Number Of Non-conforming Units Research Articles

NEW SOFTWARE MODULE FOR STATISTICAL PRODUCT QUALITY CONTROL

The article is devoted to the developed software module for statistical quality control of products that allows using the following quality tools: Pareto chart, Shewhart control maps (mean value map and span map), scatter chart, control maps of shares and the number of nonconforming units, control maps of the number of nonconformities and the number of nonconformities per unit, Ishikawa diagram. This article can be useful for specialists who are engaged in statistical quality control and are looking for an alternative to other software that can be implemented in the production process.

An NP Control Chart Using Double Inspections

The np control chart is used widely in Statistical Process Control (SPC) for attributes. It is difficult to design an np chart that simultaneously satisfies a requirement on false alarm rate and has high detection effectiveness. This is mainly because one is often unable to make the in-control Average Run Length ARL 0 of an np chart close to a specified or desired value. This article proposes a new np control chart which is able to overcome the problems suffered by the conventional np chart. It is called the Double Inspection (DI) np chart, because it uses a double inspection scheme to decide the process status (in control or out of control). The first inspection decides the process status according to the number of non-conforming units found in a sample; and the second inspection makes a decision based on the location of a particular non-conforming unit in the sample. The double inspection scheme makes the in-control ARL 0 very close to a specified value and the out-of-control Average Run Length ARL 1 quite small. As a result, the requirement on a false alarm rate is satisfied and the detection effectiveness also achieves a high level. Moreover, the DI np chart retains the operational simplicity of the np chart to a large degree and achieves the performance improvement without requiring extra inspection (testing whether a unit is conforming or not).

A Study on the Behavior of Operating Characteristic Curves of Sampling Plans Based on Polya Distribution

SYNOPTIC ABSTRACTAn implicit assumption that is made in the use of binomial distribution for number of non-conforming units under acceptance sampling procedures is that the dispersion about the process fraction non-conforming (p) or process average () is zero. When this assumption is violated or when an amount of dispersion around is present, the Polya distribution is an appropriate choice for assessing the performance of sampling plans. The Polya distribution is arrived by integrating the product of beta process distribution and the binomial sampling distribution over p. This paper presents the operating characteristic (OC) fonction of single sampling plans by attributes under the conditions of Polya distribution. An empirical study is also made on the behavior of Polya OC curves with respect to various sets of parameters.

Average outgoing quality of CSP-C continuous sampling plan under short run production processes

A CSP-C continuous sampling plan is a new single-level continuous sampling procedure developed by Govindaraju & Kandasamy (2000) by incorporating the concept of acceptance number to the CSP-1 plan for the application of continuous production processes. In this new plan, the sampling inspection phase is characterized by a maximum allowable number of non-conforming units, c, and a constant sampling rate, f. Govindaraju & Kandasamy (2000) derived the performance measures such as average outgoing quality (AOQ), average fraction inspected (AFI) etc, of the CSP-C plan using a Markov chain model for long run production processes. Yang (1983) has observed that the AOQ and AFI, being long run average measures, are not satisfactory measures of performance for short run production processes. Hence, formulas are derived in this paper, using the renewal theory approach enabling one to compute AOQ and AFI for both long run and short run production processes. Numerical illustrations are also given. By simulation, the accuracy of the short run measures is studied.

Average outgoing quality of CSP-C continuous sampling plan under short run production processes

Abstract A CSP-C continuous sampling plan is a new single-level continuous sampling procedure developed by Govindaraju & Kandasamy (2000) by incorporating the concept of acceptance number to the CSP-1 plan for the application of continuous production processes. In this new plan, the sampling inspection phase is characterized by a maximum allowable number of non-conforming units, c, and a constant sampling rate, f. Govindaraju & Kandasamy (2000) derived the performance measures such as average outgoing quality (AOQ), average fraction inspected (AFI) etc, of the CSP-C plan using a Markov chain model for long run production processes. Yang (1983) has observed that the AOQ and AFI, being long run average measures, are not satisfactory measures of performance for short run production processes. Hence, formulas are derived in this paper, using the renewal theory approach enabling one to compute AOQ and AFI for both long run and short run production processes. Numerical illustrations are also given. By simulatio...

