Chapter 36Chapter 36Quality EngineeringQuality Engineering

(Part 1)(Part 1)

EIN 3390 Manufacturing ProcessesEIN 3390 Manufacturing ProcessesSpring, 2012 Spring, 2012

36.1 Introduction36.1 IntroductionObjective of Quality Engineering:

Systematic reduction of variability, as shown in Figure 36 – 1.

Variability is measured by sigma, 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 Introduction36.1 IntroductionQE 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 MethodsProcess Control Methods

FIGURE 36-1 Over many years, many techniques have been used to reduce the variability inproducts and processes.

36.1 Introduction36.1 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 Introduction36.1 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 Introduction36.1 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. PrecisionAccuracy vs. Precision

FIGURE 36-2 The concepts ofaccuracy (aim) and precision(repeatability) are shown in thefour target outcomes. Accuracyrefers to the ability of theprocess to hit the true value(nominal) on the average, whileprecision is a measure of theinherent variability of theprocess.

Accuracy vs. PrecisionAccuracy vs. Precision

FIGURE 36-2 The concepts ofaccuracy (aim) and precision(repeatability) are shown in thefour target outcomes. Accuracyrefers to the ability of theprocess to hit the true value(nominal) on the average, whileprecision is a measure of theinherent variability of theprocess.

36.2 Determining Process 36.2 Determining Process CapabilityCapability

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 36.2 Determining Process CapabilityCapability

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 Methods36.2 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 Methods36.2 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 Histograms36.2 HistogramsA 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 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 standarddeviation . Here nominal =49.2, USL =62, LSL =38, m =50.2, =2.

36.2 Run Chart or Diagram36.2 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 ChartExample of a Run Chart

FIGURE 36-8 An example of arun chart or graph, which canreveal trends in the processbehavior not shown by thehistogram.

Process CapabilityProcess Capability

FIGURE 36-3 The process capability study compares thepart as made by the manufacturing process to thespecifications called for by the designer. Measurements fromthe parts are collected for run charts and for histograms foranalysis—see Figure 36-4.

Example of Process ControlExample of Process Control

FIGURE 36-4 Example ofcalculations to obtain estimatesof the mean (m) and standarddeviation (s) of a process

36.2 Making PC Studies by Traditional Methods36.2 Making PC Studies by Traditional Methods

+-3 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 DistributionNormal Distribution

FIGURE 36-5 The normal orbell-shaped curve with the areaswithin 1, 2, and 3 fora normal distribution; 68.26% ofthe observations will fall within1 from the mean, and99.73% will fall within 3from the mean.

Common DistributionsCommon Distributions

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

36.2 Process Capability Indexes36.2 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) / (6 = (USL – LSL) / (6)

A value of Cp >= 1.33 is considered good.

The example in Fig 36-7: Cp = (USL – LSL)/(6) = (62 – 38)/(6 x 2) =2

36.2 Process Capability Indexes36.2 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, .

Another process capability ratio Cpk for off-center processes:

Cpk = min (Cpu, Cpl)

= min[Cpu= (USL – )/(3), Cpl= ( – LSL)/(3)]

Output ShiftOutput 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 ShiftOutput 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 ShiftOutput Shift

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

1. Draw Distribution graph

2. Calculate

36.2 Process Capability Indexes36.2 Process Capability Indexes

In Fig. 36 – 10, the following five cases are covered.

a)6 < USL –LSL or Cp > 1

b)6 < USL –LSL, but process has shifted. c)6 = USL –LSL, or Cp = 1

d)6 > USL –LSL or Cp < 1

e)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 differentscenarios for a process outputversus the designer’sspecifications for the minimal(50) and upper and lowerspecifications of 65 and 38respectively.

FIGURE 36-10 Five differentscenarios for a process outputversus the designer’sspecifications for the minimal(50) and upper and lowerspecifications of 65 and 38respectively.

36.2 Process Capability Indexes36.2 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 Using LVDT for Process ControlControl

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 Check Sheet

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