## FUZZY MEMBERSHIP FUNCTION IN DETERMINING SPC ALLOCATION

### by: Erna Budhiarti Nababan, Abdul Razak Hamdan, Mohd.

**Abstract:**
Statistical Process Control (SPC) is a technical tool that is used to control and to improve almost any kind of process. However, because of cost consideration, management need to decide which process should apply SPC. In this paper, we propose the use of probability and fuzzy membership function to determine SPC allocation. Conditional probability is used to analyse process failure rate and process repair rate. Then, using Markov Matrix, we calculate the probability of out-of-control process (PO). Nevertheless, in a production line that consists of many parts, the probability value is not adequate to be used as a reference to determine SPC allocation. There are cases for instance, where 0.25 of PO in one part does not mean the same as 0.25 of PO in other parts. Furthermore, we cannot randomly choose one of those parts to apply SPC or even decide to apply SPC in all parts of the production line since each part may have different sensitivity degree to the final product. As we mentioned earlier 0.25 of PO in part 1 may have higher influence to the final product compare to 0.25 of PO in part 2 or part 3. To overcome this problem we propose fuzzy membership function that uses linguistic terms and degree of memberships to analyse PO instead of the probability values. By this mean, the SPC allocation could be determined without ambiguity. For this purpose, the membership function is classified into three categories, namely LOW, MEDIUM and HIGH. Any part with PO fall into the “HIGH” category and high degree of membership is prioritised to apply SPC.
**Key Words: **
Statistical Process Control (SPC), Conditional Probability, Markov Matrix, Fuzzy membership function

**Authors:**

Erna Budhiarti Nababan, eb24715@ftsm.ukm.my

Abdul Rahman Hamdan, arh@ftsm.ukm.my

Mohammad Khatim Hasan, khatim@ftsm.ukm.my

Hazura Mohamed, hazura@ftsm.ukm.my

**Editor:**
Xie, M,XIE_MIN@NUS.EDU.SG

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