Chapter 36 Quality Engineering (Part 1) EIN 3390 Manufacturing Processes Spring, 2012

36.1 Introduction Objective of Quality Engineering: Systematic reduction of variability, as shown in Figure 36 – 1. Variability is measured by sigma, s, standard deviation, which decreases with reduction in variability. Variation can be reduced by the application of statistical techniques, such as multiple variable analysis, ANOVA – Analysis of Variance, design of experiment (DOE), and Taguchi methods.

36.1 Introduction QE History: - Acceptance sampling - Statistical Process Control (SPC) - Companywide Quality Control (CWQC) and Total Quality Control (TQC) - Six Sigma, DOE (Design of Experiment), Taguchi methods - Lean Manufacturing: “Lean" is a production practice that considers the expenditure of resources for any goal other than the creation of value for the end customer to be wasteful, and thus a target for elimination - Poka-Yoke: developed by a Japanese manufacturing engineer named Shigeo Shingo who developed the concept. poka yoke (pronounced "poh-kah yoh-kay") means to avoid (yokeru) inadvertent errors (poka).

Process Control Methods MSD - Manu FIGURE 36-1 Over many years, many techniques have been used to reduce the variability in products and processes.

36.1 Introduction In manufacturing process, there are two groups of causes for variations: Chance causes – produces random variations, which are inherent and stable source of variation Assignable causes – that can be detected and eliminated to help improve the process.

36.1 Introduction Manufacturing process is determined by measuring the output of the process In quality control, the process is examined to determine whether or not the product conforms the design’s specification, usually the nominal size and tolerance

36.1 Introduction Accuracy is reflected in your aim (the average of all your shots, see Fig 36 – 2) Precision reflects the repeatability of the process. Process Capacity (PC) quantifies the inherent accuracy and precision. Objectives: - root out problems that can cause defective products during production, and - design the process to prevent the problem.

Accuracy vs. Precision FIGURE 36-2 The concepts of accuracy (aim) and precision (repeatability) are shown in the four target outcomes. Accuracy refers to the ability of the process to hit the true value (nominal) on the average, while precision is a measure of the inherent variability of the process.

Accuracy vs. Precision FIGURE 36-2 The concepts of accuracy (aim) and precision (repeatability) are shown in the four target outcomes. Accuracy refers to the ability of the process to hit the true value (nominal) on the average, while precision is a measure of the inherent variability of the process.

36.2 Determining Process Capability The nature of process refers to both the variability (or inherent uniformity) and the accuracy or the aim of the process. Examples of assignable causes of variation in process : multiple machines for the same components, operator blunders, defective materials, progressive wear in tools.

36.2 Determining Process Capability Sources of inherent variability in the process: variation in material properties, operators variability, vibration and chatter. These kinds of variations usually display a random nature and often cannot be eliminated. In quality control terms, these variations are referred to as chance causes.

36.2 Making PC Studies by Traditional Methods The objective of PC study is to determine the inherent nature of the process as compared to the desired specifications. The output of the process must be examined under normal conditions, the inputs (e.g. materials, setups, cycle times, temperature, pressure, and operator) are fixed or standardized. The process is allowed to run without tinkering or adjusting, while output is documented including time, source, and order production.

36.2 Making PC Studies by Traditional Methods The statistical data are used to estimate the mean and standard deviation of the distribution. 1. Histogram 2. Run chart

36.2 Histograms A histogram is a representation of a frequency distribution that uses rectangles whose widths represent class intervals and whose heights are proportional to the corresponding frequencies. All the observations within in an interval are considered to have the same value, which is the midpoint of the interval. A histogram is a picture that describes the variation in a progress. Histogram is used to 1) determine the process capacity, 2) compare the process with specifications: upper Specification (USL) and lower specification limit (LSL), 3) to suggest the shape of the population, and 4) indicate discrepancy in data. Disadvantages: 1) Trends aren’t shown, and 2) Time isn’t counted.

Mean vs. Nominal FIGURE 36-7 Histogram shows the output mean m from the process versus nominal and the tolerance specified by the designer versus the spread as measured by the standard deviation s. Here nominal =49.2, USL =62, LSL =38, m =50.2, s =2.

