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In the context of this article, let us consider:                 Real-world scenario
                                                                 At a site in a remote place, the
tc = total machining time for full coil                          machine was down because
td = downtime in minutes                                         the machine pressure wasn’t
tl = loading time                                                building up. The machine op-
ts = machine setting up time                                     erator needed support from
lc = length of coil                                              the OEM to bring the machine
Cd = cost of downtime                                            back to operational state. Nor-
Rh = revenue potential per hour                                  mally, this would have meant,
Rc = revenue potential per coil                                  someone from the OEM’s team
Nh = number of coils per hour                                    travels to the site and bring
Mc = weight of coil in kilograms                                 the machine back to the op-
Cc = cost of coil (raw material)                                 erational state. However, this
Ce = energy cost                                                 being a remote site, the jour-
Co = other costs                                                 ney alone would take at least a
SD = surface density constant of material                        day. That implies that the
ID = Inner Diameter (mm)                                         machine has to be down until
OD = Outer Diameter (mm)                                         that time.
T = Thickness (mm)                                               To understand the commercial
W = Width (mm)                                                   aspects of the machine’s oper-
                                                                 ations and downtimes in this
From the concepts of geometry of solid bodies, we arrive at      case, let’s consider the following
equations for the length, lc and weight, Mc                      machine and material properties
                                                                 (refer Table 1).
                   length, lc (mtrs) = π      *      OD2 — ID2   This was a unit that operated in       As new
                                           4              T      3 shifts. This means the machine       technol-
                                                                 would not have been avail-             ogies are
Weight, Mc (kg) = lc *          Wc                   * T * SD    able for at least 24 hours of the      being made
                               1000                              planned production time.               available,
                                                                 From the equations discussed           MSMEs
Based on practical observations, we arrive at the relations      above, we deduced that an hour-        should
between material properties and revenue as follows:              ly downtime cost would be ap-          come
                                                                 proximately `18,306 (~US$ 250)         forward to
Cost of coil, Cc = Material Rate * Mc                            for the machine and material           adopt them
                                                                 properties we chose. Now, with         and stay
Typical revenue per coil, Rc = margin * [1 + Cc]                 a 24 hours downtime, the cost of       competitive
                                                                 the downtime would be signifi-         in the glob-
                                                                 cantly high, nearly 24 times the       al manu-
                                                                 hourly cost in this case.              facturing
                                                                                                        landscape.

Typical revenue per hour, Rh = Nh * Rc

                   Coils per hour, Nh =       1   * 60
                                              tc
                                                       lc
                   Processing  time, tp           =  speed

Total machining time for full coil, tc = tp + tl + ts

Energy cost, Ce = Unit Rate * units consumed per hour

Therefore, to estimate the cost of downtime, we arrive at the
following equation:

Cost of downtime, Cd =  td     [Rh — (N * Cc) — Ce — Co]
                        60
                                                                 Source: yzThings Technologies Pvt Ltd
In most metal processing applications, other costs are neglible
compared to the raw material and energy costs hence are being
ignored in our case study here.

(Note: These are not to be treated as bench marking formula;
only used for rough cost benefit assessment.)

www.mmindia.co.in                                                | 23May-June 2021
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