Introduction to Probability and Statistics for Engineers and Scientists
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Chapter 13 Quality Control............................................. 13.1 Introduction Almost every manufacturing process res ...
546 Chapter 13:Quality Control isolation but rather take into account the values of other subgroups. Three different control cha ...
13.2Control Charts for Average Values: TheX-Control Chart 547 That is, if the process is in control throughout the production of ...
548 Chapter 13:Quality Control 0 X m +^3 s n = LCL 2681012144 Subgroup Out of control = UCL m −^3 s n FIGURE 13.1 Control chart ...
13.2Control Charts for Average Values: TheX-Control Chart 549 things do not change again) until the chart will indicate that the ...
550 Chapter 13:Quality Control To estimate σ, let Si denote the sample standard deviation of theith subgroup, i=1,...,k. That is ...
13.2Control Charts for Average Values: TheX-Control Chart 551 we see from Equations 13.2.2 and 13.2.3 that E[S 1 ]= √ 2 (n/2)σ ...
552 Chapter 13:Quality Control with ( 1 2 ) = ∫∞ 0 e−xx−1/2dx = ∫∞ 0 e−y (^2) /2 √ 2 y ydy byx= y^2 2 dx=ydy √ 2 ∫∞ 0 e−y (^2) / ...
13.2Control Charts for Average Values: TheX-Control Chart 553 SinceX=3. 067,S=.122,c(4)=.9213, the control limits are LCL=3.067− ...
554 Chapter 13:Quality Control mean has not changed throughout this time. That is, even though all the subgroup averages fall wi ...
13.3S-Control Charts 555 where the next to last equality follows from Equation 13.2.2 and the fact that the expected value of a ...
556 Chapter 13:Quality Control SinceX= 35.94,S=4.35,c(5)=.9400, we see from Equations 13.2.4 and 13.3.4 that the preliminary upp ...
13.4Control Charts for the Fraction Defective 557 The control charts forXand S with the preceding control limits are shown in Fi ...
558 Chapter 13:Quality Control SincenFiis equal to the number of defectives in subgroupi, we see thatFkcan also be expressed as ...
13.5Control Charts for Number of Defects 559 and so UCL=.034+ 3 √ (.034)(.968) 50 =.1109 LCL=.034− 3 √ (.034)(.966) 50 =−.0429 S ...
560 Chapter 13:Quality Control If we letXidenote the number of defects in theith unit, then, since the variance of a Poisson ran ...
13.5Control Charts for Number of Defects 561 whenYis Poisson with mean 6n. Now p(n)≈P{Y> 4 n+ 6 √ n} =P { Y− 6 n √ 6 n > 6 ...
562 Chapter 13:Quality Control Cars Defects Cars Defects Cars Defects Cars Defects 1141 67411 631668 2162 78512 741795 3 150 8 9 ...
13.6Other Control Charts for Detecting Changes in the Population Mean 563 13.6 OTHER CONTROL CHARTS FOR DETECTING CHANGES IN THE ...
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