36.2 Run Chart or Diagram A run chart is a plot of a quality characteristic as a function of time. It provides some idea of general trends and degree of variability. Run chart is very important at startup to identify the basic nature of a process. Without this information , one may use an inappropriate tool in analyzing the data. For example, a histogram might hide tool wear if frequent tool change and adjustment are made between groups and observations.

Example of a Run Chart FIGURE 36-8 An example of a run chart or graph, which can reveal trends in the process behavior not shown by the histogram.

Process Capability FIGURE 36-3 The process capability study compares the part as made by the manufacturing process to the specifications called for by the designer. Measurements from the parts are collected for run charts and for histograms for analysis—see Figure 36-4.

Example of Process Control FIGURE 36-4 Example of calculations to obtain estimates of the mean (m) and standard deviation (s) of a process

36.2 Making PC Studies by Traditional Methods m +-3s defines the natural capacity limits of the process, assuming the process is approximately normally distributed. A sample is of a specified, limited size and is drawn from the population. Population is the large source of items, which can include all items the process will produce under specified condition. Fig. 36 – 5 shows a typical normal curve and the areas under the curve is defined by the standard deviation. Fig. 36 – 6 shows other distributions.

Normal Distribution FIGURE 36-5 The normal or bell-shaped curve with the areas within 1s, 2s, and 3s for a normal distribution; 68.26% of the observations will fall within 1s from the mean, and 99.73% will fall within 3s from the mean.

Common Distributions FIGURE 36-6 Common probability distributions that can be used to describe the outputs from manufacturing processes. (Source: Quality Control Handbook, 3rd ed.)

36.2 Process Capability Indexes The most popular PC index indicates if the process has the ability to meet specifications. The process capacity index, Cp, is computed as follows: Cp = (tolerance spread) / (6s) = (USL – LSL) / (6s) A value of Cp >= 1.33 is considered good. The example in Fig 36-7: Cp = (USL – LSL)/(6s) = (62 – 38)/(6 x 2) =2

36.2 Process Capability Indexes The process capability ratio, Cp, only looks at variability or spread of process (compared to specifications) in term of sigmas. It doesn’t take into account the location of the process mean, m. Another process capability ratio Cpk for off-center processes: Cpk = min (Cpu, Cpl) = min[Cpu= (USL – m)/(3s), Cpl= (m – LSL)/(3s)]

Output Shift FIGURE 36-9 The output from the process is shifting toward the USL, which changes the Cpk ratio but not the Cp ratio.

Output Shift FIGURE 36-9 The output from the process is shifting toward the USL, which changes the Cpk ratio but not the Cp ratio.

Output Shift Draw Distribution graph Calculate m FIGURE 36-9 The output from the process is shifting toward the USL, which changes the Cpk ratio but not the Cp ratio.

36.2 Process Capability Indexes In Fig. 36 – 10, the following five cases are covered. 6s < USL –LSL or Cp > 1 6s < USL –LSL, but process has shifted. 6s = USL –LSL, or Cp = 1 6s > USL –LSL or Cp < 1 The mean and variability of the process have both changed. If a process capability is on the order of 2/3 to 3/4 of the design tolerance, there is a high probability that the process will produce all good parts over a long time period.

FIGURE 36-10 Five different scenarios for a process output versus the designer’s specifications for the minimal (50) and upper and lower specifications of 65 and 38 respectively.

FIGURE 36-10 Five different scenarios for a process output versus the designer’s specifications for the minimal (50) and upper and lower specifications of 65 and 38 respectively.

36.2 Process Capability Indexes In Fig 36 – 11, an automated station checks parts for the proper diameter with the aid of a linear variable differential transformer (LVDT). Embedded in the clamping device is an LVDT position sensor for measurement of the diameter of a part. Once the measurement is made, the computer releases the clamp and the part can move on. If the diameter is in tolerance, a solenoid-actuated gate operated by the computer lets the part pass, otherwise, the part is rejected into a bin.

Using LVDT for Process Control FIGURE 36-11 A linear variable differential transformer (LVDT) is a key element in an inspection station checking part diameters. Momentarily clamped into the sensor fixture, a part pushed the LVDT armature into the device winding. The LVDT output is proportional to the displacement of the armature. The transformer makes highly accurate measurements over a small displacement range.

Check Sheet FIGURE 36-12 Example of a check sheet for gathering data on a process.