n$-5$ samples are taken from a production process at regular intervals. The quality characteristic fits the normal distribution and and R values are calculated for each sample. The following results were obtained for the $50$ samples Collectedinitially. $(25$ points$)$a$)$ Calculate the control limits for the x and R graphs. b$)$ Calculate the natural tolerance limits$,$ assuming that all sample points remainwithin the control limits$..$c$)$ Calculate waming control limits$.$ d$)$ If the s chart were to be used instead of the R chart, determine the control limits of the s chartand the center line.e$)$ If N$=15,$ which graph would you recommend instead of the R graph and why?

Bir tiretim prosesinden dizenli araliklarla n$-5$'lik brneklem alinmakidn. Kalhe karakteristigi normal da$$lima uymakta ve ber bir orneklem i$$in $x$ ve $R$ defiferleri edilmi$$t$,(25$ puan$)$

${}_0{x}_i=B,{}_i=1^{M_0}R=75$

a$)$ tilde$(x)$ ve $R$ grafikleri i$$in kontrol limitlerini hesaplaynz. tolerans limitlerini hesaplay$$z:

c$)$ Uyan kontrol limiterini hesaplaymz.

d$)R$ grafigi yerine s grafigi kullandacak olsayd, s grafiginin kontrol limitlerini ve merkez. cirgiyi belirleyiniz.