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To guarantee a prefixed quality level of the monitored process, lower specification limit (LSL) and upper specification limit (USL) for a certain quality characteristic have been determined.

Let C R be the unit rejection cost incurred when the TT index falls below a lower specification limit or above an upper specification limit.

The problem of determining an optimal level of tolerance is equivalent to the problem of determining optimal specification limits since the term refers to the distance between its lower specification limit (LSL) and upper specification limit (USL).

The maximum likelihood estimator for CL is derived and used to propose a hypothesis testing procedure under a lower specification limit based on the progressive type I interval censored sample.

Similar(55)

One case is a situation in which the upper and lower specification limits (SLs) are imprecise.

where USL and LSL are the upper and lower specification limits,μ = process mean, andσ = standard deviation.

It provides an indication whether the process is operating at the center of the specified tolerance zone or nearer to the upper or lower specification limits.

For convenience we will denote the upper and lower specification limits by U and L, respectively, rather than the more customary USL and LSL notations.

Definition 4.2 Suppose we have a fuzzy process with fixed σ, for which the upper and lower specification limits are the fuzzy sets U a u, b u, c u ), L(a l, b l, c l ) ∈ F T (R), where a u ≥ c l.

It is natural to use fuzzy numbers such as U a u, b u, c u ) = T(a u, b u, c u ) ∈ F T (R) and L(a l, b l, c l ) = T(a l, b l, c l ) ∈ F T (R) for the upper and lower engineering specification limits, respectively, if the process specification limits are fuzzy rather than real numbers.

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