3 Principal Devices which are used as a tool of Quality Control in Industries

Statistical quality control provides a scientific basis for establishing standards or norms for quality characteristics of a manufactured product and for differentiating between deviations which should be expected by chance in operation and those too large to occur due to chance alone.

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The techniques are based on the mathematical theory of probability and are premised on the fact that predictions regarding the quality characteristics of a given process or lot may be made from the inspection of these characteristics in samples taken from the process or lot.

The normal distri­bution is the theoretical basis for statistical quality control. It has several characteristics. Theoretically, the normal distribution is perfectly symmetrical, it is well shaped form. Mean and standard deviation are the two parameters of normal distribution. Normal distribution is graphi­cally portrayed in Fig. 20.5.

The tools of statistical quality control include the following statistical devices (Fig. 20.6).

1. Frequency Distribution Charts:

This is a statistical quality control method by the method of variables. If sufficiently sensitive measuring devices are used in inspection, variations will found in everything produced even though the same methods, machines, tools and specifications are used in their manufacture.

If measurements are made of a single quality characteristic of a large number of parts, the bulk of them will tend to conform closely to a norm or average. This norm or average should coincide with the desired quality standard, as established for the production of the item if the process is producing the part at the quality level desired.

Some of the parts will deviate from this average more than others and a few will be very different from it. If these measurements are tabulated by size groups, and the frequency of occurrence plotted for each group, a bell shaped curved called a probability curve will result. This curve will resemble the normal frequency distribution curve.

Fig. 20.7 shows the frequency distribution of 144 sheets from thickness from 0.0235″ to 0.0270″. The variation in sheet thickness can be readily seen by examining this frequency distribution chart. The desired thickness was 0.025 and more of the sheets were classified with in this group than in any other group.

This indicates that the process is producing the desired quality level for thickness. If the sheets have been stocked according to thickness, one view of the resulting pile would have the shape of the frequency distribution in bar diagram form. Bar diagrams are frequently used to illustrate frequency distributions.

Frequency curves are used as a basis for quality control charts and to furnish information regarding variation in production. The general appearance of the curve, its symmetry, the location of the axis of symmetry, and the dispersions of points about this axis, the spread on the base time and the higher point of the curve, are important in analyzing such variations. In this way, it is possible to detect unsatisfactory average spread indicating a high percentage of scrap.

2. Quality Control Charts:

Control chart may be used in statistical quality control whether the inspection is for attributes or for variables. When the method of inspection is for attributes, the inspector simply notes the presence or absence of same quality characteristics and records the count of those with and without it.

When work is inspected and determined to be satisfactory or defective because it does or does not fit a gage, or because it is not the right colour—without any attempt to measure the variation between each item inspected it falls in this classification. But if the quality characteristic is measured by the inspector and a record kept of each measurement so that the variation between each is known, the inspection is for variables.

Control chart consist of three horizontal lines:

(a) Control line indicating the desired standard, level of quality called as CL (Control limit). This line indicates the standard quality.

(b) An upper line indicates the upper control limit (UCL).

(c) The lower line shows the lower control limit (LCL).

A random sample of output is taken periodically at frequent intervals (each hour, 2 hours or any time) and the results are plotted on the control chart. A graphical comparison of measurements with acceptable limits will show the capacity of the production process to produce desired quality level. Any deviation from the limits will mean that the process is influenced by external causes.

The upper and lower control limits serve as the decision criteria. When a sample point falls beyond these limits, steps are taken to locate and eliminate the sources of assignable variation otherwise the process is left free.

Types of Control Charts:

There are two main types of control charts:

1. Control charts for variables (measurable characteristics).

2. Control charts for attributes (non measurable characteristics).

Control charts for variables are of two types:

(a) Mean (averages) and range charts (X, R) charts.

(b) Mean (averages) and standard deviation (X, a) Charts. Control chart for attributes (non-measurable characteristics) are of two types:

Control charts for proportion of defectives (P-chart).

Control chart for number of defects (C-chart).

The most commonly used control charts are the mean (X) and (R) charts which are used when inspection in for variables. (X, R) charts can be used when the quality is measurable numerically.

P-Chart is used when quality has to be expressed in terms of attributes e.g., goods or bad.

C-Chart is used when the number of possible defects is very large but the expected occurrence is small.

Control charts for variables (Measurable characteristics) are designed to achieve the following objectives:

(a) To provide a basis for decision as to when to leave the production process alone and when to look for assignable causes.

(b) To analyze the production process with a view to establish or change specifications, production procedures and inspection procedure.

(c) To provide a basis for decisions on acceptance or rejection of a manufactured or purchased products.

Procedure for Plotting X & R Charts:

A good number of samples of items coming out of the machine are collected at random & at different intervals of time and their quality characteristics (e.g., diameter or length) are measured.

For each sample, the mean value and range is found out. For example, if the sample contains 6 items whose diameters are d₁, d₂, d₃, d₄, d₅, d₆, the sample average is.

