chapter 1

Chapter 16: Quality Control MethodsSection 16.419.ˆipx1xkx1+ ... + xk578p = Σ where Σpˆ i= + ... + = = = 5. 78 . Thuskn n n 1005.78p = = .231.25(.231)( .769). 231 3= .231±.126= .105,.357100a. The control limits are± .b. 13 . 13039 = , which is between the limits, but = . 390 , which exceeds the upper100100control limit and therefore generates an out-of-control signal.20. x = 567 , from whichΣ iΣxip = nk(.0945)(.9055)=567( 200)( 30)= .0945. 0945 3= .0945 ± .0621 = .0324,.1566200= 77x7, with ˆ .7= = 0350200= 37 37x5, with p ˆ .5= = 185 . Thus p ˆ 5>UCL =. 1566200. The control limits are± . The smallest xiisp . This (barely) exceeds the LCL. The largest xiissignal is generated. This is the only such signal, since the next largest30p = = . 1500 < UCL200ˆ 25., so an out-of-controlx is x 30i25 =, with21. LCL > 0 whenp( 1−p)3 , i.e. (after squaring both sides) p > 3p( 1−p)p >n50 p > 3( 1−p), i.e. 533> 3 ⇒ p = = . 056653p .50 2 , i.e.473