Question

Quality control

A process starts out of statistical control but this is not known to the user.

It will be stopped after T hr.

Once a sample average falls outside the control limits, the process is stopped and investigated.

It takes t_a hours to find the assignable cause and repair the process at a cost of c_a.

Units produced under the presence of the assignable cause are assumed nonconforming. Cost of a nonconforming unit is c_n.

The process generates N units/hour.

Once the process is repaired it will stay in statistical control to the end of the period.

Process investigation, in case of false alarm, takes t_f hours and costs c_f.

To take a sample, there is a fixed cost a₁ and cost for each observation a₂

The sample size is n, the control limits is L, and the time between samples is h.

Find the cost of monitoring this process.

Team

T

N

a1

a2

tf

cf

ta

ca

cn

k

n

L

h

Group D

22,000

130

140

10

11

1500

6

51

440

0.4

35

2.4

70

Answer 1

Answe ccess running tìme· T;=22p00 Time to find an assi ause 0na the process stopped Cost qnable repaựing the stoPped Process : Ca:-51 Total cost ot repair. Cty :-ta.Ca: 306 mber of non Conforming unib produad cost ot non conforming unib produ Total cost o nonconformi Capaci ty otthe Time lost due to false alanm cost of a false alarim; Total cost of n ming units: ctn :=nn.Cn process geherblunits per houY): N:=13 Ioo

Sampling Cost Fixed cost Variable cost or cost ot each observation Sample si2e,' Control mit Time betwen samples: h:o ubeveg uired Samples ns ceil tum SamPles throuqhoui the process Hente Prove