X = d₁ + d₂ + d₃ + d₄ + d₅ + d₆ /6

R = Maximum diameter — minimum diameter

A number of samples are selected and their average values and range are^ tabulated.

For X Chart:

Upper control limit (UCL) = X + A₂R

Control limit (CL) =X

Lower control limit (LCL) = X – A₂R

For R Chart:

Upper control limit (UCL) = D₄R

Control limit (CL) = R

Lower control limit (LCL) = D₃R

A₂, D₃ and D₄ are the statistical factors based on subgroup sizes. The appropriate value of these factors can be chosen from the following table 20.1:

Table 20.1

Plotting P-Chart:

X, R chart can be plotted where measurement of samples are taken in terms of particular characteristics, for example, the diameters of the shafts being produced or the thickness of the plates being produced etc.

But not in all cases we describe samples in terms of their measurable: characteristics. Many a time, the inspection, is of the go/no go or; accept/reject type. In such a case, inspection procedures have been named P-chart, where P stands for fraction defective in a sample.

P-chart is constructed like mean and range charts, with upper and lower control limits. The mean proportion defective is the point 1 at which the centre line is drawn.

Upper control limit (UCL) = P + 3 σP

Control limit (CL) = P

Lower control limit (LCL) = P – 3 σP

Where, P is a fraction defective

d is the number of defective parts found in the sample of ‘n’ pieces inspected.

The standard deviation can be calculated as

σP = √P(1 – P)/n

If the standard i.e., P is not given, and then it can be estimated by 1 finding the average fraction defective over all possible samples. Total number of defectives in k sample Total number of units inspected in k samples the value of P can never be negative. So if sometimes LCL is negative, it is taken to be zero.

Applications:

In most of the manufacturing firms, the ultimate condition would be to secure a zero error production i.e., the percentage defectives to be zero. Manufacturing in a manner which produces I number of defects, however, may not be economical or may mean that the standards of specifications are so loose that all the products produced fall within the control limits.

For these reasons, quality control managers settle on same maximum percentage defective which should not be exceeded. P-chart is used in this connection. J Plotting is done during the day (at different times) to indicate the proportion defectives in samples which are randomly taken from the production line. As long as the plotted proportion defective falls within the control limits, production is not halted. On the contrary, when the limits are exceeded, corrective action must be taken.

On the other hand, if the proportion defectives decreases during the study, the quality control manager will be satisfied with the result, of course, he will certainly see why the products are being produced with fewer defects.

He may notice that the process has been improved or that the raw material is of high quality. Whatever the cause, the quality control manager tries to incorporate the improvement in the production process.

Plotting C-Chart:

Many a time a part or product is considered defective not just based on one measurement like go/no go gauges would indicate, but on the basis of number of defects all of which have to be taken into account before a decision to accept or reject it can be arrived.

An example can be given of cloth produced which may have a number of defects per meter length. It is the total number of defects in the sample which would render a sample either acceptable or rejected.

For process control, where the number of defects is the criteria for acceptance or rejection, a special kind of chart called the C-chart is used. The procedure is to take a sample of fixed size, count the defects in the sample (suppose the numbers of defects are equal to C), then plot the distribution of C’s for all samples.

In case of C charts also, if C is known, then the control limits are given by:

UCL = C + 3√C

CL = C LCL = C – 3√C

And where C is not known, then it is estimated by calculating the average number of defectives over all possible samples.

If LCL is negative, then it is taken to be zero.

Following considerations are observed while using the control charts for defects:

(a) The defect need not be of just one kind.

(b) C-Chart can also be used for acceptance sampling.

(c) Frequently, all the defects have to be removed by 100% inspection usually, on complex sub assembles and assemblies.

(d) Some defects may be more serious than others. In such situations the defects may be classified in A, B & C etc. categories and appropriate weighting may be prescribed for each category by experts and the number of demerits rather than defects may be computed e.g., if there are two types of defects A & B. The number of defects in an item is 2 and that of B is 3 where as the weighting for A is 5 and B it is 3. Then, the demerit level of the item = (2 x 5) + (3 x 3) = 19. The control charts may then be based on demerits.

3. Acceptance Sampling:

100% inspection is impossible when testing is destructive e.g., testing match boxes. Moreover, 100% inspection involves a lot of time and money. Therefore, sample inspection is used.

Acceptance sampling is universally accepted as a sampling technique for attribute inspection. In using this system, samples of lots are inspected. The number of rejects in the sample determines whether the lot is to be accepted or rejected.

The maximum number of defects per 100 units (percent defectives) that will be permitted in the entire lot is decided in advance. That is called acceptable quality level (AQL). If AQL is 4% that means that in the sample of 100 units, the lot will be accepted if the number of defects is four or less. This level is considered satisfactory to meet the needs of the product. The probability, of acceptance for an AQL lot should be fairly large (say 95%).

Acceptance sampling is defined as a method of determining the quality of a universe or population of products from an inspection of a sample of the universe. Managers are usually concerned with the quality of the product as it goes through final inspection. At the same time, managers are also concerned with the supply of raw materials by other firms. In both the cases, acceptance sampling can be used effectively.