 Students, now let us look at quality cost model. An important consideration in selecting a vendor would be the quality which was actually ignored in or we assume that in set covering model the quality remains the same for all the vendors which might not be the case. So poor supply quality costs at the buyer end in terms of increased inspection, the repair of defective parts and downtime or poor final product of the quality. These all things actually are important. You have to inspect it and your cost of inspection is full. Why? Because the product is not of a quality. It might be possible that there is a vendor who provides me 120 products out of which 100 products are good but my cost of inspection would be higher than the vendor who is providing me 105 products out of which 100 are good. There would be a cost difference but the cost which you are bearing for for increased inspection is also very important. Then repair of the defective parts. If there are defective parts you need to repair them, then its repair cost can come to you. The downtime cost can come, the longer you repair it there is no work in your manufacturing facility that is important as well. This model actually assumes that the output or finished product of the buyer will be defective if the input or the purchased component is defective. That means if you have purchased an input or component defective or product defective then the manufacturing of the buyer that would be defective as well. So it cannot be, its like garbage in garbage out. So whatever is the input your output would be dependent upon it or if the buyer's manufacturing process is defective or both the probabilities of defective input and defective process are assumed to be independent. So what we are assuming that manufacturing is model tender the buyer's process manufacturing process is not defective it is independent of the defects which are coming. The model considers the costs of defective finished products and the cost of purchased input. So there are two distinctive costs in this model one would be the cost of your purchase that is your input and then there is a cost of a defective item if it is produced in the finished form. All costs are assumed to be linear this is the assumption of this model that your defect cost will linearly increase it would not be non-linear. The cost per unit cost would remain the same if the first defective item cost you let's say one dollar the tenth item one unit will actually be cost would be approximately one dollar as well it would increase or decrease with the output. The more defective you are getting the more cost per unit cost that would not be the phenomena. The model does not consider incoming inspection on the parts received from the vendor the inspection cost that is not the part of this model see this model the model is actually formulated in terms of the following three equations the first equation cj is equal to ci plus pj into one minus q cd plus q into one minus pj into cm q or p it's the binomial defective item and non p let's say it would be maybe in key abbreviations I will show you if p represents the good items then one minus p or q would be representing the bad items plus q pj cdm the second equation would be c0 should be equal to q cm and the difference the third equation would actually be the difference of the cost the cost we talked about the final product cost minus the initial purchase cost and that should be equal to cj plus pj into cd plus q into cdm minus cd now let us see the abbreviations now what is pj pj is the probability of defective part from vendor so what would be the q q is the probability of buyers process manufacturing a defective finished product the notations are as follows the notations used in the model let's look at them pj is the probability of defective part from vendor j that would be pj the probability of defect the chances of it being defective that probability let's say 5 percent for a vendor so pj would be 5 0.05 or 5 percent for a vendor it could be like 10 percent then what is q q is the probability of the buyers process manufacturing a defect finished product so q jo hai amne is model ke ndar quality cost model actually have two type of defective items ek toha apke jo vendor se direct apke pass defect taghya amne ka wo independent hai of the jo assumption is model ki it is independent of the buyers process manufacturing what does it mean it means your defect which is coming from the vendor has nothing to do with the manufacturing of that buyer we assume that if there is a defect which is coming from the vendor wo apne pehle yalada kar diya usko apne manufacturing mini lie toh agar apki koi finished product jo hai that is actually defective that is because of the buyers manufacturing process not because of the input which is coming the input would be fine if you have segregated your or you have checked the vendors total supply then what is CD CD is the unit cost of a defective finished product if the defect was due to the defective input yani CD wo cost hai which is only related with the defective item coming from the vendor jo vendor se apke pass hai wo agar defective woa toh uski wajah se jo hai and it is independent of the manufacturing process yani manufacturing process uska koi taluk nahi hai then what is cm cm is the unit cost of a defective finished product if the defect was due to the defective manufacturing process what does it mean agar mere manufacturing mein koi karab ho rahi hai toh uska koi taluk nahi hai meri input se this is the assumption of a model then CDM is the unit cost of a defective finished product if the defect was due to the defective manufacturing process and defective input in case if you have processed the defective input as well and defective manufacturing is there as well toh tab aap usko jo cost assign kar rahe honge that would be CDM yani mere pass ek product by after inspection bwo input mein bhi kharab tha uski vendor se hi wo kharab poncha tha usko main hai use kar liye apne manufacturing mein and that raw material actually turned out to be like garbage in garbage out is case mein mai usse cost assign karonga let's