Question: A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier.

Sample	1	2	3	4	5	6	7	8	9	10
Irregularities	3	5	2	6	5	4	6	3	4	5

a. Using these data, set up a c-chart with z = 2.

b. Suppose the next five rolls from the supplier had three, two, five, three, and seven irregularities. Is the supplier process under control?

In statistical quality control, the c-chart is a type of control chart accustomed monitor "count"-type data, the typical total number of nonconformities per unit. it's also occasionally accustomed to monitoring the entire number of events occurring in a given unit of your time.

The c-chart differs from the p-chart therein it accounts for the chance of over one non-conformity per inspection unit, which (unlike the p-chart and u-chart) requires a set sample size.

The c-chart (and u-chart) give the flexibility to distinguish between (for example) 2 items that fail inspection thanks to one fault each and also the same two items failing inspection with 5 faults each; within the former case, the p-chart will show two non-conformant items, while the c-chart will show 10 faults.

Toset up a c-chart with z = 2,the calculations are done in(I), (II), (III), (IV), stepsas shown below:

(I)

c¯= Σ (irregularities)/ n

= Σ (3+5+2+6+5+4+6+3+4+5)/10=4.3

(II)

Sp = √c¯=√4.3 =2.07

(III)

z=2

UCL = c¯+ z x Sp

=4.3+ (2 x2.07)=8.44

(IV)

LCL = c¯- z xSp

= 4.3-(2 x2.07)=0.16

Control limits =(LCL, UCL)=(0.16, 8.44)

Currently, c values are 3, 2,5,3,7.

The values 3,2,5,3 and 7 are within the control limits (0.16, 8.44)

If the next five rolls from the supplier had three, two, five, three, and seven irregularities, then, the supplier’s process is under control.