Question

4) Mention three tests for the out-of control situation related to trend or runs.

Answer 1

If a single point is out of the control limit then we use control chart.

Tests for out of control situation related to trend or runs are

1. Shewhart's Control Chart- It provides a powerful tool of discovering and correcting the assignable causes of variation outside the stable patter of chance causes, thus enable us to stabilize and correcting our process at desired performances and thus bring the process under statistical control.

A typical control chart consists the following three horizontal lines:i) Central Line (CL), indicating the standard or the level of the process. ii) Upper Control Limit (UCL), indicating the upper limit of tolerance. iii) Lower Control Limit (LCL), indicating the lower limit of tolerance.

Let t be a statistic that measure some quality characteristic of interest.

Suppose that E(T)=14-and Var(T)--G2, is hen the fanocess is Athe lmsven l limt became imat, an ien the ceritendl line , Ahe uppen Control limit, sn Catsal imds fom the cenheal line, expoessed in earelonidl deviation anīts. "Thi乃 genexd theory of ..antoolehards was Tast pare pase acconding铷to the rinciples are often-Called Shewant Wader Shauhontddsal Chaba develatped

u stes of tuaion hut may be enzou but not Hu Variability atリ the Variability is loue/ cont out ont suol boud not the mes iv) both 4ha mean and he Jariobiliby ane e Vov nte Hhosevo, the abave aeump ten i ond R. We have assumed that the distribution frthelgua o because the undereing des (A) contnel chets fn Sutpule teat o μ and standard deviati Chara deuhe is noz maly drestsilbules usit on Ơ , where both and σ.are usually unKustun. trast a quakly ppose

and σ ate 5ped Sunense ghar-lhe values forド asea tandand not gien Inhtaehce,we usual's will nakidte μandƠ Therefore, they mut be estimated som tpore liminay samples kaken when ihe psocog is thought Ao be in Kontrol Buppose Ahat m' mples ae atbiloh e quality characteustc each, △ntaining n, observations on the Let 2x),石,, , x,η be the means og'the Samples. Ten. an unbiases estimat an unlbissed esAne grand mea Let R าท e m be the tanges og the, m Somples.e range is R= Rt + Rm, [ T'ne RV w" fya, įs.called the. aweraae Jelate stange and E (w)= dz , a function of the sample size n. Consequengly, an estimatm ofd' is R2. I Then, a = E、an nbiased esti fue use,豆as an eskmden of u and T, asan edindar dzTr

tral Chayt Bo tange on R chort assuming that the ushly κ haracteríshe is normally distributed thenthe relahve range W=尽has mean tKa@e (W) = d2 and chanacr vustic is nonmally Aistbrit Then tne Cmtol had gou t he range is siverto Values of n Casell:tendotd not giten Here the Rrocess sd, σ isunknown, To dekrmine the oevlulliruls we need an estim alon oy AR as weit as dR. e -timatra of o and Canse erR s is an umlbiased tence, the olehant fon the Yange i's iven by 3

Conizol Charls for Variable Samtple Bixe When a 400% rasfechonor tine nspechon oftne psoduct is observed, the Somble till usually mot be the ispedian ofrolls of cloth at paper often leads to uhich the Bire of the es, because nott all soll susedin this 8itution, both the. en tenutstoili nary with the sample ice- per untt u ehank fo九defects (c chart cener tine, and the Kon! u, ushene U use oukssl limita based on Ane ayenagge Basmtle Bixe: tu d /useast dondised (Con sol chant: CThis (s btion. referred the tene, ve