say yaha par osakti hai cost it is let's say ten dollars ten dollars per unit mean for that manufacturing unit it means the product was the raw material was defective and the manufacturing was defective to usko main assign kar diya CDM whereas CM only let's say my CM is six dollars what does it mean mere manufacturing mein jo fault aar hai uski bhaja se koi item agar product jo hai wo kharab hota hai if it is defective the cost associated with it is six dollars and let's say my CD is what does it mean mere purchase agar defective hoti hai toh let's say the cost associated with this is four dollar per unit to ye different cost us mein wo osakti hai then what is CJ CJ is the unit cost of purchase purchasing from vendor J ye this is the unit cost and PJ into one minus Q is actually the binomial probability of producing a defective finished product if the defect was due to the defective input from vendor J what does it mean PJ into one minus Q PJ kya tha PJ aap ke pass defective probability of a defect from the vendor and Q kya tha the probability of defect in because of the manufacturing to one minus Q kya hoga it would be binomial in nature binomial means agar Q jo hai wo probability of defect in manufacturing hai to one minus Q is no defect in manufacturing that means perfect manufacturing process but PJ into one minus Q would represent that the probability of producing a defective finished product but the defect was because of the input from the vendor vendor se jo input tha wo defective thi aapka manufacturing process thi tha toh tha aapki probability hogi PJ P into one minus Q one minus Q means good item produced in the manufacturing but P represents defect coming from the input okay similarly what is Q into one minus P it is the non-defective input from the vendor kya se Q kya tha Q hai defective probability of defect in the process manufacturing process but one minus P would be the opposite of P P kya tha defective input from the vendor to one minus P means the non-defective input from the man vendor so it is the probability of producing a defective finished product if the defect was due to the defective manufacturing process not because of the input okay then Q PJ aap Q bhi defective hai probability of a defective item produced in manufacturing and P is the probability that you have a purchase which is defective to do no a kathi ho gain to it is the probability of producing a defective finished product if the defect was due to defective manufacturing as well as defective input from the vendor and that is actually associated with your CDM to cost hai jis mein aapki input bhi defective hai aur aapki manufacturing bhi defective hai ye probability us se related hai CJ is the expected unit cost cost per unit from vendor and the unit purchase cost plus the expected cost of defective finished product from your to kya hai total expected cost hai ek vendor se jis mein uski purchase cost bhi shamil hai aur uski expected cost of defect bhi shamil hai yani aap ke paas ek history maujood aas vendor ki ke uski 5% units defective hote hain to whatever cost you pay aap uski vendor uski defective cost ko bhi include kar detein to wo sirf sirf purchase cost nahi hote hai it's also the cost of defect jo ke brdaash karta hai wo manufacturer what is C naught C naught is the expected cost of defective finished products if the input were perfect yani aapki input thik thi lakin manufacturing mein defect aagya to usse jo related cost hai usko hum C naught ka naam deing aur delta C difference of C is the incremental cost per unit due to the defective part from the vendor so after looking at these agar aap if you see these notations so you can actually look at the model now and you can that what is it to is me aap ke paas CJ maujood hai which is CJ is there which is a sum and product of and you can see that there are different associated cost now yeh manufacturing se related hai jab a manufacturing se related kaya rahe hain ke manufacturing ka defect hai to Q tha defect in manufacturing manufacturing defective hone ki probability 1-p tha jo aapki jo purchase hai wo thik hai aur tisne nambar pe dekhyeega CDM do no cheezin aur unki probabilities CDM wo cost thi jab aapki input b defective hai aapki manufacturing b defective hai aur wo cost aapko ek bier karne pade yeh per unit aur uski probability kithni hai wo Q aur P Q means the probability having a defective manufacturing P means probability of having a defective supply to now you can understand the this model more clearly so the total cost actually increases with the decrease in quality yani agar quality ka mo rahe hain to is question is model me quality cost model me you will see that with the decrease in quality the cost would actually increase your cost the total cost of CM the total cost of CD and the total cost of CDM the combined cost would actually increase of supply from a vendor also if the quality costs are independent of the source of the defect or imperfection imperfections agar aapki quality cost jo hain wo independent ho jain supply se vendor se to your CD will be equal to CM would be equal to CDM which will be equal to see what does it mean supply bilkul thi ka rahe hain to jab bilkul thi ka rahe hain to is ka matlab hai wo sirf manufacturing me fault paida wo sakta to every cost yani jo aapki cost of quality hain that is actually CM or see aapku usko kuch bhi kailin to that would be fine this indicates that if the manufacturing process is perfect then the total cost from vendor j is CJ plus PJC ye also ye bhi batata hain aapko ke agar aapka manufacturing process agar perfect jo hain on the other hand ek to ye hain ki aapki supplies bilkul thi ko jain dursa ye aapki manufacturing process jo hain wo bilkul perfect ho jain to then the total cost would be CJ to cost hai sirf aap wo kya hain ke manufacturer se defect aapka hai plus the probability that the product is defective from the input into the cost wo total cost bhi jo hain wo unit cost aapki to this is actually the total quality cost model in which the stress is the main emphasis would be on the quality of the input as well as the quality of your finished product thank you