SPC Basic Concept Part II Curriculum Development of

SPC Basic Concept – Part II Curriculum Development of Master’s Degree Program in Industrial Engineering for Thailand Sustainable Smart Industry

Control Charts for Attributes • Many quality characteristics can not be represented in numerical measurement. • Quality characteristics of this type are called “attributes. ” • In such cases, we usually classify each item inspected as either conforming or nonconforming (= defective). • Items may also be classified by their number of defects.

Control Charts for Attributes • P chart for fraction nonconforming (= fraction of defective units) • NP chart for number of nonconforming units (= number of defective units) • C chart and U chart for nonconformities (= number of defects). • C charts the number of defects in each subgroup. Use C chart when the subgroup size is constant. • U charts the number of defects per unit sampled in each subgroup. Use U chart when the sample (= subgroup) size varies. • For example, if you were counting the number of flaws on the inner surface of a television screen, C chart would chart the actual number of flaws, while U chart would chart the number of flaws per square inch sampled.

P Chart Example: Suppose you work in a plant that manufactures picture tubes for televisions. For each lot, you pull some of the tubes and do a visual inspection. If a tube has scratches on the inside, you reject it. If a lot has too many rejects, you do a 100% inspection on that lot. A P chart can define when you need to inspect the whole lot.

NP Chart Example: You work in a toy manufacturing company and your job is to inspect the number of defective bicycle tires. You inspect 200 samples in each lot and then decide to create an NP chart to monitor the number of defectives. To make the NP chart easier to present at the next staff meeting, you decide to split the chart by every 10 inspection lots.

C Chart Example: Suppose you work for a linen manufacturer. Each 100 square yards of fabric can contain a certain number of blemishes before it is rejected. For quality purposes, you want to track the number of blemishes per 100 square yards over a period of several days, to see if your process is behaving predictably.

U Chart Example: As production manager of a toy manufacturing company, you want to monitor the number of defects per unit of motorized toy cars. You inspect 20 units of toys and create a U chart to examine the number of defects in each unit of toys. You want the U chart to feature straight control limits, so you fix a subgroup size of 102 (the average number of toys per unit).

Attributes Control Charts for Service Industry • To identify root causes on errors • Number of employ paychecks that are in error • Number of checks that are distributed late during a pay period • Number of incorrect part numbers, incorrect delivery dates, and wrong supply • Number Errors in computer software during product development

Demerit System “Not all types of defects are equally important” • A unit of product having one major defect (very serious defect) would probably classified as nonconforming to requirements • But, a unit containing several minor defects might not necessarily be conforming • Demerit system for attribute data is a method to classify defects according to severity and to weight the various types of defects in a reasonable manner.

Demerit System • Class A Defects- Very Serious • completely unfit for service • Class B Defects- Serious • will possibly suffer a Class A failure • will possibly reduce life or increase maintenance cost • Class C Defects- Moderately Serious • will possibly suffer a Class B failure • will possibly reduce life or increase maintenance cost • Class D Defects- Minor • will not fail in service • minor defects in finish, appearance or quality of work

Demerit System • Assume the occurrence of defects in each class is modeled by a Poisson distribution. • Number of demerits in the inspection unit di = 100 ci. A + 50 ci. B + 10 ci. C + ci. D Where, • di is the number of demerit of unit i • ci. A, ci. B, ci. C, and ci. D represent the number of defects classified in Class A, Class B, Class C, and Class D, respectively • The demerit weights of Class A (100), Class B (50), Class C (10), and Class D (1) are well accepted in practice.

U Chart for Demerit Number • Use the number of demerit instead of number of defects • Suppose that a sample of n inspection is used. • Thus, we have

Phase I and Phase II of Control Chart Application • Phase I is a retrospective analysis of process data to construct trial control limits • Charts are effective at detecting large, sustained shifts in process parameters, outliers, measurement errors, data entry errors, etc. • Facilitates identification and removal of assignable causes • In phase II, the control chart is used to monitor the process • Process is assumed to be reasonably stable • Emphasis is on process monitoring, not on bringing an unruly process into control

Control Chart Pattern • In the implementation of control charts, the process should be considered out-of-control when points fall outside the chart control limits, or when control charts present unnatural patterns [1] • Unnatural patterns in a control chart can be associated with a specific set of assignable causes provided that appropriate process knowledge is available [2] • Hence, control chart pattern (CCP) recognition is the most important supplement and enhancement to the conventional control charting [3] [1] Montgomery DC. Introduction to Statistical Quality Control (3 rd edn). Wiley: New York, 1996. [2] Western Electric. Statistical Quality Control Handbook. Western Electric Company: New York, 1958. [3] Guh, R. S. (2003). Integrating artificial intelligence into on‐line statistical process control. Quality and reliability engineering international, 19(1), 1‐ 20.

In-Control Process [Ref] Technical Note. “PREDICTIVE STATISTICAL PROCESS CONTROL”. An update on data‐ driven CNC machining at L&S Machine Company.

In-control, But Trending out [Ref] Technical Note. “PREDICTIVE STATISTICAL PROCESS CONTROL”. An update on data‐ driven CNC machining at L&S Machine Company.

Predictive Tool Wear • Tool wear is easily identified through a careful monitoring of process control charts. • In these three samples, the same tool used on three different features on the same part shows variation at the sample, indicating the presence of tool wear. [Ref] Technical Note. “PREDICTIVE STATISTICAL PROCESS CONTROL”. An update on data‐ driven CNC machining at L&S Machine Company.

Acute Process Change [Ref] Technical Note. “PREDICTIVE STATISTICAL PROCESS CONTROL”. An update on data‐ driven CNC machining at L&S Machine Company.

Implementation of Control Chart 1. Determining which process characteristics to control 2. Determining where the charts should be implemented in the process 3. Choosing the proper type of control charts 4. Taking actions to improve processes as the result of SPC/control chart analysis 5. Selecting data-collection systems and computer software

Process Capability Analysis • Process capability ratio (PCR) is a performance measurement of a process or a product • “…a proportion of the specification tolerance to the process characteristics…” [1], [2] From customers From samples • • • [1] Kane (1986); [2] Montgomery (2013) Areas of applications Process measurement Process comparison Internal/external Auditing Prototype product/process design Supplier/vender selection

Process capability analysis (cont. ) [1] Kane (1986) [2] Chan et al. (1988) [3] Pearn et al. (1992) [4] Taguchi et al. , (2005) [5] Pearn and kotz (2006)

Interpretation of the PCR

Assumptions for Interpretation of Numbers in Table 8. 2 Violation of these assumptions can lead to big trouble in using the data in Table 8. 2.

Example: Process Capability Analysis using Control Charts • Table 8. 5 presents the container bursting‐strength data in 20 samples of five observations each. • The strength is controlled using LSL only, which LSL=200. • The calculations for the x and R charts are summarized here:

Example (cond. ) Since LSL = 200 Clearly, since strength is a safety‐related parameter, the process capability is inadequate.

Summary • Histograms, probability plots, and process capability ratios summarize the performance of the process. • Control charts are very effective in • Display the potential capability of the process • Address the issue of statistical control • Show systematic patterns in process output • Thus, The control chart should be regarded as the primary technique of process capability analysis.

Curriculum Development of Master’s Degree Program in Industrial Engineering for Thailand Sustainable Smart Industry