A Modified Acceptance Test Model with Particular Applicability to Bioassay Systems

Reducing the β error to a predetermined level can be achieved by increasing the size of the tested samples. Yet, the single sample size model may require an excessive number of sample items. Double or multiple acceptance sampling models that are extensively used in acceptance sampling for attributes require a significantly lower number of sample items for identical levels of risk. Their common basis is the identification of distinct rejection and acceptance limits, and the formation of an intermediate retest zone requiring additional sample items. When this is required, the cumulative number of nonconforming units is assessed against a rejection limit that has been set for the cumulative sample size. This article presents a modified retest zone model that can be applied to sampling by variables as well. The term retest does not mean performing additional tests on the same items but rather testing additional items. The model is based on introducing an additional rejection criterion; that is, whenever the number of successive results (N) in the retest zone accumulates to a critical number (Nc), the lot is not accepted. Nc is derived from the expression , where P rt is the proportion of the normal distribution curve's area occupied by the retest zone area (i.e., the probability of randomly obtaining an individual result within this domain). The cumulative proportion of retests becomes a function of , while the cumulative proportion of tests (CPT) that includes events of decision making without a need for additional testing is a function of . It is shown that the proposed procedure requires considerably fewer tests than the comparable single sample size procedure. This advantage bears particular relevance to biological acceptance tests where the combination of large variances, along with applying the single sample size model, might dictate an impractical number of trials.

Designing Accurate Control Charts Based on the Geometric and Negative Binomial Distributions

Attribute control charts are used effectively to monitor for process change. Their accuracy can be improved by judiciously selecting the sample size. The required sample sizes to achieve accuracy can be quite restrictive, especially when the nominal proportions of non-conforming units are quite small. The usual attribute control chart has a set sample size and the number of non-conforming units in the sample is plotted. If, instead of setting a specific sample size the number of non-conforming units is set, an alternative monitoring process is possible. Specifically, the cumulative count of conforming (CCC-r) control chart is a plot of the number of units that must be tested to find the rth non-conforming unit. These charts, based on the geometric and negative binomial distributions, are often suggested for monitoring very high quality processes. However, they can also be used very efficiently to monitor processes of lesser quality. This procedure has the potential to find process deterioration more quickly and efficiently. Xie et al. (Journal of Quality and Reliability Management 1999; 16(2):148–157) provided tables of control limits for CCC-r charts for but focused mainly on high-quality processes and the tables do not include any assessments of the risk of a false alarm or the reliability of detecting process change. In this paper, these tables are expanded for processes of lesser quality and include such assessments using the number of expected monitoring periods (average run lengths (ARLs)) to detect process change. Also included is an assessment of the risk of a false alarm, that is, a false indication of process deterioration. Such assessments were not included by Xie et al. but are essential for the quality engineer to make sound decisions. Furthermore, a hybrid of the control charts based on the binomial, geometric and negative binomial distributions is proposed to monitor for process change. Copyright © 2005 John Wiley & Sons, Ltd.

Modified CSP-C Continuous Sampling Plan for Consumer Protection

Dodge (1943) introduced a single level attribute continuous sampling plan designated as CSP-1 for the application of continuous production processes. Govindaraju & Kandasamy (2000) developed a new single level continuous sampling plan whose sampling inspection phase is characterized by a maximum allowable number of non-conforming units c, and a constant sampling rate f and was designated as CSP-C. In this paper, a modification is proposed on the CSP-C continuous sampling plan. In this modified plan, sampling inspection is continued until the occurrence of c+1 non-conforming units, provided the first m sampled units have been found conforming during the sampling phase. Using a Markov chain model, expressions for the performance measures of the modified CSP-C plan are derived. The main advantage of the modified plan is that it is possible to lower the average outgoing quality limit.

Improved p charts to monitor process quality

It is a common practice to monitor the fraction p of non-conforming units to detect whether the quality of a process improves or deteriorates. Users commonly assume that the number of non-conforming units in a subgroup is approximately normal, since large subgroup sizes are considered. If p is small this approximation might fail even for large subgroup sizes. If in addition, both upper and lower limits are used, the performance of the chart in terms of fast detection may be poor. This means that the chart might not quickly detect the presence of special causes. In this paper the performance of several charts for monitoring increases and decreases in p is analyzed based on their Run Length (RL) distribution. It is shown that replacing the lower control limit by a simple runs rule can result in an increase in the overall chart performance. The concept of RL unbiased performance is introduced. It is found that many commonly used p charts and other charts proposed in the literature have RL biased performance. For this reason new control limits that yield an exact (or nearly) RL unbiased chart are proposed.

Improved p charts to monitor process quality

It is a common practice to monitor the fraction p of non-conforming units to detect whether the quality of a process improves or deteriorates. Users commonly assume that the number of non-conforming units in a subgroup is approximately normal, since large subgroup sizes are considered. If p is small this approximation might fail even for large subgroup sizes. If in addition, both upper and lower limits are used, the performance of the chart in terms of fast detection may be poor. This means that the chart might not quickly detect the presence of special causes. In this paper the performance of several charts for monitoring increases and decreases in p is analyzed based on their Run Length (RL) distribution. It is shown that replacing the lower control limit by a simple runs rule can result in an increase in the overall chart performance. The concept of RL unbiased performance is introduced. It is found that many commonly used p charts and other charts proposed in the literature have RL biased performance. For this reason new control limits that yield an exact (or nearly) RL unbiased chart are proposed.