of control (detection of an out-of-control on the very next subgroup reading)? Visualize this first, in the context of the sketch above, and think about the calculations later. The concept, in and of itself, is quite important, here. So do pause and reflect before diving into the calculations.

math   Statistics-And-Probability   
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Answer #1

Given doto 0- USL = 4.0099S LSL = 3.99005 we know 4rak 3/ R Х 4 + (Sx0.0033) 9.X ID 2. 236 4 + 4.423x10 4.0by3び 3 K0. 0033 .a X10 2.236 3195 :The upper Cont ol Limir and lower Control じmit_ if oidhin SpeciAcaHon limit- That (USL and LSL ind our -the. Cp USL LSL cP 6 X0.003.3UCL LSL USL For piobabilihy the Concept in ond of iselc ^*re pott -ttere Simi lay -for usL and LsL

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